خيارات الأسهم أساسيات بت

15 خيارات الأسهم.

نشرت من قبل فيفيرونيكا سيمبسون تعديل منذ 1 سنة.

عروض مماثلة.

عرض حول الموضوع: "15 خيارات الأسهم" - نص العرض:

1 15 خيارات الأسهم.

2 أهداف التعلم في هذا الفصل، سنناقش السمات العامة للخيارات، ولكننا سنركز على الخيارات المتعلقة بالمخزونات المشتركة الفردية. وسوف نرى المرونة الهائلة التي توفرها الخيارات للمستثمرين في تصميم استراتيجيات الاستثمار. 1- أساسيات عقود الخيارات وكيفية الحصول على أسعار الأسعار. 2. الفرق بين تعويضات الخيار والأرباح الخيار. 3. عمل بعض استراتيجيات تداول الخيارات الأساسية. 4. المنطق وراء حالة التكافؤ وضع الدعوة.

3 أساسيات الخيار خيار الأسهم هو مشتقة الأمن، لأن قيمة الخيار هو "مشتقة" من قيمة الأسهم المشتركة الأساسية. والخيار هو عقد يمنح صاحبها الحق، وليس الالتزام، بشراء (أو بيع) أصل بسعر معين سلفا في غضون فترة زمنية محددة. هناك نوعان أساسيان من الخيارات المالية. خيارات الاتصال هي خيارات لشراء الأصل الأساسي. عند ممارسة خيار الاتصال، يمكنك "استدعاء" الأصول. خيارات الخيارات هي خيارات لبيع الأصل الأساسي. عند ممارسة وضع، كنت "وضع" الأصول لشخص ما. يتم توحيد عقود الخيارات المدرجة لتسهيل التداول واإلبالغ عن األسعار. خيارات الأسهم المدرجة تعطي حق الخيار لشراء أو بيع 100 سهم من الأسهم.

4 أساسيات الخيار، كونت. عقود الخيارات هي اتفاقيات قانونية بين طرفين - مشتر الخيار، وبائع الخيار. الشروط الدنيا المنصوص عليها في عقود خيار الأسهم هي: هوية المخزون الأساسي. سعر الإضراب، أو سعر التمرين. حجم عقد الخيار. تاريخ انتهاء صلاحية الخيار، أو استحقاق الخيار. أسلوب ممارسة الخيار (الأمريكية أو الأوروبية). التسليم، أو التسوية، الإجراء. تداول خيارات الأسهم في خيارات الخيارات المنظمة، مثل كبوي، فضلا عن أسواق الخيارات المتاحة خارج البورصة (أوتك).

5 سعر المفردات ممارسة (أو الإضراب) السعر: السعر المنصوص عليه في عقد الخيار الذي يمكن شراء أو بيع الأمن. سعر الخيار (قسط): سعر السوق لعقد الخيار. تاريخ انتهاء الصلاحية: تاريخ نضوج الخيار. قيمة التمرين: قيمة مكالمة أو خيار وضع إذا كان يمارس اليوم إيف من كال = ماكس (ست ─ X، 0) إيف من بوت = ماكس (X ─ ست، 0)

6 مصطلحات أخرى المكالمات في المال: مكالمة سعر ممارسة أقل من السعر الحالي للمخزون الأساسي. مكالمة خارج المال: خيار الاتصال الذي يتجاوز سعر ممارسة سعر السهم الحالي. مكالمة في المال: خيار الاتصال الذي يساوي سعر ممارسة سعر السهم الحالي.

7 أسعار أسعار الخيار تعرف قائمة عقود الخيارات المتاحة وأسعارها لأمن معين بسلسلة الخيارات. سلاسل الخيارات متاحة عبر الإنترنت من خلال مصادر عديدة، بما في ذلك كبوي (quote. cboe) وياهو! فينانس (finance. yahoo). وتشمل رموز الأسهم الخيار الأسهم: رسائل لتحديد المخزون الأساسي. رسالة لتحديد شهر انتهاء الصلاحية، وكذلك ما إذا كان الخيار هو مكالمة أو وضع. (من A إلى L للمكالمات؛ M من خلال X ل يضع). رسالة لتحديد سعر الإضراب (قليلا أكثر تعقيدا-انظر ياهو أو الأسهم تراك للجداول لشرح هذه الرسالة.)

8 التغيير في المخزون خيارات رمز السهم.

9 الخيار الأسهم رمز السهم و ستريك برايس كوديس.

10 أسعار الخيار المدرج في Yahoo! المالية.

(11) شركة مقاصة الخيارات.

شركة المقاصة الخيارات (أوك) هي وكالة خاصة تضمن أن شروط عقد الخيار سيتم الوفاء بها إذا تم ممارسة الخيار. قضايا أوك ويزيل جميع عقود الخيارات التداول في البورصات الأمريكية. لاحظ أن التبادلات و أوك تخضع جميعها للتنظيم من قبل لجنة الأوراق المالية والبورصة (سيك). زيارة أوك في:

12 مثال: خيار الاتصال يمكنك شراء عقد خيار المكالمة الذي سيسمح لك بشراء 100 سهم من شركة عب بسعر 50 دولار للسهم في أي وقت خلال الأشهر الثلاثة المقبلة. يتم تداول خيار المكالمة بسعر $ 1 لكل سهم من الأسهم الأساسية. سعر التمرين (أو الإضراب) = $ 50 سعر الخيار = $ 1 انتهاء الصلاحية: ثلاثة أشهر افترض أن سعر سهم آي بي إم يرتفع إلى 55 $. يمكنك ممارسة الخيار لشراء سهم آي بي إم بسعر ممارسة (50 $). وبالتالي، فإن قيمة ممارسة هو 5 $ (55 $ - 50 $).

13 مثال: خيار الاتصال افترض أن سهم آي بي إم سيرتفع إلى 55 $، والبقاء عند 50 $ أو هبوط إلى 40 $ للسهم الواحد في ثلاثة أشهر. كال برايس = $ 1 نو مونثس عب سبوت برايس = $ 55 قيمة التمرين = $ 5 الربح = $ 4 عب السعر الفوري = $ 50 قيمة التمرين = $ 0 الربح = - $ 1 لنفترض أن لدينا 10،000 $ للاستثمار الخيار أ: شراء 200 سهم من أسهم عب عند 50 $ الخيار ب: شراء 100 مكالمة بسعر $ 1 للسهم الواحد ($ 1x100x100) إذا كان السعر النهائي هو 55 $، الخيار A = $ 5 x200 = $ 1،000 الربح (عائد 10٪) الخيار B = $ 4x100x100 = $ 40،000 الربح (400٪ ريتورن) السعر $ 50 للسهم سعر بقعة عب السعر = $ 40 قيمة التمرين = $ 0 الربح = - $ 1.

14 كيف نحقق أرباحا من تداول الخيارات؟

من المثال السابق، على افتراض أن الخيار هو في المال عند انتهاء الصلاحية، يمكنك شراء حصة عب في 50 $ من بائع الخيار وبيعها بسعر السوق الحالي (55 $). لقد حققت أرباحا صافية بلغت 4 دولارات فقط (=). وبالتالي، فإن المشتري خيار الشراء يراهن على ارتفاع سعر الأصول الأساسية، في حين أن المشتري الخيار الخيار يراهن على انخفاض سعر الأصول الأساسية.

15 كيف نفقد المال من تداول الخيارات؟

من المثال السابق، لنفترض أن أسهم عب ترتفع أبدا فوق 50 $. ثم تنتهي صلاحية الخيار الخاص بك لا قيمة لها، لذلك تفقد سعر الخيار بأكمله ($ 1).

16 خيار المكالمة المكافآت سعر التمرين = $ 50 60 40 شراء مكالمة 20.

مكافآت الخيار ($) 10 20 30 40 50 60 70 80 90 100 سعر السهم ($) -20 -40 -60 سعر التمرين = 50 $.

17 مثال: بوت أوبتيون يمكنك شراء عقد خيار الشراء الذي يسمح لك ببيع 100 سهم من شركة عب بسعر 50 دولار للسهم في أي وقت خلال الأشهر الثلاثة المقبلة. يتم تداول الخيار وضع في 3 $ لكل حصة من الأسهم الأساسية. سعر التمرين (أو الإضراب) = $ 50 سعر الخيار = $ 3 انتهاء الصلاحية: ثلاثة أشهر لنفترض أن سعر سهم آي بي إم ينخفض ​​إلى 40 دولارا. يمكنك ممارسة الخيار الخاص بك لبيع حصة عب بسعر ممارسة فوق السوق (50 $). وبالتالي، فإن قيمة ممارسة هو 5 $ (55 $ - 50 $).

18 مثال: بوت أوبتيون لنفترض أن حصة آي بي إم سترتفع إلى 55 $، والبقاء في 50 $ أو هبوط إلى 40 $ للسهم الواحد في ثلاثة أشهر. السعر = $ 3 الآن قيمة عب السعر = $ 55 قيمة التمرين = $ 0 الربح = - $ 3 عب السعر الفوري = $ 50 قيمة التمرين = $ 0 الربح = - $ 3 السعر الفوري لشركة عب السعر $ 50 للسهم السعر الفوري لشركة عب السعر $ $ قيمة التمرين = $ 10 الربح = $ 7 .

19 وضع خيار الاستحقاقات 60 40 شراء وضع 20 عوائد الخيار ($) 10 20 30 40.

مكافآت الخيار ($) 10 20 30 40 50 60 70 80 90 100 سعر السهم ($) -20 -40 -60.

20 لماذا الخيارات؟ والسؤال الأساسي الذي طرحه المستثمرون هو: "لماذا تشتري خيارات الأسهم بدلا من الأسهم في الأسهم الأساسية؟" للإجابة على هذا السؤال، نقارن النتائج المحتملة من هاتين الاستراتيجيتين الاستراتيجيتين: شراء المخزون الأساسي. شراء الخيارات على الأسهم الأساسية.

21 مثال: شراء المخزون الأساسي مقابل شراء خيار الاتصال.

لنفترض أن شركة آي بي إم تبيع 90 دولارا للسهم الواحد، وخيارات الاتصال بسعر 90 دولارا هي 5 دولارات للسهم الواحد. الاستثمار ل 100 سهم: عب سهم: 9،000 $ واحد المدرجة خيار خيار المكالمة: 500 $ نفترض كذلك أن الخيار تنتهي في ثلاثة أشهر. وأخيرا، لنفترض أنه في غضون ثلاثة أشهر، سيكون سعر أسهم شركة عب إما: 100 دولار أمريكي أو 80 دولارا أمريكيا أو 90 دولارا أمريكيا.

22 مثال: شراء المخزون الأساسي مقابل شراء خيار الاتصال، كونت.

شراء 100 دولار أسهم ($ 9000 الاستثمار): شراء خيار واحد دعوة (500 $ الاستثمار): الدولار الربح: النسبة المئوية العائد: الحالة 1: 100 $ 1،000 1،000 11.11٪ 500 500 100٪ الحالة 2: $ 80 - $ 1،000 -11.11٪ - $ 500 -100٪ كيس 3: $ 90 $ 0 0٪

ما إذا كانت هناك استراتيجية مفضلة على آخر هو أمر بالنسبة لكل مستثمر فردي لاتخاذ قرار. وهذا يعني، في بعض الحالات، أن الاستثمار في المخزون الأساسي سيكون أفضل. وفي حالات أخرى، سيكون الاستثمار في الخيار أفضل. ويجب على كل مستثمر أن يوزع المخاطر وعوائد المبادلة التي توفرها الاستراتيجيات. من المهم أن نرى أن خيارات المكالمة توفر وسيلة بديلة لصياغة استراتيجيات الاستثمار. ل 100 سهم، وخسارة الدولار المحتملة مع خيارات المكالمة أقل. بالنسبة ل 100 سهم، فإن احتمال زيادة الدولار مع خيارات الاتصال أقل. النسبة المئوية الإيجابية للعودة مع خيارات الاتصال أعلى. النسبة المئوية السلبية للعائد مع خيارات الاتصال أقل.

24 لماذا شراء الخيارات المالية هو وسيلة محفوفة بالمخاطر جدا للاستثمار للمستثمرين الأفراد؟

استثمار أقصر أجلا، على الرغم من أن خطط العمل القطرية تم إدخالها مؤخرا. لابس: الأسهم طويلة الأجل أنتيسيباتيون الأوراق المالية التي تشبه الخيارات التقليدية إلا أنها خيارات طويلة الأجل مع آجال استحقاق تصل إلى 2 1/2 سنوات. مستوى عال من التقلب.

25 السعر تقلب الخيارات: أول تايم وارنر سبيل المثال.

26 جانب مشرق من الخيارات المالية.

تعريف التحوط: استراتيجية للحد من التعرض للمخاطر غير المرغوب فيها، مع الاستمرار في السماح للربح من الاستثمار لنفترض أن مدير محفظة يحمل حاليا 10 ملايين دولار من أسهم غوغ. أفق الاستثمار هو 3 أشهر. في غضون ثلاثة أشهر، وقالت انها سوف تتخلص من الحيازات. سعر السوق الحالي من غوغ هو 500 $ للسهم الواحد. ويبلغ عدد الأسهم في الأسهم الحالية 20،000 (10 مليون / 500) سهم. وهي تخشى من انخفاض الأسعار خلال فترة الثلاثة أشهر القادمة. ما الذي يمكن أن تفعله للحد من المخاطر باستخدام وضع؟

27 لا توجد إستراتيجية خيار إذا غوغ نقدر بنسبة 20٪ في 3 أشهر،

القيمة السوقية للمحفظة = 12 مليون دولار الربح = 2 مليون دولار إذا انخفضت قيمة غوغ بنسبة 20٪ خلال 3 أشهر، القيمة السوقية للمحفظة = $ 8 مليون الخسارة = 2 مليون دولار التوقعات المتوقعة = 4 مليون دولار.

28 وضع استراتيجية الخيار اليوم، وقالت انها تشتري 200 يضع مع X = 500 $، P = $ 10 للسهم الواحد. وقالت انها تدفع الخيار البائع $ 0.2M اليوم. إذا كانت قيمة غوغ تقدر بنسبة 20٪ خلال 3 أشهر، القيمة السوقية للمحفظة = 12 مليون دولار (بدون ممارسة) الربح = 12 مليون دولار - 10 مليون - 0.2 مليون = 1.8 مليون دولار إذا انخفضت قيمة غوغ بنسبة 20٪ خلال 3 أشهر، القيمة السوقية للمحفظة = $ 10M (ممارسة!) خسارة = 10M $ - 10M - 0.2M = - 0.2M $ (الخسارة) المتوقع التقلب = 2M $.

29 هل هناك أي طريقة علمية لاستخلاص سعر الخيارات؟

نعم فعلا. نموذج التسعير الخيار بلاك سكولز.

30 بلاك-سكولز الخيار التسعير نموذج.

وضعت أصلا في أوائل 1970s من قبل بلاك وشولز وصقلها في وقت لاحق من قبل ميرتون. خيار الأسهم، خيار المؤشر، خيار العملة الأجنبية، خيار سعر الفائدة، الخ خمسة مدخلات: سعر السهم الحالي، سعر التمارين، معدل الخالية من المخاطر، النضج، تقلب الأصول الأساسية زيارة مجلس شيكاغو لتبادل الخيارات (كبو)

31 ما هي المعادلات الثلاث التي تشكل أوب؟

32 ما هي قيمة خيار المكالمة التالي وفقا ل أوب.

ما هي قيمة خيار الاتصال التالي وفقا ل أوب؟ افترض: P = $ 27؛ X = $ 25؛ رفف = 6٪؛ t = 0.5 سنة: σ2 = 0.11 (أو σ =)

33 تابع N (d1) = N (0.5736) = 0.7168. N (d2) = N (0.3391) = 0.6327.

ملاحظة: القيم التي تم الحصول عليها من إكسيل باستخدام الدالة نورمزديست. V = 27 دولار (0.7168) - 25e-0.03 دولار (0.6327) = $ - $ 25 () (0.6327) = $ 16.

34 بلاك سكولز نموذج التسعير الخيار.

سعر السهم (P): $ 27.00 D1 = 0.5733 سعر التمارين (إكس): 25.00 $ D2 = 0.3388 معدل الخلو من المخاطر: 0.06 N (D1) = 0.7168 عائد توزيعات الأرباح (د): N (D2) = 0.6326 وقت انتهاء الصلاحية (T): 0.5 N (-D1) = 0.2832 معيار ديف. (سد): 33.17٪ N (-D2) = 0.3674 سعر المكالمة = $ 4.01 بوت برايس = $ 1.27 دلتا = غاما = 0.0535 رو = 7.6741 فيغا = 6.4622 ثيتا =

35 فيكس من كبوي مؤشر تقلب البنك المركزي العماني (VIX®) هو مقياس رئيسي لتوقعات السوق للتذبذب على المدى القريب الذي تنقله أسعار مؤشر ستاندرد أند بورز 500 لأسهم الأسهم. منذ طرحه في عام 1993، اعتبر العديدون أن فيكس هو البارومتر الأول في العالم من مشاعر المستثمرين وتقلبات السوق. ويبين فيكس توقعات السوق لتقلبات لمدة 30 يوما. يتم إنشاؤه باستخدام التقلبات الضمنية لمجموعة واسعة من الخيارات مؤشر S & P 500. فيكس هو مقياس يستخدم على نطاق واسع لمخاطر السوق وغالبا ما يشار إليه باسم "مقياس خوف المستثمرين".

36 فيكس - مقياس الخوف.

37 ما هو تأثير المعلمات التالية على قيمة خيار الاتصال؟

سعر السهم الحالي: تزداد قيمة خيار المكالمة مع ارتفاع سعر السهم الحالي. سعر التمرين: مع زيادة سعر التمرين، تنخفض قيمة خيار المكالمة. فترة الخيار: مع إطالة تاريخ انتهاء الصلاحية، تزيد قيمة خيار المكالمة (فرصة أكبر في أن تصبح في المال.) معدل الخالية من المخاطر: تميل قيمة خيار المكالمة إلى الزيادة مع زيادة رفف (تقلل الكهروضوئية من سعر التمرين). تباين عائد الأسهم: تزداد قيمة الخيار مع تباين المخزون الأساسي (مزيد من فرصة أن تصبح في المال).

38 النظر في خيار الاتصال مع ممارسة السعر = $ 20.

39 استدعاء مخطط قسط 5 10 15 20 25 30 35 40 45 50 قيمة الخيار 30 25.

سعر السوق قيمة التمارين سعر السهم.

40 ملاحظات سعر السوق للخيار هو دائما تقريبا أكبر من أو يساوي قيمة التمرين. لماذا ا؟ سعر السوق للخيار أكبر من الصفر حتى عندما يكون الخيار خارج المال. لماذا ا؟

41 القيمة الجوهرية والمضاربة القيمة.

الفرق بين سعر ممارسة الخيار والسعر الفوري للأصل الأساسي. وهذا هو، ممارسة القيمة. قيمة المضاربة (أو قيمة الوقت) الفرق بين سعر الخيار والقيمة الذاتية للخيار. القيمة السعر القيمة الجوهرية القيمة المضاربة + =

42 مثال في الجدول السابق، عندما سعر السهم هو 21 $، وقيمة ممارسة هو 1 $ (= 21-20). ومع ذلك، فإن القيمة السوقية هي $ وهكذا، سعر الخيار = القيمة الجوهرية + القيمة الزمنية 9.75 (سعر الخيار) = 1 (قيمة التمرين) (قيمة الوقت)

43 خيارات مؤشر الأسهم خيار مؤشر الأسهم هو خيار على مؤشر سوق الأسهم. الخيارات الأكثر شعبية مؤشر الأسهم هي الخيارات على S & P 100، S & P 500، ومعدل داو جونز الصناعي. ولأن التسليم الفعلي لجميع الأسهم التي تشمل مؤشر الأسهم غير عملي، فإن خيارات مؤشر الأسهم لديها إجراء لتسوية النقدية. وهذا هو، إذا كان الخيار تنتهي في المال، وكاتب الخيار ببساطة يدفع الخيار حامل القيمة الجوهرية للخيار. إجراء التسوية النقدية هو نفسه بالنسبة للمكالمات ووضع.

خيار الخيار "المال" "في المال": خيار من شأنه أن يحقق عائد إيجابي إذا مارس خيار "خارج المال": خيار لن يسفر عن مردود إيجابي إذا تم ممارسته استخدام العلاقة بين S (سعر السهم) و K (سعر الإضراب): ملاحظة لسعر إضراب معين، فقط المكالمة أو فقط وضع يمكن أن يكون "في المال". في المال من خارج المال خيار الاتصال S & غ؛ K S ≤ K بوت أوبتيون S & لوت؛ K S ≥ K.

47 كتابة الخیارات یشار إلی فعل بیع الخیار بکتابة الخیار. ويسمى البائع لعقد الخيار الكاتب. كاتب عقد خيار المكالمة ملزم ببيع الأصل الأساسي إلى حامل خيار الاتصال. يحق لحامل خيار المكالمة ممارسة خيار الاتصال (أي شراء الأصل الأساسي بسعر الإضراب). إن كاتب عقد خيار الشراء ملزم بشراء الأصل الأساسي من حامل الخيار. يحق لحامل الخيار وضع خيار الشراء (أي بيع الأصل الأساسي بسعر الإضراب). لأن كتابة الخيار تلزم الكاتب الخيار، كاتب الخيار يتلقى سعر الخيار اليوم من المشتري الخيار.

48 الخيار الخيار ممارسة أصحاب الحق في ممارسة خيارهم. إذا كان هذا الحق هو متاح فقط في تاريخ انتهاء الصلاحية الخيار، ويقال الخيار أن يكون ممارسة على النمط الأوروبي. إذا كان هذا الحق هو متاح في أي وقت تصل إلى بما في ذلك تاريخ انتهاء الصلاحية الخيار، ويقال أن الخيار ممارسة على الطريقة الأمريكية. لا يرتبط أسلوب التمرين بالمكان الذي يتداول فيه الخيار. على غرار الطراز الأوروبي والتجارة الأمريكية على غرار الخيارات في الولايات المتحدة، وكذلك على تبادل الخيارات الأخرى في جميع أنحاء العالم. مهم جدا: أصحاب الخيار أيضا الحق في بيع خيارهم في أي وقت. أي أنه ليس عليهم ممارسة الخيار إذا لم يعودوا يريدون ذلك.

49 تعويضات الخيار مقابل أرباح الخيار.

وتشمل استراتيجيات الاستثمار في الخيار التدفقات النقدية الأولية والنهائية. التدفق النقدي الأولي: سعر الخيار (غالبا ما يسمى علاوة الخيار). التدفقات النقدية النهائية: قيمة خيار عند انتهاء الصلاحية) غالبا ما تسمى خيار العائد، ويمكن أن يتحقق التدفق النقدي للطرف من قبل صاحب الخيار عن طريق ممارسة الخيار: أرباح الخيار = التدفق النقدي للطرف - التدفق النقدي األولي.

50 استدعاء خيار المردود.

51 وضع خيار الاستحقاقات.

52 أرباح خيار المكالمة.

53 وضع أرباح الخيار.

54 استخدام خيارات لإدارة المخاطر، I.

وضع واقية - استراتيجية شراء خيارات وضع لحماية ضد الوقوع القيم. وتوفر "الحماية" "تأمينا" لقيمة أصل ما أو مجموعة من التدفقات النقدية الداخلة.

55 استخدام خيارات لإدارة المخاطر، إي.

دعوة وقائية - استراتيجية شراء خيارات المكالمة للحماية من ارتفاع الأسعار. توفر المكالمات الوقائية وسيلة "لقفل" قيمة التزام أو تدفق التدفقات النقدية الخارجة.

56 ثلاثة أنواع من استراتيجيات التداول الخيار.

النوع الأول: يقوم المتداولون بإضافة موضع خيار إلى موضع أسهمهم. تساعد هذه الاستراتيجيات التجار على تعديل مخاطر مخزونهم. مثال: المكالمات المغطاة (بيع خيار الاتصال على الأسهم المملوكة بالفعل). النوع الثاني: ينتشر. موضع مع خيارين أو أكثر من نفس النوع (أي المكالمات فقط أو يضع فقط). مثال: انتشار الفراشة. ثلاثة مواقف الخيار باستخدام: الضربات متساوية التباعد بنفس انتهاء الصلاحية. شراء خيار مكالمة واحدة مع أدنى ضربة. شراء خيار مكالمة واحدة مع أعلى الإضراب. بيع اثنين من خيارات المكالمة مع الضربة الوسطى. النوع الثالث: تركيبات. موقف في خليط من الدعوة ووضع الخيارات. مثال: سترادل (شراء مكالمة واحدة وواحدة وضعت بنفس المخالفة وانتهاء الصلاحية). هناك العديد من استراتيجيات التداول الخيار. تحقق من موقع ويب كبوي.

القيمة الجوهرية للخيار هي العائد الذي يحصل عليه حامل الخيار إذا لم يتغير سعر السهم الأساسي من قيمته الحالية. وهذا هو، إذا كان S هو سعر السهم الحالي، و K هو سعر الإضراب للخيار: قيمة الاتصال قيمة جوهرية = ماكس [0، S - K] بالكلمات: القيمة الفعلية للخيار المكالمة هي الحد الأقصى من الصفر أو السهم السعر ناقص سعر الإضراب. وضع القيمة الجوهرية للخيار = ماكس [0، K - S] بالكلمات: القيمة الفعلية للخيار هو الحد الأقصى للسعر أو سعر الإضراب مطروحا منه سعر السهم.

"في المال" خيارات لها قيمة جوهرية إيجابية. بالنسبة للمكالمات، سعر الإضراب أقل من سعر السهم. بالنسبة للسعر، فإن سعر الإضراب أكبر من سعر السهم. خيارات "خارج المال" لها قيمة جوهرية صفرية. للمكالمات، سعر الإضراب أكبر من سعر السهم. بالنسبة للسعر، فإن سعر الإضراب أقل من سعر السهم. "في المال" الخيارات هو مصطلح يستخدم للخيارات عندما يكون سعر السهم وسعر الإضراب هي نفسها تقريبا.

59 حدود التسعير والخيارات.

لا يوجد احتمال الخسارة خسارة محتملة لا يوجد مصروف نقدي في التمويل، لا يسمح بالمراجحة. "غياب التحكيم" = "لا يوجد غداء مجاني" غالبا ما تستخدم قاعدة "غياب التحكيم" في التمويل لحساب أسعار الخيارات. فكر في ما سيحدث إذا سمح بالاستمرار في المراجحة. (من السهل المال للجميع)

60 سعر خيار الحد الأعلى للاتصال.

يجب أن يكون سعر خيار الاتصال أقل من سعر السهم. وإلا، فإن المراجحة ستكون ممكنة. ماذا؟ لنفترض أنك ترى خيارا لبيع المكالمات مقابل 65 دولارا أمريكيا (أو ما يعادله بالعملة المحلية)، وأن المخزون الأساسي يبيع مقابل 60 دولارا أمريكيا التحكيم: بيع المكالمة، وشراء الأسهم. الحالة الأسوأ؟ يتم ممارسة الخيار وأنت جيب $ 5. أفضل حالة؟ يبيع السهم بأقل من 65 دولارا عند انتهاء صلاحية الخيار، وتبقى كل 65 دولارا. صفر الانفاق النقدي اليوم، لا إمكانية الخسارة، وإمكانية لكسب.

(61) الحد الأعلى لأسعار خيارات الشراء الأوروبية، أولا.

يجب أن يكون سعر الخيار الأوروبي وضع أقل من سعر الإضراب. لنفترض أن خيار الشراء مع سعر إضراب قدره 50 دولارا يبيع مقابل 50 دولارا أمريكيا. المراجحة: بيع وضع، واستثمار 50 $ في البنك. (ملاحظة لديك الصفر النقدية النفقات). أسوأ حالة؟ سعر السهم يذهب إلى الصفر. يجب أن تدفع 50 دولارا للسهم (لأنك كنت وضعت الكاتب). ولكن، لديك 50 $ من بيع وضع (بالإضافة إلى الفائدة). أفضل حالة؟ سعر السهم هو $ 50 على الأقل عند انتهاء الصلاحية. وينتهي وضع مع قيمة صفر (وأنت قبالة هوك). يمكنك الحفاظ على كامل $ 50، بالإضافة إلى الفائدة. لذلك، فإننا نرى أنه إذا كان سعر الخيار وضع يساوي سعر الإضراب، وهناك المراجحة.

(62) الحد الأعلى لأسعار خيار الشراء الأوروبي، ثانيا.

سيكون هناك التحكيم إذا كان سعر وضع، بالإضافة إلى الفائدة التي يمكن أن تكسب على مدى حياة الخيار، هو أكبر من سعر السهم. على سبيل المثال، لنفترض أن معدل الخلو من المخاطر هو 3٪ كل ربع سنة. لدينا خيار وضع مع سعر ممارسة من 50 $ و 90 يوما حتى الاستحقاق. ما هو الحد الأقصى لقيمة وضع لا يؤدي إلى المراجحة؟ لاحظ أن الجواب، 48.54 $، هو القيمة الحالية لسعر الإضراب المحسوبة بمعدل خالي من المخاطر. ولذلك، فإن السعر الأقصى لخيار وضع الأوروبي هو القيمة الحالية لسعر الإضراب المحسوب بمعدل خالي من المخاطر.

63 الحد الأدنى لأسعار الخيارات.

يجب أن تكون أسعار الخيارات صفر على الأقل. يمكن لحامل الخيار ببساطة تجاهل الخيار. وهذا يعني أن أحدا لن يدفع لشخص ما أن يأخذ خيارا بعيدا عن أيديهم. ولذلك، فإن سعر الخيار لا يمكن أن يكون سلبيا. المكالمات الأمريكية. هل يمكن للمكالمة الأمريكية أن تبيع أقل من قيمتها الجوهرية؟ لا افترض S = $ 60، وخيار المكالمة لديه سعر إضراب K = 50 $ وسعر 5 $. سعر المكالمات $ 5 هو أقل من القيمة الجوهرية ل S - K = $ 10. إستراتيجية التحكيم: شراء خيار المكالمة بسعره C = $ 5. على الفور ممارسة خيار الدعوة وشراء الأسهم في K = 50 $. ثم، بيع الأسهم بسعر السوق الحالي من S = 60 $. ولذلك، فإن سعر خيار المكالمة الأمريكية لا يقل أبدا عن قيمته الجوهرية. أمريكان كال أوبتيون برايس = ماكس [S - K، 0]

64 الحد الأدنى على الأمريكيين.

هل يمكن لأميركي أن يبيع أقل من قيمته الجوهرية؟ لا يفترض S = $ 40، وخيار وضع لديه سعر الإضراب من K = 50 $ وسعر 5 $. سعر الشراء $ 5 هو أقل من القيمة الجوهرية ل K - S = $ 10. إستراتيجية التحكيم: قم بشراء خيار الشراء بسعر P = $ 5. اشتر السهم بسعره S = $ 40. على الفور ممارسة الخيار وضع وبيع الأسهم في K = 50 $. ولذلك، فإن سعر الخيار الأمريكي وضعه لا يقل أبدا عن قيمته الجوهرية. أمريكان بوت أوبتيون برايس = ماكس [K - S، 0]

65 الحدود الدنيا للخيارات الأوروبية.

المكالمات الأوروبية. لا يمكن ممارسة الخيارات الأوروبية قبل انتهاء الصلاحية. ولذلك، لا يمكننا استخدام استراتيجيات المراجحة لتحديد حدود أقل للخيارات الأمريكية. ويجب أن نستخدم نهجا مختلفا (يمكن العثور عليه بسهولة). ويكون الحد الأدنى لخيار النداء الأوروبي أكبر من قيمته الجوهرية. السعر الأوروبي سعر الخيار ≥ ماكس [S - K / (1 + r) T، 0] الأوروبي يضع. الحد الأدنى لسعر الخيار الأوروبي وضع أقل من قيمته الجوهرية. في الواقع، فإن المال في أوروبا في كثير من الأحيان تبيع لأقل من قيمتها الجوهرية. كم أقل؟ استخدام إستراتيجية المراجحة التي تدل على أن الخيارات الأوروبية لا يمكن ممارستها قبل انتهاء الصلاحية: سعر خيار الشراء الأوروبي ≥ ماكس [K / (1 + r) T - S، 0]

66 التكافؤ في وضع المكالمة قد يكون التكافؤ في وضع النداء هو العلاقة الأساسية في تسعير الخيارات. يستخدم التكافؤ وضع المكالمة عموما للخيارات مع ممارسة على النمط الأوروبي. تعادل سعر المكالمة: الفرق بين سعر المكالمة وسعر الشراء يساوي الفرق بين سعر السهم وسعر الإضراب المخفض.

في الصيغة: C هو سعر خيار الدعوة اليوم S هو سعر السهم اليوم ص هو سعر الفائدة الخالية من المخاطر P هو سعر الخيار وضعت اليوم K هو سعر الإضراب من وضع والدعوة T هو الوقت المتبقي حتى الخيار انتهاء الصلاحية ملاحظة: يمكن إعادة ترتيب هذه الصيغة:

وإذا كان هناك اثنان من الأوراق المالية لهما نفس المبلغ المستحق للمخاطر في المستقبل، يجب أن يبيعا بنفس السعر اليوم. اليوم، لنفترض أن المستثمر يشكل محفظة التالية: شراء 100 سهم من أسهم مايكروسوفت. يكتب عقد خيار مكالمة ميكروسوفت واحد. شراء واحد عقد مايكروسوفت عقد الخيار. عند انتهاء صلاحية الخيار، ستكون هذه الحافظة جديرة بما يلي:

69 مالحظات تعادل األسعار لاحظ أن الحافظة تستحق دائما قيمة K $ عند انتهاء صلاحيتها. أي أنه من غير المجازفة. ولذلك، فإن قيمة هذه المحفظة اليوم هي $ K / (1 + r) T. وهذا هو، لمنع المراجحة: تكلفة اليوم لشراء 100 سهم وشراء واحدة وضعت (صافي من عائدات كتابة مكالمة واحدة)، يجب أن يساوي سعر الأمن أقل المخاطر مع القيمة الاسمية $ K، ونضج T. فان فاكت: إذا كان S = K (وإذا كان r & غ؛ 0)، ثم C & غ؛ P.

70 مواقع مفيدة للحصول على معلومات عن رموز رموز الخيارات، راجع:

لمزيد من المعلومات حول خيارات التعليم: لمعرفة المزيد عن الخيارات، انظر: التبادلات التي تشمل خيارات فهرس التجارة:

(71) استعراض الفصل الأول - الخيارات المتعلقة بالأرصدة المشتركة.

الخيار أساسيات الخيار أسعار الأسعار شركة المقاصة خيارات لماذا الخيارات؟ خيارات مؤشر الأسهم الميزات و مؤشر التسوية الخيار السعر أسعار خيار "المال" الخيار الاستحقاقات والأرباح الخيار خيار الكتابة مردود رسوم بيانية مكافأة الأرباح الخيار.

(72) الفصل الثاني، الفصل الثاني. استخدام خيارات لإدارة المخاطر.

الخيارات الثلاثة لخيارات تداول الخيارات إضافة الخيارات إلى تركيبات المراكز المالية ينتشر الخيار القيم الجوهرية الخيار الأسعار والقيم الجوهرية والمراجحة الخيار الأعلى لخصم سعر الخيار الحد الأعلى لوضع الخيار السعر الحد الأدنى لأسعار الخيارات نداء التكافؤ.

74 افترض أنك تريد شراء الحق في شراء 100 سهم من شركة عب بمبلغ 140 دولارا في أي وقت من الآن وحتى يوليو (أي الخيار 4 من الجدول). تقييم المكاسب والخسائر المحتملة عند انتهاء صلاحية الخيار لأسعار الأسهم من 120 $، 140 $، و 160 $. أرباح / خسائر سعر السهم ($) الأرباح / الخسائر (٪) $٪ $٪ $٪

75 الربح / الخسارة ($) الربح / الخسارة (٪) $ 120 1725 627٪ $ 140 -275 -100٪

وبالنظر إلى المعلومات في السؤال 5، إجراء نفس التحليل لخيارات عب 140 يوليو بوت. أرباح / خسائر السهم ($) الربح / الخسارة (٪) $٪ $٪ $٪

76 افترض أنك مارك كوبي، الابن.

لنفترض أنك مارك كوبي، الابن الذي يشغل حاليا 100،000 سهم من عب. اليوم، سعر السوق من أسهم عب هو $$ 138.25، كما هو مبين في الجدول. كنت تخشى من تقلبات متزايدة في أسعار سهم آي بي إم وتريد التحوط ضد انخفاض أسعار الأسهم للأشهر القليلة القادمة المنتهية في أغسطس 2004 (أي الخيار 5 من الجدول). ماذا ستفعل باستخدام خيارات الأسهم المتاحة أعلاه؟ تأكد من تحديد عدد عقود الخيارات التي سيتم شراؤها، وقسط الخيارات، وانتهاء أشهر. لنفترض أن سعر سهم عب في أغسطس 2004 عندما تنتهي صلاحية الخيارات هو 100 دولار. حساب صافي الربح أو الخسارة من الاستراتيجية الخاصة بك باستخدام عقود الخيارات. في الحساب الخاص بك، وتشمل المكاسب أو الخسائر من التغير في القيمة السوقية في عقد الخاص بك من أسهم عب.

عروض مماثلة.

الفصل 12: نظرية الخيار الأساسي.

خيارات الأسواق: مقدمة.

الاستثمارات | بودي، كين، ماركوس حقوق الطبع والنشر © 2018 من قبل شركات ماكجرو هيل، وشركة جميع الحقوق محفوظة. مغراو هيل / إيروين الفصل 17 خيارات الأسواق:

الفصل التاسع عشر خيارات. أنواع عقود الخيارات n ما هو الخيار؟ تعريف: نوع من العقد بين اثنين من المستثمرين حيث واحد يمنح الآخر.

فيسنتيو كوفريج 1 خيارات خيارات (الفصل 19 جونز)

Fi8000 أساسيات الخيارات: المكالمات، يضع.

الفصل 22 - الخيارات. 2 خيارات §If لديك خيار، ثم لديك الحق في القيام بشيء ما. أي، يمكنك اتخاذ قرار أو اتخاذ بعض الإجراءات.

1 الفصل 15 الخيارات 2 أهداف التعلم وجدول الأعمال  فهم ما هي الدعوة وخيارات وضع.  فهم ما هي عقود الخيارات وكيف.

الفصل ماكجرو هيل / إيروين حقوق الطبع والنشر © 2009 من قبل شركات ماكجرو هيل، وشركة جميع الحقوق محفوظة. 15 خيارات الأسهم.

1 الفصل 6 الخيارات المالية. 2 الموضوعات في الفصل الخيارات المالية المصطلحات الخيار السعر العلاقات بلاك سكولز الخيار التسعير نموذج وضع نداء.

خيارات الفصل 2.5 الفصل 15.

14- 1 الفصل 14 خيارات خيارات الأسهم المشتركة خيارات الأسهم المشتركة لماذا الخيارات لماذا خيارات الخيار "مالينيس" الخيار "موانيس" تعويضات الخيار.

خيارات الأسبوع 7. ما هي الأصول المشتقة؟ إن أي أصل "یستمد" قیمتھ من أصل أساسي آخر یسمی أصول المشتقات. الأساس.

 الخيار المالي  عقد يمنح مالكه الحق (وليس الالتزام) بشراء أو بيع أصل بسعر ثابت كما في تاريخ لاحق.

الفصل 18 المشتقات وإدارة المخاطر.

خيارات ومشتقات ل 9.220، مصطلح 1، 2002/03 02_Lecture17 و 18.ppt نسخة الطالب.

الفصل 19 الخيارات. تحديد الخيارات ومناقشة أسباب استخدامها. وصف كيفية عمل الخيارات وإعطاء بعض الاستراتيجيات الأساسية. اشرح تقييم الخيارات.

فيسنتيو كوفريج 1 خيارات خيارات (الفصل 18 هيرسشي و نوفسنجر)

مقدمة للأوراق المالية المشتقة.

تقييم خيارات الأسهم هاكان باستورك مجلس أسواق رأس المال في تركيا 22 أبريل 2003.

الفصل 19 الخيارات. تحديد الخيارات ومناقشة أسباب استخدامها. وصف كيفية عمل الخيارات وإعطاء بعض الاستراتيجيات الأساسية. اشرح تقييم الخيارات.

15 خيارات الأسهم.

تم النشر بواسطة فيفيرجينيا دورسي تم تعديلها قبل أكثر من عامين.

عروض مماثلة.

عرض حول الموضوع: "15 خيارات الأسهم" - نص العرض:

1 15 خيارات الأسهم.

2 الخيار أساسيات الخيار الأسهم = الأمن المشتقة.

القيمة "المشتقة" من قيمة الأسهم المشتركة الأساسية (الأصول الأساسية) عقود الخيارات المتداولة في البورصة الموحدة تسهل التداول وتقارير الأسعار. العقد = 100 سهم من الأسهم صفر مجموع لعبة 2.

3 وضع وخيارات الاتصال خيار الاتصال وضع الخيار.

يعطي حامل الحق وليس الالتزام بشراء الأصول الأساسية بسعر محدد في وقت محدد. خيار الخيار يعطي المالك الحق ولكن ليس الالتزام ببيع الأصل الأساسي بسعر محدد في وقت محدد. يعطي خيار المكالمة حق المالك ولكن ليس إلزامه بشراء الأصل الأساسي بسعر محدد في وقت محدد. يعطي خيار الخيار الحامل الحق وليس التزام بيع الأصل الأساسي بسعر محدد في وقت محدد. والكلمات الرئيسية في كلا التعريفين هي "الحق وليس الالتزام". ويملك المشتري لعقد الخيار "الخيار" لاستكمال عملية الشراء أو البيع بالسعر المحدد أو لا. 3.

هوية الأسهم الأساسية إضراب أو سعر التمرين حجم العقد تاريخ انتهاء الصلاحية أو استحقاق دورة التمرين إجراءات أمريكية أو أوروبية التسليم أو التسوية دعونا نراجع العناصر الأساسية للخيار: نظرا لأننا نركز على خيارات الأسهم، علينا أن نعرف هوية الأسهم الأساسية. الخيار لديه ضربة أو ممارسة السعر الذي هو الثمن الذي سيتم دفع أو تلقي إذا تم ممارسة الخيار. بالنسبة لخيارات الأسهم، فإن حجم العقد هو 100 سهم على الرغم من أن أسعار الخيارات يتم اقتباسها على أساس السهم الواحد. الخيارات هي عادة أدوات قصيرة الأجل مع آجال استحقاق أقل من سنة واحدة. يتم تحديد أشهر انتهاء صلاحية الخيار عن طريق تبادل البيانات. "دورة التمرين" تشير إلى نوع الخيار - الأمريكية أو الأوروبية، التي لا علاقة لها مع أمريكا أو أوروبا. يمكن ممارسة الخيارات الأمريكية في أي وقت قبل انتهاء الصلاحية؛ يمكن ممارسة الخيارات الأوروبية فقط عند انتهاء الصلاحية. معظم خيارات الأسهم هي الأمريكية في الاسلوب. وأخيرا، نحن بحاجة إلى معرفة إجراءات التسليم أو التسوية. وبالنسبة لخيارات الأسهم العادية، فإن التسليم هو تسليم المخزون الأساسي، والخيارات على مؤشرات الأسهم هي "تسوية نقدية" لأنه لن يكون من المعقول تسليم جميع الأسهم في S & P500 على سبيل المثال. 4.

5 الخيار المدرج الاقتباسات وج.

6 أسعار الخيار أسعار سلسلة الخيار: رموز الأسهم الخيار الخيار ما يلي:

قائمة عقود الخيارات المتاحة والأسعار لأمن معين وتشمل رموز الخيارات الخيار الأسهم: رسائل تحديد المخزون الأساسي يحدد رسالة انتهاء الشهر وندعو / وضع A من خلال L للمكالمات. M من خلال X ل يضع يحدد رسالة سعر الإضراب 6.

7 الأسهم الخيار رمز السهم و ستريك برايس كوديس.

8 الخيار المدرج اقتباسات على شبكة الإنترنت.

9 تغييرات اتفاقية تسمية التسمية.

Instituted by the Options Clearing Corporation Length increased from 5 to 21 characters New style includes letters and numbers Old style presented difficulties: Hard to use for Nasdaq stocks Hard for investors to interpret Proliferation of new option types.

10 “Old Style” Option Naming Convention.

“OPRA” = Options Price Reporting Authority 5 characters Letters only 3 data elements.

11 “New Style” Option Naming Convention.

“OCC Series Key” 21 characters Letters and numbers 4 data elements.

The table above recaps call options on Microsoft stock expiring in July 2008. Microsoft closed at $25.98 on this trading day. Notice that options are available for July expiration with strike prices varying from $15 to $27.50 (and more actually) at intervals of $2.50.’ As we’ve seen previously, we have the last sale or closing price, both bid and ask prices, daily volume and open interest. These are call options, giving the buyer or holder the right – but not the obligation – to buy Microsoft stock at the strike price. Not surprisingly, as the strike price on a call declines, the price of the option rises. It’s more valuable to be able to buy the stock at a lower strike price. 12.

This table gives put prices for Microsoft stock options expiring in July 2008. Though similar to the table on the previous slide, notice that with puts, the price of the option increases as the strike price increases. Again, this is not surprising since a put gives the holder the right to sell stock at the strike price. 13.

14 Option Price Quotes These two small tables recap Calls and Puts on Microsoft with a strike price of $25.00 for 4 expiration months. In this case, notice that as the time to maturity increases, the price of the options also increase for both puts and calls. Again, this makes sense since the more time before the option expires, the more chance for it the price of the underlying stock to move to a point to make exercising the option profitable. 14.

15 The Options Clearing Corporation.

Private agency Guarantees contract fulfillment “Buyer to every seller; seller to every buyer” Issues and clears all option contracts trading on U. S. exchanges Subject to regulation by the Securities and Exchange Commission (SEC) Visit the OCC at: 15.

16 Buying an Option Option holder = buyer of an option contract.

Call option holder has the right but not the obligation to buy the underlying asset from the call option writer. Put option holder has the right but not the obligation to sell the underlying asset to the put option writer. The option holder pays the option premium when the contract is entered.

17 Option Writing The act of selling an option.

Option writer = seller of an option contract Call option writer obligated to sell the underlying asset to the call option holder. Put option writer obligated to buy the underlying asset from the put option holder. Option writer receives the option premium when contract entered 17.

18 Option Exercise American-style European-style.

Exercisable at any time up to and including the option expiration date European-style Exercisable only at the option expiration date Very Important: Option holders also have the right to sell their option at any time. That is, they do not have to exercise the option if they no longer want it. 18.

Notation: S = current stock price per share K = option exercise or strike price C = call option premium per share P = put option premium per share “+” = Buy “-” = Sell As we go forward, looking at various aspects of options and option trading strategies, we’ll be using the notation shown on the slide. S will indicate the current stock price per share. K will indicate the strike or exercise price. C will represent the call option price or premium on a per share basis. P will represent the put option price or premium on a per share basis. A plus sign indicates “buy.” A minus signs means “sell.” For example, “+S-C” (read “plus S minus C”) means buy the stock and sell the call. 19.

20 Option Payoffs vs. Option Profits.

Initial cash flow: Option price = option premium Paid by buyer (holder) to writer Terminal cash flow: Value of option at expiration Option payoff Realized by option holder by exercising the option. Profit = Terminal cash flow − Initial cash flow 20.

21 Option Payoffs & Profits Call Holder.

Payoff to Call Holder (S - K) if S >K 0 if S < K Profit to Call Holder Payoff - Option Premium Profit =MAX(S-K, 0) - C = MAX(S-K,0) Before we look at how to use options, we need to understand how they work – meaning what are the payoffs and profits to the buyers or holders and sellers or writers of calls and puts. We’ll start with the payoff and profit to the holder of a call option. Regardless of the ending stock price, the payoff to the holder of a call can never be less than zero. If the option is worthless, it won’t be exercised. If the stock price is above the exercise price at expiration, then the payoff is simply the stock price minus the strike price (S-K). We have to account for the premium we paid for the option contract so our net profit equals the payoff minus that premium. The payoff to a call holder can never be negative, but the profit (or loss) can be negative but never more than the premium. 21.

22 Option Payoffs & Profits Call Writer.

Payoff to Call Writer - (S - K) if S > K = - MAX(S-K, 0) 0 if S < K = MIN(K-S, 0) Profit to Call Writer Payoff + Option Premium Profit = MIN(K-S, 0) + C Options are what is called a “zero sum game” meaning the profit to the holder is mirrored by the loss to the writer. The payoff to a call writer is exactly the negative of the payoff to the holder. You may remember from algebra that minus the maximum of S minus K or zero equals the minimum of K minus S or zero. For a call writer the BEST case is to sell the call and never hear from it again! In that case, the writer gains the call premium. The payoff and profit for a call writer can be negative. We’ll see the payoffs to both the holder and writer graphically on the next slides. 22.

23 Call Option Payoffs 23.

24 Call Option Profits 24.

25 Payoff & Profit Profiles for Calls.

Call Holder The dashed line is the payoff to the call holder. The solid line is the profit to the holder. The distance between the zero line (x-axis) and this line is the call premium. The dotted line is the profit to the call writer. Notice that it is exactly the reflection of the profit to the holder. Also, notice that the call holder’s downside risk is bounded at the call premium price, but the holder’s gain is theoretically unlimited as the stock price rises. The exact opposite is true for the call writer. His profit is bounded at the call premium but his downside risk is unlimited. Call Writer Stock Price 25.

26 Option Payoffs and Profits Put Holder.

Payoffs to Put Holder 0 if S > K (K - S) if S < K Profit to Put Holder Payoff - Option Premium Profit = MAX(K-S, 0) - P = MAX(K-S, 0) It would seem that the payoff to puts would be the opposite of calls, but that isn’t the case. The payoff to a put holder is again bounded on the lower end by zero and on the upper end by the strike price. Since the stock price, “S”, cannot drop below zero, K minus S cannot be more than K, the strike price. Again, the profit must be reduced by the premium paid for the option. 26.

27 Option Payoffs and Profits Put Writer.

Payoffs to Put Writer 0 if S > K = - MAX(K-S, 0) -(K - S) if S < K = MIN(S-K, 0) Profits to Put Writer Payoff + Option Premium Profit = MIN(S-K, 0) + P As with the call, the payoff to the put writer is the exact negative mirror of the holder’s. As with the writer if a call, a put writer wants to sell the put and never hear from it again, pocketing the option premium. That is the best case for him Let’s look at these payoffs graphically on the next slide. 27.

28 Put Option Payoffs 28.

29 Put Option Profits 29.

30 Payoff & Profit Profiles for Puts.

Profits Put Writer The put holder’s loss is bounded by the premium paid. Theoretically, the put holder’s payoff is bounded on the upper end by the strike price since the stock price will not go below zero. Again, the put writer’s payoff is bounded on the upper end by the option premium. Put Holder Stock Price 30.

CALL PUT Holder: Payoff MAX(S-K,0) MAX(K-S,0) (Long) Profit MAX(S-K,0)-C MAX(K-S,0)-P “Bullish” “Bearish” Writer: Payoff MIN(K-S,0) MIN(S-K,0) (Short) Profit MIN(K-S,0)+C MIN(S-K,0)+P “Bearish” “Bullish” This table recaps the payoff and profit fundamentals that we have just reviewed. 31.

32 Stock Index Options Option on a stock market index.

Cash settlement procedure Actual delivery of all stocks comprising a stock index = impractical If option expires in the money: Option writer pays option holder the intrinsic value of the option Cash settlement procedure same for calls and puts 32 32.

33 American style European style Stock Index Options.

OEX = S&P100 index options European style SPX = S&P500 index options DJX = DJIA index options Stock index options are very popular vehicles for managing broad market risk. The three most popular are the “OEX” which is an option on the S&P100 index, the SPX which is an index on the S&P500 and the DJX which is an option on the Dow. As shown on the slide, note that the three are not exactly the same. The OEX is an American style option meaning it can be exercised at any time before its expiration date. Both the SPX and the DJX are European in style, permitting exercise only at expiration. Stock index options are cash-settled. 33 33.

34 Index Option Trading.

35 Index Option Trading.

Suppose you bought 5 October 1500 SPX call option contracts at a quoted price of $4.75. (Price per SPX = 100 x quote) How much did you pay? $4.75 X 5 X 100 = $2,375 If the index is at 1520 at expiration, what would you receive? $100 X ( ) X 5 = $10,000 Here’s an example of investing in a stock index option. The October SPX call option with a strike price of 1500 is quoted at $4.75. You pay 100 times the quoted option price. If you buy 5 contracts you would pay $4.75 times 100 times 5 equalling $2,375. If the index is at 1520 at expiration, you would receive $100 times the difference between the index value and your strike price times the number of contracts you hold. In this example, that comes out to $10,000. 36 36.

The intrinsic value of an option = the payoff that an option holder receives if the underlying stock price does not change from its current value. If S = the current stock price, and K = the strike price: Call option intrinsic value = MAX [S-K,0 ] The call option intrinsic value is the maximum of zero or the stock price minus the strike price. Put option intrinsic value = MAX [K – S, 0 ] The put option intrinsic value is the maximum of zero or the strike price minus the stock price.

Option “Moneyness” “In-the-money” = an option that would yield a positive payoff if exercised “Out-of-the-money” = an option that would NOT yield a positive payoff if exercised In-the-Money At or Out-of-the-Money Call Option S > K S ≤ K Put Option S < K S ≥ K S = stock price K = exercise price 38 38.

39 Option “Moneyness” “Moneyness” relates to the payoff (or lack of one) if an option were exercised immediately. Suppose you hold a call option on Microsoft with a strike price of $25.00. If the stock is currently selling for $20 per share, then your option is “out-of-the-money” since there is no value in exercising it now. Why would you want to exercise an option to buy shares at $25 when you can buy them in the market for $20? If Microsoft is selling for $25, with the strike price on your call at $25, your option is “at-the-money,” indicating that the strike and market price are the same. If Microsoft rises to $30, your call option is “in-the-money” since the value of exercising it immediately is positive - $30 minus $25. 39 39.

40 Arbitrage, Intrinsic Values and Option Pricing Bounds.

No possibility of a loss A potential for a gain No cash outlay In finance, arbitrage is not allowed to persist. “Absence of Arbitrage” = “No Free Lunch” The “Absence of Arbitrage” rule is often used in finance to calculate option prices.

41 Intrinsic Values and Arbitrage: Calls.

Call options with American-style exercise must sell for at least their intrinsic value. Suppose: S = $60; C = $5; K = $50. Instant Arbitrage: Buy the call for $5. Immediately exercise the call, and buy the stock for $50. In the next instant, sell the stock at the market price of $60. Profit = $5 per share American call option price = MAX[S - K, 0] 41 41.

42 Intrinsic Values and Arbitrage: Puts.

Put options with American-style exercise must sell for at least their intrinsic value. Suppose: S = $40; P = $5; K = $50. Instant Arbitrage: Buy the put for $5. Buy the stock for $40. Immediately exercise the put, and sell the stock for $50. Profit = $5 per share profit American put option price = MAX[K - S, 0] 42 42.

43 Upper Bound for a Call Option Price.

Call option price must be < stock price A call option is selling for $65; the underlying stock is selling for $60. Arbitrage: Sell the call, Buy the stock. Worst case: Option is exercised; you pocket $5. Best case: Stock price < $65 at expiration, you keep all of the $65. 43.

44 Upper Bound for a European Put Option Price.

European Put option price must be < strike price Put option with a $50 strike price is selling for $60. Arbitrage: Sell the put, Invest the $60 Worse case: Stock price goes to zero You must pay $50 for the stock But, you have $60 from the sale of the put (plus interest) Best case: Stock price ≥ $50 at expiration Put expires with zero value You keep the entire $60, plus interest 44.

45 The Upper Bound for European Put Option Prices.

Risk-free rate = 3 % per quarter. Put option with an exercise price of $50 and 90 days to maturity. What is the maximum put value that does not result in an arbitrage? The maximum price for a European put option is the present value of the strike price computed at the risk-free rate.

Type I: Add an option position to a stock position Helps traders modify their stock risk Example: Covered Calls Type II: Spreads. Two or more options of the same type (i. e., only calls or only puts). Example: Butterfly Spread Three option positions using equally-spaced strikes with the same expiration.

Type III: Combinations A position in a mixture of call and put options. Example: Straddle Buy one call and one put with the same strike and expiration There are many option trading strategies. Check out the CBOE’s web site.

48 Option Strategies Protective put Covered call Straddle.

Buy a put option on a stock already owned Protects against a decline in value Covered call Selling a call option on stock already owned Exchanges “upside” potential for current income. Straddle Buying or selling a call and a put with the same exercise price. Buying = long straddle; selling = short straddle. 48 48.

49 Protective Put Limit loss; portfolio insurance.

+P +S Limit loss; portfolio insurance Position - long the stock and long the put A protective put is a way to limit the loss on a stock holding providing a type of portfolio insurance. Very simply, you buy the stock and buy a put on the stock. You could employ this strategy if you fear a stock’s price may fall, you don’t want to sell your shares but you would like to limit your downside risk. You can see in the table above that, assuming the strike price on the put is below the current price of the stock, the strike price is your downside bound. We’ll see an example on the next slides. 49 49.

50 Protective Put Profit Profit Stock Protective Put Portfolio S - P 50.

This graph show you the payoff pattern for holding the stock alone versus the stock plus a put. Again, the distance between the two lines represents the option premium. As described, the protective put strategy limits your downside loss. S - P 50 50.

Suppose you own 100 shares of Microsoft (MSFT) which you bought at the current price of $25.00. You fear MSFT’s price may drop over the next 3-months but you do not want to sell the stock. Put options on MSFT with a strike price of $24 are available. What will be the payoff if you buy a put contract on MSFT? In our example, we own 100 shares of Microsoft selling at $25 per share. You buy a 3-month put contract on Microsoft with a strike price of $24. We’ll see the outcome on the next slide. 51 51.

As you can see in the table, if the stock price falls below $24, you exercise your put and sell your shares for $24, limiting your loss. If the price is above $24, then your option expires worthless, but you still own the shares. 52 52.

53 Covered Call Income enhancement; sell discipline.

Position - Own the stock and write a call. Another option strategy is a covered call. In this case you sell a call option on a stock you own. Portfolio managers use this strategy to enhance the portfolio’s income as well as to enforce a decision to sell. Deciding when to sell a stock is difficult. A portfolio manager might buy a stock with the idea that if the price rises to a certain point, it’s time to sell. Employing the covered call strategy enforces that sell decision, as we’ll see on the next few slides. 53 53.

54 Covered Call Profit Profit Stock Covered Call Portfolio S - P 54.

This graph demonstrates the payoff pattern for holding the stock alone versus the covered call strategy. While generating income in the form of the option premium, the covered call limits upside potential by having the stock called away as the price rises. S - P 54 54.

55 Covered Call Strategy Suppose you own 100 shares of Microsoft (MSFT) which you bought at the current price of $25.00. You expect the price to rise and you decide to sell if the price hits $35 per share. Call options on MSFT with a strike price of $35 are available. You decide to sell a call contract on MSFT. What will be your outcomes at option expiration? Again – you own 100 shares of Microsoft at $25. You have decided that if the price hits $35, its time to sell. To enforce your decision you sell a call contract on Microsoft with a strike price of $35. We’ll see the results on the next slide. 55 55.

56 Covered Call Strategy If Microsoft’s price stays or falls below $35, then you have profited by the amount of the call premium. If the price rises above $35, then the call you wrote will be exercised and you will be obligated to sell your shares for $35 each. 56 56.

+ S – C + P Provides payoff if stock rises or falls Put and Call have the same strike price (K) and same expiration. There are a wide variety of option combinations that can be created to take advantage of the unique properties of options. We’ll look at one more strategy called a straddle. With a straddle, you buy or already own the stock. You think the price is going to move, possibly due to some impending announcement, but you don’t know which way it will go. To hedge yourself, you buy a put and sell a call with the same strike price and same expiration date. As you can see in the table above, your worst case payoff is the strike price. We’ll look at an example of this strategy on the next slide. 57 57.

Suppose you own stock in a gold-mining company called Bre-X Gold. The stock is currently selling for $100 per share. Accusations have arisen about the validity of Bre-X’s claims of finds in Australia. An announcement is expected within a month. If the company’s claims are true, the stock will increase; if they are not, it will fall dramatically. How can you take advantage of this? Bre-X was a real gold mining company in the 1990’s and this situation actually existed in the market at that time. Beginning as a penny stock, Bre-X reached a high of $ per share on the Toronto Stock Exchange before collapsing in 1997. Accusations arose about the validity of Bre-X’s claims of finds in Australia. Investigators were sent to verify the company’s claims. Had you owned Bre-X stock, you could have employed a straddle to protect yourself from the outcome of the investigation of their claims. We’ll see how on the next slide. 58 58.

59 Option Straddle If you sell a call on Bre-X with a strike price of $100 and simultaneously buy a put with the same strike price, your payoff will be $100 regardless of the news on Bre-X. With Bre-X at $100 a share, you sell a call and buy a put with strike prices of $100. As you can see from the table, regardless of what happened to Bre-X’s stock price, your payoff would be $100 per share. This would, of course be reduced by the net premium paid. 59 59.

60 Put-Call Parity The difference between the call price and the put price equals the difference between the stock price and the discounted strike price. Most fundamental relationship in option pricing Generally used for European-style options 60.

Where: C = Call option price today S = Stock price today r = Risk-free interest rate P = Put option price today K = Strike price of the put and the call T = Time remaining until option expiration in years Note: this formula can be rearranged: 61.

If two securities have the same risk-less pay-off in the future, they must sell for the same price today. An investor forms the following portfolio: Buy 100 shares of Microsoft stock Write one Microsoft call option contract Buy one Microsoft put option contract. At option expiration, this portfolio will be worth: 62.

63 Put Call Parity Disequilibrium Example.

S = K = 105 r = 10.25% C = P = T = 0.5 yrs C = P + S - K / (1 + r)T 17 = (105/1.05) 17  15  Call is overpriced at 17 (should be 15) (or Put is underpriced) One use of the parity relationship permits us to find if an option is fairly valued. In the example above we have a stock selling for $110. We also have two options on this stock – a put and a call – both with a strike price of $105, and both expiring in 6 months. If the call is selling for $17 and the put for $5, with a risk-free rate of 10.25%, are these options correctly priced? Using the Put-Call Parity equation, we solve it for the price of the call, then substitute our values and find that equality doesn’t hold. Either the call is overpriced or the put is underpriced. On the next slide, we’ll see how to take advantage of this discrepancy. 63.

C = P S - K/(1+r)T Overpriced Underpriced - C P S PV(X) Sell the call Buy the put Buy the stock “sell the bond” borrow at r We found the call to be overpriced, so we sell (short) it, buy the underpriced put and buy the stock. To complete the equation, we should borrow the discounted value of the strike price at the risk free rate. 64.

65 Synthetic Options C = P + S - K / (1 + r)T - S = + P - C - K/(1+r)T.

Sell the stock = Buy Put Sell call Sell bond ( borrow at r) Synthetic Replicate Another use of the Put-Call Parity relationship allows us to create synthetic positions. If a negative means “sell” and a positive means “buy”, we can solve the equation for the position we wish to simulate. In the example above, we want to simulate shorting a stock. The equivalent position in options is to buy a put, sell a call and borrow at the risk-free rate. Note the solid and dotted lines. Synthesizing (without using the risk-free asset) will result in a payoff pattern that graphs exactly the same as shorting the stock but not at the same dollar amounts. Replicating – including the risk-free asset - will result in exactly the same payoff pattern and dollar amounts as shorting the stock. 65.

66 Put-Call Parity with Dividends.

(15.4) Where “Div” = the present value of the dividend to be paid before the option expires. The Put-Call Parity equation we have worked with so far assumes no dividends are paid during the life of the option. Equation 15.4 above includes a provision for dividends paid by the underlying stock during the option period. Note that “Div” means the discounted value of the upcoming dividend as shown in the modified equation on the slide. Where dy = dividend yield on the underlying stock 66.

67 Implied Option Prices Suppose a stock is currently selling for $25.

A call option with a strike price of $30 maturing in 6 months is priced at $3.00. The stock will pay a dividend of $1.00 in 3 months. The risk-free rate is 5%. What is the implied price for a 6-month put with a strike price of $30? We have a stock selling for $25. A call option with a strike price of $30 maturing in 6 months is priced at $3.00. The risk-free rate is 5%. If the stock is expected to pay a dividend of one dollar in 3 months, what is the implied price of a 6-month put with a $30 strike price? We’ll work this out on the next slide. 67.

68 Implied Option Price S = $25 K = $30 Div = $1.00.

C = $3.00 rf = 5% TD = 3 months = .25 T = 6 months = .5 yrs Substituting into our equation, we find that the implied put price is $8.26. 68.

69 Why Options? “Why buy stock options instead of shares in the underlying stock?” Compare possible outcomes from these two investment strategies: Buy the underlying stock Buy options on the underlying stock 69.

70 Buying the Underlying Stock vs. Buying a Call Option.

IBM = $90 per share Call options = $5 per share w/$90 strike price Investment for 100 shares: IBM Shares: $9,000 One call option contract: $500 When the option expires in three months, the price of IBM shares will be: $100, $80, or $90. 70.

71 Example: Buying the Underlying Stock versus Buying a Call Option, Cont.

Buy 100 IBM Shares $9,000 Investment Buy One Call Option $500 Investment Dollar Profit: Percentage Return: Case 1: $100 $1,000 11.11% $500 100% Case 2: $80 -$1,000 -11.11% -$500 -100% Case 3: $90 $0 0% 71.

Call options offer an alternative means of formulating investment strategies: With call options: Lower dollar loss potential Lower dollar gain potential Higher positive percentage return Lower negative percentage return Insider trading venue 72.

73 Useful Websites For information on options ticker symbols, see:

For more information on options education: To learn more about options, see: Exchanges that trade index options include:

عروض مماثلة.

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Presentation on theme: "15 Stock Options."— Presentation transcript:

1 15 Stock Options.

2 Learning Objectives In this chapter, we will discuss general features of options, but will focus on options on individual common stocks. We will see the tremendous flexibility that options offer investors in designing investment strategies. 1. The basics of option contracts and how to obtain price quotes. 2. The difference between option payoffs and option profits. 3. The workings of some basic option trading strategies. 4. The logic behind the put-call parity condition.

3 Option Basics A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock. An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time. There are two basic financial option types. Call options are options to buy the underlying asset. When exercising a call option, you “call in” the asset. Put options are options to sell the underlying asset. When exercising a put, you “put” the asset to someone. Listed option contracts are standardized to facilitate trading and price reporting. Listed stock options give the option holder the right to buy or sell 100 shares of stock.

4 Option Basics, Cont. Option contracts are legal agreements between two parties—the buyer of the option, and the seller of the option. The minimum terms stipulated by stock option contracts are: The identity of the underlying stock. The strike price, or exercise price. The option contract size. The option expiration date, or option maturity. The option exercise style (American or European). The delivery, or settlement, procedure. Stock options trade at organized options exchanges, such as the CBOE, as well as over-the-counter (OTC) options markets.

5 Option Vocabulary Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold. Option price (premium): The market price of the option contract. Expiration date: The date the option matures. Exercise value: The value of a call or put option if it were exercised today EV of Call = Max (ST ─ X, 0) EV of Put = Max (X ─ ST, 0)

6 More Terminologies In-the-money call: A call whose exercise price is less than the current price of the underlying stock. Out-of-the-money call: A call option whose exercise price exceeds the current stock price. At-the-money call: A call option whose exercise price is equal to the current stock price.

7 Option Price Quotes A list of available option contracts and their prices for a particular security is known as an option chain. Option chains are available online through many sources, including the CBOE (quote. cboe) and Yahoo! Finance (finance. yahoo). Stock option ticker symbols include: Letters to identify the underlying stock. A letter to identify the expiration month as well as whether the option is a call or a put. (A through L for calls; M through X for puts). A letter to identify the strike price (a bit more complicated—see Yahoo or Stock-Trak for tables to explain this letter.)

8 The Change in Stock Option Ticker Symbols.

9 Stock Option Ticker Symbol and Strike Price Codes.

10 Listed Option Quotes at Yahoo! المالية.

11 The Options Clearing Corporation.

The Options Clearing Corporation (OCC) is a private agency that guarantees that the terms of an option contract will be fulfilled if the option is exercised. The OCC issues and clears all option contracts trading on U. S. exchanges. Note that the exchanges and the OCC are all subject to regulation by the Securities and Exchange Commission (SEC). Visit the OCC at:

12 Example: Call Option You buy the call option contract that will allow you to buy from an option seller 100 shares of IBM for $50 per share at any time during the next three months. The call option is traded at $1 for each share of underlying stock. Exercise (or strike) price = $50 Option Price = $1 Expiration: Three months Suppose the price of IBM share rises to $55. You can exercise your option to buy IBM share at an exercise price ($50). Thus, the exercise value is $5 ($55 - $50).

13 Example: Call Option Suppose an IBM share will rise to $55, stay at $50 or fall to $40 per share in three months. Call price = $1 Now months IBM spot price = $55 Exercise value = $5 Profit = $4 IBM spot price = $50 Exercise value = $0 Profit = -$1 Let’s say we have $10,000 to invest Option A: Buy 200 shares of IBM stocks at $50 per share Option B: Buy 100 Calls at $1 per share ($1x100x100) If the ending price is $55, Option A = $5 x200= $1,000 profit (10% return) Option B = $4x100x100=$40,000 profit (400% return) IBM spot price $50 per share IBM spot price = $40 Exercise value = $0 Profit = -$1.

14 How do we make profits from option trading?

From the previous example, assuming that the option is in-the-money at expiration, you can buy IBM share at $50 from an option seller and sell them at current market price ($55). You just made net profit of $4 profit (= ). Thus, the call option buyer is betting on price appreciation of the underlying assets, while the put option buyer is betting on price depreciation of the underlying assets.

15 How do we lose money from option trading?

From the previous example, suppose IBM shares never rises above $50. Then your option expires worthless, so you lose an entire option price ($1).

16 Call Option Payoffs Exercise price = $50 60 40 Buy a call 20.

Option payoffs ($) 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Exercise price = $50.

17 Example: Put Option You buy the put option contract that will allow you to sell from an option seller 100 shares of IBM for $50 per share at any time during the next three months. The put option is traded at $3 for each share of underlying stock. Exercise (or strike) price = $50 Option Price = $3 Expiration: Three months Suppose the price of IBM share falls to $40. You can exercise your option to sell IBM share at an above-market exercise price ($50). Thus, the exercise value is $5 ($55 - $50).

18 Example: Put Option Suppose an IBM share will rise to $55, stay at $50 or fall to $40 per share in three months. Put price = $3 Now months IBM spot price = $55 Exercise value = $0 Profit = -$3 IBM spot price = $50 Exercise value = $0 Profit = -$3 IBM spot price $50 per share IBM spot price = $40 Exercise value = $10 Profit = $7.

19 Put Option Payoffs 60 40 Buy a put 20 Option payoffs ($) 10 20 30 40.

Option payoffs ($) 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60.

20 Why Options? A basic question asked by investors is: “Why buy stock options instead of shares in the underlying stock?” To answer this question, we compare the possible outcomes from these two investment strategies: Buy the underlying stock. Buy options on the underlying stock.

21 Example: Buying the Underlying Stock versus Buying a Call Option.

Suppose IBM is selling for $90 per share and call options with a strike price of $90 are $5 per share. Investment for 100 shares: IBM Shares: $9,000 One listed call option contract: $500 Suppose further that the option expires in three months. Finally, let’s say that in three months, the price of IBM shares will either be: $100, $80, or $90.

22 Example: Buying the Underlying Stock versus Buying a Call Option, Cont.

Let’s calculate the dollar and percentage returns given each of the prices for IBM stock: Buy 100 IBM Shares ($9000 Investment): Buy One Call Option ($500 Investment): Dollar Profit: Percentage Return: Case 1: $100 $1,000 11.11% $500 100% Case 2: $80 -$1,000 -11.11% -$500 -100% Case 3: $90 $0 0%

Whether one strategy is preferred over another is a matter for each individual investor to decide. That is, in some instances investing in the underlying stock will be better. In other instances, investing in the option will be better. Each investor must weight the risk and return trade-off offered by the strategies. It is important to see that call options offer an alternative means of formulating investment strategies. For 100 shares, the dollar loss potential with call options is lower. For 100 shares, the dollar gain potential with call options is lower. The positive percentage return with call options is higher. The negative percentage return with call options is lower.

24 Why buying financial options is very risky way to invest for individual investors?

Shorter-term investment, although LEAPs are introduced recently. LEAPs: Long-term Equity AnticiPation securities that are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years. High level of volatility.

25 Price Volatility of Options: AOL Time Warner example.

26 Bright Side of Financial Options.

Definition Hedging: A strategy to minimize exposure to unwanted risk, while still allowing to profit from investment Suppose a portfolio manger currently holds $10 million of GOOG stocks. The investment horizon is 3-month period. In three month, she will dispose the holdings. The current market price of GOOG is $500 per share. The number of shares of current holdings is 20,000 (=10M/500) shares. She fears of a price drop over the next 3-month period. What can she do to minimize risk using puts?

27 No option strategy If GOOG appreciate by 20% in 3-month,

Market value of portfolio = $12M Gain = $2M If GOOG depreciate by 20% in 3-month, Market value of portfolio = $8M Loss = $2M Expected Volatility = $4M.

28 Put option strategy Today, she buys 200 puts with X=$500, P=$10 per share. She pays the option seller $0.2M today. If GOOG appreciates by 20% in 3-month, Market value of portfolio = $12M (No exercise) Gain = $12M – 10M – 0.2M = $1.8M If GOOG depreciates by 20% in 3-month, Market value of portfolio = $10M (Exercise!) Loss = $10M – 10M – 0.2M = −$0.2M (Loss) Expected Volatility = $2M.

29 Is there any scientific way to derive the price of options?

نعم فعلا. The Black-Scholes Option Pricing Model.

30 Black-Scholes Option Pricing Model.

Originally developed in the early 1970s By Black and Scholes and later refined by Merton. Equity option, index option, foreign currency option, interest rate option, etc Five inputs: current stock price, exercise price, risk-free rate, maturity, volatility of the underlying asset Visit Chicago Board of Options Exchange (cboe)

31 What are the three equations that make up the OPM?

32 What is the value of the following call option according to the OPM.

What is the value of the following call option according to the OPM? Assume: P = $27; X = $25; rRF = 6%; t = 0.5 years: σ2 = 0.11 (or σ = )

33 continued N(d1) = N(0.5736) = 0.7168. N(d2) = N(0.3391) = 0.6327.

Note: Values obtained from Excel using NORMSDIST function. V = $27(0.7168) − $25e−0.03(0.6327) = $ − $25( )(0.6327) = $ 16.

34 Black-Scholes Option Pricing Model.

Stock Price (P): $27.00 D1 = 0.5733 Exercise Price (EX): $25.00 D2 = 0.3388 Risk-free rate (r): 0.06 N(D1) = 0.7168 Dividend Yield (d): N(D2) = 0.6326 Time to Expiration (T): 0.5 N(-D1) = 0.2832 Standard Dev. (SD): 33.17% N(-D2) = 0.3674 CALL PRICE = $4.01 PUT PRICE = $1.27 DELTA = GAMMA = 0.0535 RHO = 7.6741 VEGA = 6.4622 THETA =

35 VIX from CBOE The CBOE Volatility Index® (VIX®) is a key measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices. Since its introduction in 1993, VIX has been considered by many to be the world's premier barometer of investor sentiment and market volatility. VIX shows the market's expectation of 30-day volatility. It is constructed using the implied volatilities of a wide range of S&P 500 index options. The VIX is a widely used measure of market risk and is often referred to as the "investor fear gauge".

36 VIX – Fear Gauge.

37 What impact do the following parameters have on a call option’s value?

Current stock price: Call option value increases as the current stock price increases. Exercise price: As the exercise price increases, a call option’s value decreases. Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.) Risk-free rate: Call option’s value tends to increase as rRF increases (reduces the PV of the exercise price). Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money).

38 Consider a call option with Exercise Price = $20.

39 Call Premium Diagram 5 10 15 20 25 30 35 40 45 50 Option value 30 25.

Market price Exercise value Stock Price.

40 Observations The market price of the option is almost always greater than or equal to the exercise value. لماذا ا؟ The market price of the option is greater than zero even when the option is out-of-the money. لماذا ا؟

41 Intrinsic Value and Speculative Value.

The difference between the exercise price of the option and the spot price of the underlying asset. That is, exercise value. Speculative Value (or Time Value) The difference between the option price and the intrinsic value of the option. Option Price Intrinsic Value Speculative Value + =

42 Example In the earlier table, when stock price is $21, the exercise value is $1 (=21-20). However, the market value is $ Thus, Option price = Intrinsic value +Time value 9.75 (Option Price) = 1 (Exercise Value ) (Time Value)

43 Stock Index Options A stock index option is an option on a stock market index. The most popular stock index options are options on the S&P 100, S&P 500, and Dow Jones Industrial Average. Because the actual delivery of all stocks comprising a stock index is impractical, stock index options have a cash settlement procedure. That is, if the option expires in the money, the option writer simply pays the option holder the intrinsic value of the option. The cash settlement procedure is the same for calls and puts.

46 Option “Moneyness” “In-the-money” option: An option that would yield a positive payoff if exercised “Out-of-the-money” option: An option that would NOT yield a positive payoff if exercised Use the relationship between S (the stock price) and K (the strike price): Note for a given strike price, only the call or only the put can be “in-the-money.” In-the-Money Out-of-the-Money Call Option S > K S ≤ K Put Option S < K S ≥ K.

47 Option Writing The act of selling an option is referred to as option writing. The seller of an option contract is called the writer. The writer of a call option contract is obligated to sell the underlying asset to the call option holder. The call option holder has the right to exercise the call option (i. e., buy the underlying asset at the strike price). The writer of a put option contract is obligated to buy the underlying asset from the put option holder. The put option holder has the right to exercise the put option (i. e., sell the underlying asset at the strike price). Because option writing obligates the option writer, the option writer receives the price of the option today from the option buyer.

48 Option Exercise Option holders have the right to exercise their option. If this right is only available at the option expiration date, the option is said to have European-style exercise. If this right is available at any time up to and including the option expiration date, the option is said to have American-style exercise. Exercise style is not linked to where the option trades. European-style and American-style options trade in the U. S., as well as on other option exchanges throughout the world. Very Important: Option holders also have the right to sell their option at any time. That is, they do not have to exercise the option if they no longer want it.

49 Option Payoffs versus Option Profits.

Option investment strategies involve initial and terminal cash flows. Initial cash flow: option price (often called the option premium). Terminal cash flow: the value of an option at expiration (often called the option payoff. The terminal cash flow can be realized by the option holder by exercising the option. Option Profits = Terminal cash flow − Initial cash flow.

50 Call Option Payoffs.

51 Put Option Payoffs.

52 Call Option Profits.

53 Put Option Profits.

54 Using Options to Manage Risk, I.

Protective put - Strategy of buying put options to protect against falling values. Protective puts provide “insurance” for the value of an asset or a stream of cash inflows.

55 Using Options to Manage Risk, II.

Protective call - Strategy of buying call options to protect against rising prices. Protective calls provide a way to “lock-in” the value of a liability or a stream of cash outflows.

56 The Three Types of Option Trading Strategies.

Type I: Traders add an option position to their stock position. These strategies help traders modify their stock risk. Example: Covered Calls (Selling a call option on a stock already owned). Type II: Spreads. A position with two or more options of the same type (i. e., only calls or only puts). Example: Butterfly Spread. Three option positions using: equally-spaced strikes with the same expiration. Buy one call option with the lowest strike. Buy one call option with the highest strike. Sell two call options with the middle strike. Type III: Combinations. A position in a mixture of call and put options. Example: Straddle (buy one call and one put with the same strike and expiration). There are many option trading strategies. Check out the CBOE’s web site.

The intrinsic value of an option is the payoff that an option holder receives if the underlying stock price does not change from its current value. That is, if S is the current stock price, and K is the strike price of the option: Call option intrinsic value = MAX [0, S – K ] In words: The call option intrinsic value is the maximum of zero or the stock price minus the strike price. Put option intrinsic value = MAX [0, K – S ] In words: The put option intrinsic value is the maximum of zero or the strike price minus the stock price.

“In the Money” options have a positive intrinsic value. For calls, the strike price is less than the stock price. For puts, the strike price is greater than the stock price. “Out of the Money” options have a zero intrinsic value. For calls, the strike price is greater than the stock price. For puts, the strike price is less than the stock price. “At the Money” options is a term used for options when the stock price and the strike price are about the same.

59 Arbitrage and Option Pricing Bounds.

No possibility of a loss A potential for a gain No cash outlay In finance, arbitrage is not allowed to persist. “Absence of Arbitrage” = “No Free Lunch” The “Absence of Arbitrage” rule is often used in finance to calculate option prices. Think about what would happen if arbitrage were allowed to persist. (Easy money for everybody)

60 The Upper Bound for a Call Option Price.

Call option price must be less than the stock price. Otherwise, arbitrage will be possible. ماذا؟ Suppose you see a call option selling for $65, and the underlying stock is selling for $60. The Arbitrage: sell the call, and buy the stock. Worst case? The option is exercised and you pocket $5. Best case? The stock sells for less than $65 at option expiration, and you keep all of the $65. Zero cash outlay today, no possibility of loss, and potential for gain.

61 The Upper Bound for European Put Option Prices, I.

European put option price must be less than the strike price. Suppose a put option with a strike price of $50 is selling for $50. The Arbitrage: Sell the put, and invest the $50 in the bank. (Note you have zero cash outlay). Worse case? Stock price goes to zero. You must pay $50 for the stock (because you were the put writer). But, you have $50 from the sale of the put (plus interest). Best case? Stock price is at least $50 at expiration. The put expires with zero value (and you are off the hook). You keep the entire $50, plus interest. So, we see that if the put option price equals the strike price, there is an arbitrage.

62 The Upper Bound for European Put Option Prices, II.

There will be an arbitrage if price of the put, plus the interest you could earn over the life of the option, is greater than the stock price. For example, suppose the risk-free rate is 3 percent per quarter. We have a put option with an exercise price of $50 and 90 days to maturity. What is the maximum put value that does not result in an arbitrage? Notice that the answer, $48.54, is the present value of the strike price computed at the risk-free rate. Therefore: The maximum price for a European put option is the present value of the strike price computed at the risk-free rate.

63 The Lower Bound on Option Prices.

Option prices must be at least zero. An option holder can simply discard the option. This means that no one would pay someone to take an option off their hands. Therefore, the price of the option cannot be negative. American Calls. Can an American call sell for less than its intrinsic value? No. Suppose S = $60, and a call option has a strike price of K = $50 and a price of $5. The $5 call price is less than the intrinsic value of S - K = $10. The Arbitrage Strategy: Buy the call option at its price of C = $5. Immediately exercise the call option and buy the stock at K = $50. Then, sell the stock at the current market price of S = $60. Therefore, an American call option price is never less than its intrinsic value. American call option price = MAX[S - K, 0]

64 The Lower Bound on American Puts.

Can an American put sell for less than its intrinsic value? No. Suppose S = $40, and a put option has a strike price of K = $50 and a price of $5. The $5 put price is less than the intrinsic value of K - S = $10. The Arbitrage Strategy: Buy the put option at its price of P = $5. Buy the stock at its price of S = $40. Immediately exercise the put option and sell the stock at K = $50. Therefore, an American put option price is never less than its intrinsic value. American put option price = MAX[K - S, 0]

65 The Lower Bounds for European Options.

European Calls. European options cannot be exercised before expiration. Therefore, we cannot use the arbitrage strategies to set lower bounds for American options. We must use a different approach (which can easily be found). The lower bound for a European call option is greater than its intrinsic value. European call option price ≥ MAX[S - K/(1 + r)T, 0] European Puts. The lower bound for a European put option price is less than its intrinsic value. In fact, in-the-money European puts will frequently sell for less than their intrinsic value. How much less? Using an arbitrage strategy that accounts for the fact that European put options cannot be exercised before expiration: European put option price ≥ MAX[K/(1 + r)T – S, 0]

66 Put-Call Parity Put-Call Parity is perhaps the most fundamental relationship in option pricing. Put-Call Parity is generally used for options with European-style exercise. Put-Call Parity states: the difference between the call price and the put price equals the difference between the stock price and the discounted strike price.

In the formula: C is the call option price today S is the stock price today r is the risk-free interest rate P is the put option price today K is the strike price of the put and the call T is the time remaining until option expiration Note: this formula can be rearranged:

If two securities have the same risk-less pay-off in the future, they must sell for the same price today. Today, suppose an investor forms the following portfolio: Buys 100 shares of Microsoft stock. Writes one Microsoft call option contract. Buys one Microsoft put option contract. At option expiration, this portfolio will be worth:

69 Put-Call Parity Notes Notice that the portfolio is always worth $K at expiration. That is, it is riskless. Therefore, the value of this portfolio today is $K/(1+r)T. That is, to prevent arbitrage: today’s cost of buying 100 shares and buying one put (net of the proceeds of writing one call), should equal the price of a risk-less security with a face value of $K, and a maturity of T. Fun fact: If S = K (and if r > 0), then C > P.

70 Useful Websites For information on options ticker symbols, see:

For more information on options education: To learn more about options, see: Exchanges that trade index options include:

71 Chapter Review, I. Options on Common Stocks.

Option Basics Option Price Quotes The Options Clearing Corporation Why Options? Stock Index Options Features and Settlement Index Option Price Quotes Option “Moneyness” Option Payoffs and Profits Option Writing Option Payoffs Payoff Diagrams Option Profits.

72 Chapter Review, II. Using Options to Manage Risk.

The Three Types of Option Trading Strategies Adding Options to a Stock Position Combinations Spreads Option Intrinsic Values Option Prices, Intrinsic Values, and Arbitrage The Upper Bound for a Call Option Price The Upper Bound for a Put Option Price The Lower Bounds on Option Prices Put-Call Parity.

74 Suppose you want to buy the right to BUY 100 shares of IBM with a $140 anytime between now and July (i. e., the Option 4 from the table). Evaluate your potential gains and losses at option expiration for stock prices of $120, $140, and $160. Stock price gain/loss ($) gains/loss (%) $ % $ % $ %

75 Stock Gain/Loss ($) Gain/Loss (%) $120 1725 627% $140 -275 -100%

Given information in question 5, conduct the same analysis for IBM 140 July PUT options. Stock Gain/Loss ($) Gain/Loss (%) $ % $ % $ %

76 Suppose you are Mark Cuban, Jr.

Suppose you are Mark Cuban, Jr. who is currently holding 100,000 shares of IBM. Today, the market price of IBM shares is $$138.25, as shown in the table. You fear of growing volatility of IBM share prices and want to hedge against falling share prices for next several months ending August 2004 (i. e., the Option 5 from the table). What would you do using options on stocks available above? Be sure to identify the number of options contracts to be bought, the options premium, and expiration months. Suppose an IBM share price in August 2004 when the options expire is $100. Calculate net gain or loss from your strategy using options contracts. In your calculation, include gains or losses from the market value change in your holding of IBM shares.

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Chapter 12: Basic option theory.

خيارات الأسواق: مقدمة.

INVESTMENTS | BODIE, KANE, MARCUS Copyright © 2018 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 17 Options Markets:

CHAPTER NINETEEN OPTIONS. TYPES OF OPTION CONTRACTS n WHAT IS AN OPTION? Definition: a type of contract between two investors where one grants the other.

Vicentiu Covrig 1 Options Options (Chapter 19 Jones)

Fi8000 Basics of Options: Calls, Puts.

الفصل 22 - الخيارات. 2 خيارات §If لديك خيار، ثم لديك الحق في القيام بشيء ما. أي، يمكنك اتخاذ قرار أو اتخاذ بعض الإجراءات.

1 Chapter 15 Options 2 Learning Objectives & Agenda  Understand what are call and put options.  Understand what are options contracts and how they.

Chapter McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. 15 Stock Options.

1 Chapter 6 Financial Options. 2 Topics in Chapter Financial Options Terminology Option Price Relationships Black-Scholes Option Pricing Model Put-Call.

Options Chapter 2.5 Chapter 15.

14- 1 Chapter 14 Options Options on common stocks Options on common stocks Why options Why options Option “Moneyness” Option “Moneyness” Option payoffs.

خيارات الأسبوع 7. ما هي الأصول المشتقة؟ إن أي أصل "یستمد" قیمتھ من أصل أساسي آخر یسمی أصول المشتقات. الأساس.

 Financial Option  A contract that gives its owner the right (but not the obligation) to purchase or sell an asset at a fixed price as some future date.

CHAPTER 18 Derivatives and Risk Management.

خيارات ومشتقات ل 9.220، مصطلح 1، 2002/03 02_Lecture17 و 18.ppt نسخة الطالب.

Chapter 19 Options. Define options and discuss why they are used. Describe how options work and give some basic strategies. Explain the valuation of options.

Vicentiu Covrig 1 Options Options (Chapter 18 Hirschey and Nofsinger)

AN INTRODUCTION TO DERIVATIVE SECURITIES.

تقييم خيارات الأسهم هاكان باستورك مجلس أسواق رأس المال في تركيا 22 أبريل 2003.

CHAPTER NINETEEN Options CHAPTER NINETEEN Options Cleary / Jones Investments: Analysis and Management.

15 Stock Options.

Published byVeronica Simpson Modified about 1 year ago.

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Presentation on theme: "15 Stock Options."— Presentation transcript:

1 15 Stock Options.

2 Learning Objectives In this chapter, we will discuss general features of options, but will focus on options on individual common stocks. We will see the tremendous flexibility that options offer investors in designing investment strategies. 1. The basics of option contracts and how to obtain price quotes. 2. The difference between option payoffs and option profits. 3. The workings of some basic option trading strategies. 4. The logic behind the put-call parity condition.

3 Option Basics A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock. An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time. There are two basic financial option types. Call options are options to buy the underlying asset. When exercising a call option, you “call in” the asset. Put options are options to sell the underlying asset. When exercising a put, you “put” the asset to someone. Listed option contracts are standardized to facilitate trading and price reporting. Listed stock options give the option holder the right to buy or sell 100 shares of stock.

4 Option Basics, Cont. Option contracts are legal agreements between two parties—the buyer of the option, and the seller of the option. The minimum terms stipulated by stock option contracts are: The identity of the underlying stock. The strike price, or exercise price. The option contract size. The option expiration date, or option maturity. The option exercise style (American or European). The delivery, or settlement, procedure. Stock options trade at organized options exchanges, such as the CBOE, as well as over-the-counter (OTC) options markets.

5 Option Vocabulary Exercise (or strike) price: The price stated in the option contract at which the security can be bought or sold. Option price (premium): The market price of the option contract. Expiration date: The date the option matures. Exercise value: The value of a call or put option if it were exercised today EV of Call = Max (ST ─ X, 0) EV of Put = Max (X ─ ST, 0)

6 More Terminologies In-the-money call: A call whose exercise price is less than the current price of the underlying stock. Out-of-the-money call: A call option whose exercise price exceeds the current stock price. At-the-money call: A call option whose exercise price is equal to the current stock price.

7 Option Price Quotes A list of available option contracts and their prices for a particular security is known as an option chain. Option chains are available online through many sources, including the CBOE (quote. cboe) and Yahoo! Finance (finance. yahoo). Stock option ticker symbols include: Letters to identify the underlying stock. A letter to identify the expiration month as well as whether the option is a call or a put. (A through L for calls; M through X for puts). A letter to identify the strike price (a bit more complicated—see Yahoo or Stock-Trak for tables to explain this letter.)

8 The Change in Stock Option Ticker Symbols.

9 Stock Option Ticker Symbol and Strike Price Codes.

10 Listed Option Quotes at Yahoo! المالية.

11 The Options Clearing Corporation.

The Options Clearing Corporation (OCC) is a private agency that guarantees that the terms of an option contract will be fulfilled if the option is exercised. The OCC issues and clears all option contracts trading on U. S. exchanges. Note that the exchanges and the OCC are all subject to regulation by the Securities and Exchange Commission (SEC). Visit the OCC at:

12 Example: Call Option You buy the call option contract that will allow you to buy from an option seller 100 shares of IBM for $50 per share at any time during the next three months. The call option is traded at $1 for each share of underlying stock. Exercise (or strike) price = $50 Option Price = $1 Expiration: Three months Suppose the price of IBM share rises to $55. You can exercise your option to buy IBM share at an exercise price ($50). Thus, the exercise value is $5 ($55 - $50).

13 Example: Call Option Suppose an IBM share will rise to $55, stay at $50 or fall to $40 per share in three months. Call price = $1 Now months IBM spot price = $55 Exercise value = $5 Profit = $4 IBM spot price = $50 Exercise value = $0 Profit = -$1 Let’s say we have $10,000 to invest Option A: Buy 200 shares of IBM stocks at $50 per share Option B: Buy 100 Calls at $1 per share ($1x100x100) If the ending price is $55, Option A = $5 x200= $1,000 profit (10% return) Option B = $4x100x100=$40,000 profit (400% return) IBM spot price $50 per share IBM spot price = $40 Exercise value = $0 Profit = -$1.

14 How do we make profits from option trading?

From the previous example, assuming that the option is in-the-money at expiration, you can buy IBM share at $50 from an option seller and sell them at current market price ($55). You just made net profit of $4 profit (= ). Thus, the call option buyer is betting on price appreciation of the underlying assets, while the put option buyer is betting on price depreciation of the underlying assets.

15 How do we lose money from option trading?

From the previous example, suppose IBM shares never rises above $50. Then your option expires worthless, so you lose an entire option price ($1).

16 Call Option Payoffs Exercise price = $50 60 40 Buy a call 20.

Option payoffs ($) 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Exercise price = $50.

17 Example: Put Option You buy the put option contract that will allow you to sell from an option seller 100 shares of IBM for $50 per share at any time during the next three months. The put option is traded at $3 for each share of underlying stock. Exercise (or strike) price = $50 Option Price = $3 Expiration: Three months Suppose the price of IBM share falls to $40. You can exercise your option to sell IBM share at an above-market exercise price ($50). Thus, the exercise value is $5 ($55 - $50).

18 Example: Put Option Suppose an IBM share will rise to $55, stay at $50 or fall to $40 per share in three months. Put price = $3 Now months IBM spot price = $55 Exercise value = $0 Profit = -$3 IBM spot price = $50 Exercise value = $0 Profit = -$3 IBM spot price $50 per share IBM spot price = $40 Exercise value = $10 Profit = $7.

19 Put Option Payoffs 60 40 Buy a put 20 Option payoffs ($) 10 20 30 40.

Option payoffs ($) 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60.

20 Why Options? A basic question asked by investors is: “Why buy stock options instead of shares in the underlying stock?” To answer this question, we compare the possible outcomes from these two investment strategies: Buy the underlying stock. Buy options on the underlying stock.

21 Example: Buying the Underlying Stock versus Buying a Call Option.

Suppose IBM is selling for $90 per share and call options with a strike price of $90 are $5 per share. Investment for 100 shares: IBM Shares: $9,000 One listed call option contract: $500 Suppose further that the option expires in three months. Finally, let’s say that in three months, the price of IBM shares will either be: $100, $80, or $90.

22 Example: Buying the Underlying Stock versus Buying a Call Option, Cont.

Let’s calculate the dollar and percentage returns given each of the prices for IBM stock: Buy 100 IBM Shares ($9000 Investment): Buy One Call Option ($500 Investment): Dollar Profit: Percentage Return: Case 1: $100 $1,000 11.11% $500 100% Case 2: $80 -$1,000 -11.11% -$500 -100% Case 3: $90 $0 0%

Whether one strategy is preferred over another is a matter for each individual investor to decide. That is, in some instances investing in the underlying stock will be better. In other instances, investing in the option will be better. Each investor must weight the risk and return trade-off offered by the strategies. It is important to see that call options offer an alternative means of formulating investment strategies. For 100 shares, the dollar loss potential with call options is lower. For 100 shares, the dollar gain potential with call options is lower. The positive percentage return with call options is higher. The negative percentage return with call options is lower.

24 Why buying financial options is very risky way to invest for individual investors?

Shorter-term investment, although LEAPs are introduced recently. LEAPs: Long-term Equity AnticiPation securities that are similar to conventional options except that they are long-term options with maturities of up to 2 1/2 years. High level of volatility.

25 Price Volatility of Options: AOL Time Warner example.

26 Bright Side of Financial Options.

Definition Hedging: A strategy to minimize exposure to unwanted risk, while still allowing to profit from investment Suppose a portfolio manger currently holds $10 million of GOOG stocks. The investment horizon is 3-month period. In three month, she will dispose the holdings. The current market price of GOOG is $500 per share. The number of shares of current holdings is 20,000 (=10M/500) shares. She fears of a price drop over the next 3-month period. What can she do to minimize risk using puts?

27 No option strategy If GOOG appreciate by 20% in 3-month,

Market value of portfolio = $12M Gain = $2M If GOOG depreciate by 20% in 3-month, Market value of portfolio = $8M Loss = $2M Expected Volatility = $4M.

28 Put option strategy Today, she buys 200 puts with X=$500, P=$10 per share. She pays the option seller $0.2M today. If GOOG appreciates by 20% in 3-month, Market value of portfolio = $12M (No exercise) Gain = $12M – 10M – 0.2M = $1.8M If GOOG depreciates by 20% in 3-month, Market value of portfolio = $10M (Exercise!) Loss = $10M – 10M – 0.2M = −$0.2M (Loss) Expected Volatility = $2M.

29 Is there any scientific way to derive the price of options?

نعم فعلا. The Black-Scholes Option Pricing Model.

30 Black-Scholes Option Pricing Model.

Originally developed in the early 1970s By Black and Scholes and later refined by Merton. Equity option, index option, foreign currency option, interest rate option, etc Five inputs: current stock price, exercise price, risk-free rate, maturity, volatility of the underlying asset Visit Chicago Board of Options Exchange (cboe)

31 What are the three equations that make up the OPM?

32 What is the value of the following call option according to the OPM.

What is the value of the following call option according to the OPM? Assume: P = $27; X = $25; rRF = 6%; t = 0.5 years: σ2 = 0.11 (or σ = )

33 continued N(d1) = N(0.5736) = 0.7168. N(d2) = N(0.3391) = 0.6327.

Note: Values obtained from Excel using NORMSDIST function. V = $27(0.7168) − $25e−0.03(0.6327) = $ − $25( )(0.6327) = $ 16.

34 Black-Scholes Option Pricing Model.

Stock Price (P): $27.00 D1 = 0.5733 Exercise Price (EX): $25.00 D2 = 0.3388 Risk-free rate (r): 0.06 N(D1) = 0.7168 Dividend Yield (d): N(D2) = 0.6326 Time to Expiration (T): 0.5 N(-D1) = 0.2832 Standard Dev. (SD): 33.17% N(-D2) = 0.3674 CALL PRICE = $4.01 PUT PRICE = $1.27 DELTA = GAMMA = 0.0535 RHO = 7.6741 VEGA = 6.4622 THETA =

35 VIX from CBOE The CBOE Volatility Index® (VIX®) is a key measure of market expectations of near-term volatility conveyed by S&P 500 stock index option prices. Since its introduction in 1993, VIX has been considered by many to be the world's premier barometer of investor sentiment and market volatility. VIX shows the market's expectation of 30-day volatility. It is constructed using the implied volatilities of a wide range of S&P 500 index options. The VIX is a widely used measure of market risk and is often referred to as the "investor fear gauge".

36 VIX – Fear Gauge.

37 What impact do the following parameters have on a call option’s value?

Current stock price: Call option value increases as the current stock price increases. Exercise price: As the exercise price increases, a call option’s value decreases. Option period: As the expiration date is lengthened, a call option’s value increases (more chance of becoming in the money.) Risk-free rate: Call option’s value tends to increase as rRF increases (reduces the PV of the exercise price). Stock return variance: Option value increases with variance of the underlying stock (more chance of becoming in the money).

38 Consider a call option with Exercise Price = $20.

39 Call Premium Diagram 5 10 15 20 25 30 35 40 45 50 Option value 30 25.

Market price Exercise value Stock Price.

40 Observations The market price of the option is almost always greater than or equal to the exercise value. لماذا ا؟ The market price of the option is greater than zero even when the option is out-of-the money. لماذا ا؟

41 Intrinsic Value and Speculative Value.

The difference between the exercise price of the option and the spot price of the underlying asset. That is, exercise value. Speculative Value (or Time Value) The difference between the option price and the intrinsic value of the option. Option Price Intrinsic Value Speculative Value + =

42 Example In the earlier table, when stock price is $21, the exercise value is $1 (=21-20). However, the market value is $ Thus, Option price = Intrinsic value +Time value 9.75 (Option Price) = 1 (Exercise Value ) (Time Value)

43 Stock Index Options A stock index option is an option on a stock market index. The most popular stock index options are options on the S&P 100, S&P 500, and Dow Jones Industrial Average. Because the actual delivery of all stocks comprising a stock index is impractical, stock index options have a cash settlement procedure. That is, if the option expires in the money, the option writer simply pays the option holder the intrinsic value of the option. The cash settlement procedure is the same for calls and puts.

46 Option “Moneyness” “In-the-money” option: An option that would yield a positive payoff if exercised “Out-of-the-money” option: An option that would NOT yield a positive payoff if exercised Use the relationship between S (the stock price) and K (the strike price): Note for a given strike price, only the call or only the put can be “in-the-money.” In-the-Money Out-of-the-Money Call Option S > K S ≤ K Put Option S < K S ≥ K.

47 Option Writing The act of selling an option is referred to as option writing. The seller of an option contract is called the writer. The writer of a call option contract is obligated to sell the underlying asset to the call option holder. The call option holder has the right to exercise the call option (i. e., buy the underlying asset at the strike price). The writer of a put option contract is obligated to buy the underlying asset from the put option holder. The put option holder has the right to exercise the put option (i. e., sell the underlying asset at the strike price). Because option writing obligates the option writer, the option writer receives the price of the option today from the option buyer.

48 Option Exercise Option holders have the right to exercise their option. If this right is only available at the option expiration date, the option is said to have European-style exercise. If this right is available at any time up to and including the option expiration date, the option is said to have American-style exercise. Exercise style is not linked to where the option trades. European-style and American-style options trade in the U. S., as well as on other option exchanges throughout the world. Very Important: Option holders also have the right to sell their option at any time. That is, they do not have to exercise the option if they no longer want it.

49 Option Payoffs versus Option Profits.

Option investment strategies involve initial and terminal cash flows. Initial cash flow: option price (often called the option premium). Terminal cash flow: the value of an option at expiration (often called the option payoff. The terminal cash flow can be realized by the option holder by exercising the option. Option Profits = Terminal cash flow − Initial cash flow.

50 Call Option Payoffs.

51 Put Option Payoffs.

52 Call Option Profits.

53 Put Option Profits.

54 Using Options to Manage Risk, I.

Protective put - Strategy of buying put options to protect against falling values. Protective puts provide “insurance” for the value of an asset or a stream of cash inflows.

55 Using Options to Manage Risk, II.

Protective call - Strategy of buying call options to protect against rising prices. Protective calls provide a way to “lock-in” the value of a liability or a stream of cash outflows.

56 The Three Types of Option Trading Strategies.

Type I: Traders add an option position to their stock position. These strategies help traders modify their stock risk. Example: Covered Calls (Selling a call option on a stock already owned). Type II: Spreads. A position with two or more options of the same type (i. e., only calls or only puts). Example: Butterfly Spread. Three option positions using: equally-spaced strikes with the same expiration. Buy one call option with the lowest strike. Buy one call option with the highest strike. Sell two call options with the middle strike. Type III: Combinations. A position in a mixture of call and put options. Example: Straddle (buy one call and one put with the same strike and expiration). There are many option trading strategies. Check out the CBOE’s web site.

The intrinsic value of an option is the payoff that an option holder receives if the underlying stock price does not change from its current value. That is, if S is the current stock price, and K is the strike price of the option: Call option intrinsic value = MAX [0, S – K ] In words: The call option intrinsic value is the maximum of zero or the stock price minus the strike price. Put option intrinsic value = MAX [0, K – S ] In words: The put option intrinsic value is the maximum of zero or the strike price minus the stock price.

“In the Money” options have a positive intrinsic value. For calls, the strike price is less than the stock price. For puts, the strike price is greater than the stock price. “Out of the Money” options have a zero intrinsic value. For calls, the strike price is greater than the stock price. For puts, the strike price is less than the stock price. “At the Money” options is a term used for options when the stock price and the strike price are about the same.

59 Arbitrage and Option Pricing Bounds.

No possibility of a loss A potential for a gain No cash outlay In finance, arbitrage is not allowed to persist. “Absence of Arbitrage” = “No Free Lunch” The “Absence of Arbitrage” rule is often used in finance to calculate option prices. Think about what would happen if arbitrage were allowed to persist. (Easy money for everybody)

60 The Upper Bound for a Call Option Price.

Call option price must be less than the stock price. Otherwise, arbitrage will be possible. ماذا؟ Suppose you see a call option selling for $65, and the underlying stock is selling for $60. The Arbitrage: sell the call, and buy the stock. Worst case? The option is exercised and you pocket $5. Best case? The stock sells for less than $65 at option expiration, and you keep all of the $65. Zero cash outlay today, no possibility of loss, and potential for gain.

61 The Upper Bound for European Put Option Prices, I.

European put option price must be less than the strike price. Suppose a put option with a strike price of $50 is selling for $50. The Arbitrage: Sell the put, and invest the $50 in the bank. (Note you have zero cash outlay). Worse case? Stock price goes to zero. You must pay $50 for the stock (because you were the put writer). But, you have $50 from the sale of the put (plus interest). Best case? Stock price is at least $50 at expiration. The put expires with zero value (and you are off the hook). You keep the entire $50, plus interest. So, we see that if the put option price equals the strike price, there is an arbitrage.

62 The Upper Bound for European Put Option Prices, II.

There will be an arbitrage if price of the put, plus the interest you could earn over the life of the option, is greater than the stock price. For example, suppose the risk-free rate is 3 percent per quarter. We have a put option with an exercise price of $50 and 90 days to maturity. What is the maximum put value that does not result in an arbitrage? Notice that the answer, $48.54, is the present value of the strike price computed at the risk-free rate. Therefore: The maximum price for a European put option is the present value of the strike price computed at the risk-free rate.

63 The Lower Bound on Option Prices.

Option prices must be at least zero. An option holder can simply discard the option. This means that no one would pay someone to take an option off their hands. Therefore, the price of the option cannot be negative. American Calls. Can an American call sell for less than its intrinsic value? No. Suppose S = $60, and a call option has a strike price of K = $50 and a price of $5. The $5 call price is less than the intrinsic value of S - K = $10. The Arbitrage Strategy: Buy the call option at its price of C = $5. Immediately exercise the call option and buy the stock at K = $50. Then, sell the stock at the current market price of S = $60. Therefore, an American call option price is never less than its intrinsic value. American call option price = MAX[S - K, 0]

64 The Lower Bound on American Puts.

Can an American put sell for less than its intrinsic value? No. Suppose S = $40, and a put option has a strike price of K = $50 and a price of $5. The $5 put price is less than the intrinsic value of K - S = $10. The Arbitrage Strategy: Buy the put option at its price of P = $5. Buy the stock at its price of S = $40. Immediately exercise the put option and sell the stock at K = $50. Therefore, an American put option price is never less than its intrinsic value. American put option price = MAX[K - S, 0]

65 The Lower Bounds for European Options.

European Calls. European options cannot be exercised before expiration. Therefore, we cannot use the arbitrage strategies to set lower bounds for American options. We must use a different approach (which can easily be found). The lower bound for a European call option is greater than its intrinsic value. European call option price ≥ MAX[S - K/(1 + r)T, 0] European Puts. The lower bound for a European put option price is less than its intrinsic value. In fact, in-the-money European puts will frequently sell for less than their intrinsic value. How much less? Using an arbitrage strategy that accounts for the fact that European put options cannot be exercised before expiration: European put option price ≥ MAX[K/(1 + r)T – S, 0]

66 Put-Call Parity Put-Call Parity is perhaps the most fundamental relationship in option pricing. Put-Call Parity is generally used for options with European-style exercise. Put-Call Parity states: the difference between the call price and the put price equals the difference between the stock price and the discounted strike price.

In the formula: C is the call option price today S is the stock price today r is the risk-free interest rate P is the put option price today K is the strike price of the put and the call T is the time remaining until option expiration Note: this formula can be rearranged:

If two securities have the same risk-less pay-off in the future, they must sell for the same price today. Today, suppose an investor forms the following portfolio: Buys 100 shares of Microsoft stock. Writes one Microsoft call option contract. Buys one Microsoft put option contract. At option expiration, this portfolio will be worth:

69 Put-Call Parity Notes Notice that the portfolio is always worth $K at expiration. That is, it is riskless. Therefore, the value of this portfolio today is $K/(1+r)T. That is, to prevent arbitrage: today’s cost of buying 100 shares and buying one put (net of the proceeds of writing one call), should equal the price of a risk-less security with a face value of $K, and a maturity of T. Fun fact: If S = K (and if r > 0), then C > P.

70 Useful Websites For information on options ticker symbols, see:

For more information on options education: To learn more about options, see: Exchanges that trade index options include:

71 Chapter Review, I. Options on Common Stocks.

Option Basics Option Price Quotes The Options Clearing Corporation Why Options? Stock Index Options Features and Settlement Index Option Price Quotes Option “Moneyness” Option Payoffs and Profits Option Writing Option Payoffs Payoff Diagrams Option Profits.

72 Chapter Review, II. Using Options to Manage Risk.

The Three Types of Option Trading Strategies Adding Options to a Stock Position Combinations Spreads Option Intrinsic Values Option Prices, Intrinsic Values, and Arbitrage The Upper Bound for a Call Option Price The Upper Bound for a Put Option Price The Lower Bounds on Option Prices Put-Call Parity.

74 Suppose you want to buy the right to BUY 100 shares of IBM with a $140 anytime between now and July (i. e., the Option 4 from the table). Evaluate your potential gains and losses at option expiration for stock prices of $120, $140, and $160. Stock price gain/loss ($) gains/loss (%) $ % $ % $ %

75 Stock Gain/Loss ($) Gain/Loss (%) $120 1725 627% $140 -275 -100%

Given information in question 5, conduct the same analysis for IBM 140 July PUT options. Stock Gain/Loss ($) Gain/Loss (%) $ % $ % $ %

76 Suppose you are Mark Cuban, Jr.

Suppose you are Mark Cuban, Jr. who is currently holding 100,000 shares of IBM. Today, the market price of IBM shares is $$138.25, as shown in the table. You fear of growing volatility of IBM share prices and want to hedge against falling share prices for next several months ending August 2004 (i. e., the Option 5 from the table). What would you do using options on stocks available above? Be sure to identify the number of options contracts to be bought, the options premium, and expiration months. Suppose an IBM share price in August 2004 when the options expire is $100. Calculate net gain or loss from your strategy using options contracts. In your calculation, include gains or losses from the market value change in your holding of IBM shares.

عروض مماثلة.

Chapter 12: Basic option theory.

خيارات الأسواق: مقدمة.

INVESTMENTS | BODIE, KANE, MARCUS Copyright © 2018 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 17 Options Markets:

CHAPTER NINETEEN OPTIONS. TYPES OF OPTION CONTRACTS n WHAT IS AN OPTION? Definition: a type of contract between two investors where one grants the other.

Vicentiu Covrig 1 Options Options (Chapter 19 Jones)

Fi8000 Basics of Options: Calls, Puts.

الفصل 22 - الخيارات. 2 خيارات §If لديك خيار، ثم لديك الحق في القيام بشيء ما. أي، يمكنك اتخاذ قرار أو اتخاذ بعض الإجراءات.

1 Chapter 15 Options 2 Learning Objectives & Agenda  Understand what are call and put options.  Understand what are options contracts and how they.

Chapter McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved. 15 Stock Options.

1 Chapter 6 Financial Options. 2 Topics in Chapter Financial Options Terminology Option Price Relationships Black-Scholes Option Pricing Model Put-Call.

Options Chapter 2.5 Chapter 15.

14- 1 Chapter 14 Options Options on common stocks Options on common stocks Why options Why options Option “Moneyness” Option “Moneyness” Option payoffs.

خيارات الأسبوع 7. ما هي الأصول المشتقة؟ إن أي أصل "یستمد" قیمتھ من أصل أساسي آخر یسمی أصول المشتقات. الأساس.

 Financial Option  A contract that gives its owner the right (but not the obligation) to purchase or sell an asset at a fixed price as some future date.

CHAPTER 18 Derivatives and Risk Management.

خيارات ومشتقات ل 9.220، مصطلح 1، 2002/03 02_Lecture17 و 18.ppt نسخة الطالب.

Chapter 19 Options. Define options and discuss why they are used. Describe how options work and give some basic strategies. Explain the valuation of options.

Vicentiu Covrig 1 Options Options (Chapter 18 Hirschey and Nofsinger)

AN INTRODUCTION TO DERIVATIVE SECURITIES.

تقييم خيارات الأسهم هاكان باستورك مجلس أسواق رأس المال في تركيا 22 أبريل 2003.

1 Chapter 15 Options 2 Learning Objectives & Agenda  Understand what are call and put options.  Understand what are options contracts and how they.

Financial Options: Introduction. Option Basics A stock option is a derivative security, because the value of the option is “derived” from the value of.

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Presentation on theme: "Financial Options: Introduction. Option Basics A stock option is a derivative security, because the value of the option is “derived” from the value of."— Presentation transcript:

1 Financial Options: Introduction.

2 Option Basics A stock option is a derivative security, because the value of the option is “derived” from the value of the underlying common stock. Derivatives are contingent claims because their payoffs depend on the value of other securities. An option is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time. There are two basic financial option types. – Call options are options to buy the underlying asset. When exercising a call option, you “call in” the asset. – Put options are options to sell the underlying asset. When exercising a put, you “put” the asset to someone. 2.

strike." class="image_link uk-text-large uk-margin-small-left uk-margin-small-right"> 3 The Option Contract A call option gives its holder the right to buy an asset: – At the exercise or strike price – On or before the expiration date – Exercise the option to buy the underlying asset if market value > strike. A put option gives its holder the right to sell an asset: – At the exercise or strike price – On or before the expiration date – Exercise the option to sell the underlying asset if market value XS = X 6" class="image_link uk-text-large uk-margin-small-left uk-margin-small-right"> 6 Option “Moneyness” “In-the-money” option: An option that would yield a positive payoff if exercised “Out-of-the-money” option: An option that would NOT yield a positive payoff if exercised Use the relationship between S (the stock price) and X (the strike price): Note for a given strike price, only the call or only the put can be “in-the - money.” In-the-MoneyOut-of-the-MoneyAt-the-Money Call OptionS > XS XS = X 6.

7 Option Price Quotes A list of available option contracts and their prices for a particular security is known as an option chain. Option chains are available online through many sources, including the CBOE (quote. cboe) and Yahoo! Finance (finance. yahoo).quote. cboefinance. yahoo Stock option ticker symbols include: – Letters to identify the underlying stock. – A letter to identify the expiration month as well as whether the option is a call or a put. (A through L for calls; M through X for puts). – A letter to identify the strike price (a bit more complicated—see Yahoo for tables to explain this letter.) 7.

8 Listed Option Quotes at Yahoo! Finance 8.

9 The Options Clearing Corporation The Options Clearing Corporation (OCC) is a private agency that guarantees that the terms of an option contract will be fulfilled if the option is exercised. The OCC issues and clears all option contracts trading on U. S. exchanges. Note that the exchanges and the OCC are all subject to regulation by the Securities and Exchange Commission (SEC). Visit the OCC at: optionsclearing. optionsclearing 9.

10 Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options Different Types of Options 10.

12 Example: Call Option You buy the call option contract that will allow you to buy from an option seller 100 shares of IBM for $50 per share at any time during the next three months. The call option is traded at $1 for each share of underlying stock. Exercise (or strike) price = $50 Option Price = $1 Expiration: Three months Suppose the price of IBM share rises to $55. You can exercise your option to buy IBM share at an exercise price ($50). Thus, the exercise value is $5 ($55 - $50). 12.

13 Example: Call Option Suppose an IBM share will rise to $55, stay at $50 or fall to $40 per share in three months. Call price = $1 IBM spot price $50 per share IBM spot price = $55 Exercise value = $5 Profit = $4 Now3 months IBM spot price = $50 Exercise value = $0 Profit = -$1 IBM spot price = $40 Exercise value = $0 Profit = -$1 13.

14 How do we make profits (or lose money) from option trading? From the previous example, assuming that the option is in-the-money at expiration, you can buy IBM share at $50 from an option seller and sell them at current market price ($55). You just made net profit of $4 profit (=55-50-1). Thus, the call option buyer is betting on price appreciation of the underlying assets, while the put option buyer is betting on price depreciation of the underlying assets. From the previous example, suppose IBM shares never rises above $50. Then your option expires worthless, so you lose an entire option price ($1). 14.

15 Call Option Profits -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option profit ($) Buy a call Exercise price = $50 15.

16 Example: Put Option You buy the put option contract that will allow you to sell from an option seller 100 shares of IBM for $50 per share at any time during the next three months. The put option is traded at $3 for each share of underlying stock. Exercise (or strike) price = $50 Option Price = $3 Expiration: Three months Suppose the price of IBM share falls to $40. You can exercise your option to sell IBM share at an above-market exercise price ($50). Thus, the exercise value is $5 ($55 - $50). 16.

17 Example: Put Option Suppose an IBM share will rise to $55, stay at $50 or fall to $40 per share in three months. Put price = $3 Now3 months IBM spot price $50 per share IBM spot price = $55 Exercise value = $0 Profit = -$3 IBM spot price = $50 Exercise value = $0 Profit = -$3 IBM spot price = $40 Exercise value = $10 Profit = $7 17.

18 Put Option Profits -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option profit ($) Buy a put 18.

19 Option Payoffs versus Option Profits Option investment strategies involve initial and terminal cash flows. – Initial cash flow: option price (often called the option premium). – Terminal cash flow: the value of an option at expiration (often called the option payoff). The terminal cash flow can be realized by the option holder by exercising the option. Option Profits = Terminal cash flow − Initial cash flow 19.

20 Payoff and Profit Expiration 20.

21 Option Payoffs 21.

22 Option Writing The act of selling an option is referred to as option writing. The seller of an option contract is called the writer. If holder exercises the option, the option writer must make (call) or take (put) delivery of the underlying asset. – The writer of a call option contract is obligated to sell the underlying asset to the call option holder. – The writer of a put option contract is obligated to buy the underlying asset from the put option holder. The purchase price of the option is called the premium. Because option writing obligates the option writer, the option writer receives the price (premium income) of the option today from the option buyer. 22.

23 Example: Profit and Loss on a Call A January 2018 call on IBM with an exercise price of $130 was selling on December 2, 2009, for $2.18. The option expires on the third Friday of the month, or January 15, 2018. If IBM remains below $130, the call will expire worthless. Option payoff= 0, Profit = -$2.18 per share 23.

24 Profit and Loss on a Call Suppose IBM sells for $132 on the expiration date. Option value (payoff) = stock price-exercise price $132- $130= $2 Profit = Final value – Original investment $2.00 - $2.18 = -$0.18 Option will be exercised to offset loss of premium. Call will not be strictly profitable unless IBM’s price exceeds $132.18 (strike + premium) by expiration. 24.

25 Example: Profit and Loss on a Put Consider a January 2018 put on IBM with an exercise price of $130, selling on December 2, 2009, for $4.79. Option holder can sell a share of IBM for $130 at any time until January 15. If IBM goes above $130, the put is worthless. Option payoff= 0, Profit = -$4.79 per share 25.

26 Profit and Loss on a Put Suppose IBM’s price at expiration is $123. Value at expiration = exercise price – stock price: $130 - $123 = $7 Investor’s profit: $7.00 - $4.79 = $2.21 Holding period return = 46.1% over 44 days! 26.

X = 0if S T X = 0 if S T 27 Payoffs and Profits at Expiration - Calls Stock Price = S T Exercise Price = X Payoff to Call Holder = (S T - X) if S T >X = 0if S T X = 0 if S T X -(X - S T )if S T 28 Payoffs and Profits at Expiration - Puts Payoffs to Put Holder 0if S T > X (X - S T ) if S T X -(X - S T )if S T.

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