1 / 30

Derivatives

Derivatives. Lecture 16. Option Value. Components of the Option Price 1 - Underlying stock price 2 - Striking or Exercise price 3 - Volatility of the stock returns (standard deviation of annual returns) 4 - Time to option expiration 5 - Time value of money (discount rate). Option Value.

yitro
Télécharger la présentation

Derivatives

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Derivatives Lecture 16

  2. Option Value Components of the Option Price 1 - Underlying stock price 2 - Striking or Exercise price 3 - Volatility of the stock returns (standard deviation of annual returns) 4 - Time to option expiration 5 - Time value of money (discount rate)

  3. Option Value Black-Scholes Option Pricing Model

  4. Black-Scholes Option Pricing Model OC- Call Option Price P - Stock Price N(d1) - Cumulative normal density function of (d1) PV(EX) - Present Value of Strike or Exercise price N(d2) - Cumulative normal density function of (d2) r - discount rate (90 day comm paper rate or risk free rate) t - time to maturity of option (as % of year) v - volatility - annualized standard deviation of daily returns

  5. Black-Scholes Option Pricing Model

  6. Black-Scholes Option Pricing Model N(d1)=

  7. Cumulative Normal Density Function

  8. Cumulative Normal Density Function

  9. Call Option Example - Genentech What is the price of a call option given the following? P = 80 r = 5% v = .4068 EX = 80 t = 180 days / 365

  10. Call Option Example - Genentech What is the price of a call option given the following? P = 80 r = 5% v = .4068 EX = 80 t = 180 days / 365

  11. Call Option Example - Genentech What is the price of a call option given the following? P = 80 r = 5% v = .4068 EX = 80 t = 180 days / 365

  12. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

  13. .3070 = .3 = .00 = .007

  14. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

  15. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

  16. Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = .40 EX = 40 t = 90 days / 365

  17. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 41 40 .422 2 ln + ( .1 + ) 30/365 (d1) = .42 30/365 (d1) = .3335 N(d1) =.6306

  18. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 41 40 .422 2 ln + ( .1 + ) 30/365 (d1) = .42 30/365 (d1) = .3335 N(d1) =.6306

  19. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 (d2) = d1 - v t = .3335 - .42 (.0907) (d2) = .2131 N(d2) = .5844

  20. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 OC = Ps[N(d1)] - S[N(d2)]e-rt OC = 41[.6306] - 40[.5844]e - (.10)(.0822) OC = $ 2.67

  21. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365

  22. Call Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 • Intrinsic Value = 41-40 = 1 • Time Premium = 2.67 + 40 - 41 = 1.67 • Profit to Date = 2.67 - 1.70 = .94 • Due to price shifting faster than decay in time premium

  23. Call Option • Q: How do we lock in a profit? • A: Sell the Call

  24. Call Option • Q: How do we lock in a profit? • A: Sell the Call

  25. Call Option • Q: How do we lock in a profit? • A: Sell the Call

  26. Call Option • Q: How do we lock in a profit? • A: Sell the Call

  27. Put Option Black-Scholes Op = EX[N(-d2)]e-rt - Ps[N(-d1)] Put-Call Parity (general concept) Put Price = Oc + EX - P - Carrying Cost + D Carrying cost = r x EX x t Call + EXe-rt = Put + Ps Put = Call + EXe-rt - Ps

  28. Put Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 N(-d1) = .3694 N(-d2)= .4156 Black-Scholes Op = EX[N(-d2)]e-rt - Ps[N(-d1)] Op = 40[.4156]e-.10(.0822) - 41[.3694] Op = 1.34

  29. Put Option Example What is the price of a call option given the following? P = 41 r = 10% v = .42 EX = 40 t = 30 days / 365 Put-Call Parity Put = Call + EXe-rt - Ps Put = 2.67 + 40e-.10(.0822) - 41 Put = 42.34 - 41 = 1.34

  30. Put Option Put-Call Parity & American Puts Ps - EX < Call - Put < Ps - EXe-rt Call + EX - Ps > Put > EXe-rt - Ps + call Example - American Call 2.67 + 40 - 41 > Put > 2.67 + 40e-.10(.0822) - 41 1.67 > Put > 1.34 With Dividends, simply add the PV of dividends

More Related