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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.

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Derivatives

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  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

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