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Financial Engineering

Financial Engineering. Lecture 2. Option Review. Options Review. Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time. Call Option - The right to buy a security at a specified price within a specified time.

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Financial Engineering

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  1. Financial Engineering Lecture 2

  2. Option Review

  3. Options Review • Option - Gives the holder the right to buy or sell a security at a specified price during a specified period of time. • Call Option - The right to buy a security at a specified price within a specified time. • Put Option - The right to sell a security at a specified price within a specified time. • Option Premium - The price paid for the option, above the price of the underlying security. • Intrinsic Value - Diff between the strike price and the stock price • Time Premium - Value of option above the intrinsic value • Exercise Price - (Striking Price) The price at which you buy or sell the security. • Expiration Date - The last date on which the option can be exercised.

  4. Option Review Option ends by… • Expiration • Exercise • Sales • American option • European option • Intrinsic Value = P – E • Time Premium = O + E – P • Moneyness • In the money • Out of the money • At the money

  5. Option Review Profit Loss Asset Price

  6. Option Concepts • Market Makers • Round Trip • Lot size is 100 shares • Naked positions • Covered positions CBOE Quotes (web) • Open interest • Volume • Bid-ask • Prices

  7. Option Value Price 0 30 60 90 (expiration) Time (days)

  8. Time Decay Example – Given an exercise price of $55, what are the likely call option premiums, given stock prices of 50, 56, and 60 dollars?

  9. Time Decay • Intrinsic Value & Time Premium graphed Days to Expiration 90 60 30 Option Price Stock Price

  10. Exotic Options • Swaptions • Index options • Futures options • Currency options • Convertible bond • Warrant

  11. Barrier Options • Knock out options • Down and out • Up and out • Knock in options • Down and in • Up and in

  12. Current Events • Executive Stock Options • “To Expense or Not to Expense”

  13. 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) 6 - PV of Dividends = D = (div)e-rt

  14. Option Value Black-Scholes Option Pricing Model

  15. 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

  16. Black-Scholes Option Pricing Model

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

  18. Cumulative Normal Density Function

  19. Cumulative Normal Density Function

  20. 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

  21. 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

  22. 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

  23. 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

  24. .3070 = .3 = .00 = .007

  25. 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

  26. 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

  27. 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

  28. 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

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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 = .97 • Due to price shifting faster than decay in time premium

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

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

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

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

  38. 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

  39. 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

  40. 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

  41. 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

  42. Dividends Example Price = 36 Ex-Div in 60 days @ $0.72 t = 90/365 r = 10% PD = 36 - .72e-.10(.1644) = 35.2917 Put-Call Parity Amer D+ C + S - Ps > Put > Se-rt - Ps + C + D Euro Put = Se-rt - Ps + C + D + CC

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