1. Lecture 2

3.  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 ends by… 1. Expiration 2. Exercise 3. 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. Asset Price Profit Loss Option Review

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

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

10.  Swaptions  Index options  Futures options  Currency options  Convertible bond  Warrant

11.  Knock out options ◦ Down and out ◦ Up and out  Knock in options ◦ Down and in ◦ Up and in

12.  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. O C - Call Option Price P - Stock Price N(d 1 ) - Cumulative normal density function of (d 1 ) PV(EX) - Present Value of Strike or Exercise price N(d 2 ) - Cumulative normal density function of (d 2 ) 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 Black-Scholes Option Pricing Model

17. N(d 1 )= Black-Scholes Option Pricing Model

18. Cumulative Normal Density Function

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

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

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

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

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

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

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

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

28. (d 1 ) = ln + (.1 + ) 30/365 41 40.42 2 2.42 30/365 (d 1 ) =.3335N(d 1 ) =.6306 Example What is the price of a call option given the following? P = 41r = 10%v =.42 EX = 40t = 30 days / 365

29. (d 1 ) = ln + (.1 + ) 30/365 41 40.42 2 2.42 30/365 (d 1 ) =.3335N(d 1 ) =.6306 Example What is the price of a call option given the following? P = 41r = 10%v =.42 EX = 40t = 30 days / 365

30. (d 2 ) =.2131 N(d 2 ) =.5844 (d 2 ) = d 1 -v t =.3335 -.42 (.0907) Example What is the price of a call option given the following? P = 41r = 10%v =.42 EX = 40t = 30 days / 365

31. O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C = 41[.6306] - 40[.5844]e - (.10)(.0822) O C = $ 2.67 Example What is the price of a call option given the following? P = 41r = 10%v =.42 EX = 40t = 30 days / 365

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

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

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

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

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

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

38. Black-Scholes O p = EX[N(-d 2 )]e -rt - P s [N(-d 1 )] Put-Call Parity (general concept) Put Price = Oc + EX - P - Carrying Cost + D Carrying cost = r x EX x t Call + EXe -rt = Put + P s Put = Call + EXe -rt - P s

39. N(-d 1 ) =.3694 N(-d 2 )=.4156 Black-Scholes O p = EX[N(-d 2 )]e -rt - P s [N(-d 1 )] O p = 40[.4156]e -.10(.0822) - 41[.3694] O p = 1.34 Example What is the price of a call option given the following? P = 41r = 10%v =.42 EX = 40t = 30 days / 365

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

41. Put-Call Parity & American Puts P s - EX < Call - Put < P s - EXe -rt Call + EX - P s > Put > EXe -rt - P s + 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. Example Price = 36Ex-Div in 60 days @ $0.72 t = 90/365r = 10% P D = 36 -.72 e -.10(.1644) = 35.2917 Put-Call Parity Amer D+ C + S - P s > Put > Se -rt - P s + C + D Euro Put = Se -rt - P s + C + D + CC