 Spotting and Valuing Options Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will Chapter 20 © The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Topics Covered  Calls, Puts and Shares  Financial Alchemy with Options  What Determines Option Value  Option Valuation

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Terminology Call Option Right to buy an asset at a specified exercise price on or before the exercise date.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Terminology Put Option Right to sell an asset at a specified exercise price on or before the exercise date. Call Option Right to buy an asset at a specified exercise price on or before the exercise date.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Obligations

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value  The value of an option at expiration is a function of the stock price and the exercise price.

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value  The value of an option at expiration is a function of the stock price and the exercise price. Example - Option values given a exercise price of $85

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Call option value (graphic) given a $85 exercise price. Share Price Call option value $20

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Put option value (graphic) given a $85 exercise price. Share Price Put option value $5

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Call option payoff (to seller) given a $85 exercise price. Share Price Call option $ payoff 85

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Put option payoff (to seller) given a $85 exercise price. Share Price Put option $ payoff 85

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Protective Put - Long stock and long put Share Price Position Value Long Stock

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Protective Put - Long stock and long put Share Price Position Value Long Put

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Protective Put - Long stock and long put Share Price Position Value Protective Put Long Put Long Stock

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Protective Put - Long stock and long put Share Price Position Value Protective Put

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Long call

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Long put

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Straddle

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Straddle - Long call and long put - Strategy for profiting from high volatility Share Price Position Value Straddle

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Upper Limit Stock Price

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Upper Limit Stock Price Lower Limit (Stock price - exercise price) or 0 whichever is higher

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill 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)

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Option Value Black-Scholes Option Pricing Model O C = P s [N(d 1 )] - S[N(d 2 )]e -rt

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C - Call Option Price P s - Stock Price N(d 1 ) - Cumulative normal density function of (d 1 ) S - 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

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill (d 1 )= ln + ( r + ) t PsSPsS v22v22 v t N(d 1 )= Black-Scholes Option Pricing Model

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill (d 1 )= ln + ( r + ) t PsSPsS v22v22 v t Cumulative Normal Density Function (d 2 ) = d 1 -v t

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Call Option Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Call Option (d 1 ) = ln + ( r + ) t PsSPsS v22v22 v t (d 1 ) = N(d 1 ) = =.3794 Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Call Option (d 2 ) = N(d 2 ) = =.3065 (d 2 ) = d 1 -v t Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Call Option O C = P s [N(d 1 )] - S[N(d 2 )]e -rt O C = 36[.3794] - 40[.3065]e - (.10)(.2466) O C = $ 1.70 Example What is the price of a call option given the following? P = 36r = 10%v =.40 S = 40t = 90 days / 365

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Put - Call Parity Put Price = Oc + S - P - Carrying Cost + Div. Carrying cost = r x S x t

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Example ABC is selling at $41 a share. A six month May 40 Call is selling for $4.00. If a May $.50 dividend is expected and r=10%, what is the put price? Put - Call Parity

© The McGraw-Hill Companies, Inc., 2000 Irwin/McGraw Hill Example ABC is selling at $41 a share. A six month May 40 Call is selling for $4.00. If a May $.50 dividend is expected and r=10%, what is the put price? Put - Call Parity Op = Oc + S - P - Carrying Cost + Div. Op = (.10x 40 x.50) +.50 Op = Op = $1.50