Principles of Corporate Finance Brealey and Myers Sixth Edition Spotting and Valuing Options Slides by Matthew Will Irwin/McGraw Hill Chapter 20 ©The McGraw-Hill Companies, Inc., 200 20- Topics Covered Calls, Puts and Shares Financial Alchemy with Options What Determines Option Value Option Valuation Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- Option Terminology Call Option Right to buy an asset at a specified exercise price on or before the exercise date Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- Option Terminology Call Option Right to buy an asset at a specified exercise price on or before the exercise date Put Option Right to sell an asset at a specified exercise price on or before the exercise date Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- Option Obligations Buyer Seller Call option Right to buy asset Obligation to sell asset Put option Right to sell asset Obligation to buy asset Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- Option Value The value of an option at expiration is a function of the stock price and the exercise price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 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 Stock Price $60 Call Value Put Value 25 Irwin/McGraw Hill 70 15 80 90 100 15 110 25 ©The McGraw-Hill Companies, Inc., 200 20- Option Value Call option value Call option value (graphic) given a $85 exercise price $20 85 105 Share Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- Option Value Put option value Put option value (graphic) given a $85 exercise price $5 80 85 Share Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 10 Option Value Call option $ payoff Call option payoff (to seller) given a $85 exercise price 85 Share Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 19 Option Value Position Value Straddle - Long call and long put - Strategy for profiting from high volatility Straddle Share Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 20 Option Value Stock Price Upper Limit Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 21 Option Value Stock Price Upper Limit Lower Limit (Stock price - exercise price) or whichever is higher Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 22 Option Value Components of the Option Price - Underlying stock price - Striking or Exercise price - Volatility of the stock returns (standard deviation of annual returns) - Time to option expiration - Time value of money (discount rate) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 23 Option Value Black-Scholes Option Pricing Model OC = Ps[N(d1)] - S[N(d2)]e-rt Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 24 Black-Scholes Option Pricing Model OC = Ps[N(d1)] - S[N(d2)]e-rt OC- Call Option Price Ps - Stock Price N(d1) - Cumulative normal density function of (d1) S - 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 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 25 Black-Scholes Option Pricing Model ln (d1)= Ps S v + (r + v2 )t t N(d1)= 32 34 36 38 40 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 26 Cumulative Normal Density Function ln (d1)= Irwin/McGraw Hill Ps S + (r + v t (d2) = d1 - v t v2 )t ©The McGraw-Hill Companies, Inc., 200 20- 27 Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = 40 S = 40 t = 90 days / 365 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 28 Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = 40 S = 40 t = 90 days / 365 ln (d1) = Ps S v (d1) = - 3070 Irwin/McGraw Hill + (r + v2 )t t N(d1) = - 6206 = 3794 ©The McGraw-Hill Companies, Inc., 200 20- 29 Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = 40 S = 40 t = 90 days / 365 (d2) = d1 - v t (d2) = - 5056 N(d2) = - 6935 = 3065 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 30 Call Option Example What is the price of a call option given the following? P = 36 r = 10% v = 40 S = 40 t = 90 days / 365 OC = Ps[N(d1)] - S[N(d2)]e-rt OC = 36[.3794] - 40[.3065]e - (.10)(.2466) OC = $ 1.70 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 31 Put - Call Parity Put Price = Oc + S - P - Carrying Cost + Div Carrying cost = r x S x t Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 32 Put - Call Parity 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? Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 33 Put - Call Parity 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? Op = Oc + S - P - Carrying Cost + Div Op = + 40 - 41 - (.10x 40 x 50) + 50 Op = - + Op = $1.50 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 ... Companies, Inc., 200 20- Option Value The value of an option at expiration is a function of the stock price and the exercise price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- Option... Companies, Inc., 200 20- 10 Option Value Call option $ payoff Call option payoff (to seller) given a $85 exercise price 85 Share Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- 11 Option... Companies, Inc., 200 20- Option Value Call option value Call option value (graphic) given a $85 exercise price $20 85 105 Share Price Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 20- Option