1. David KilgourLecture 91 Foundations of Finance Lecture 6 Option Pricing Read: Brealey and Myers Chapter 20 Practice Questions 2, 3 and 14 on page612 Workshop Question 8 on handouts

2. David KilgourLecture 92 Topics Covered Hedging Forwards and Futures Calls, Puts Financial Alchemy with Options What Determines Option Value Option Valuation –Binomial model –Black-Scholes formula

3. David KilgourLecture 93 Hedging Business has risk –They insure or hedge to reduce risks! Not to make money! HOW? Kellogg produces cereal. A major component and cost factor is sugar. To fix your sugar costs, you would ideally like to purchase all your sugar today, since you like today’s price, and made your forecasts based on it. But, you can not! You can, however, sign a contract to purchase sugar at various points in the future for a price negotiated today. This contract is called a “Futures Contract.” This technique of managing your sugar costs is called “Hedging.”

4. David KilgourLecture 94 Forward and Futures Contracts 1- Spot Contract –A contract for immediate sale & delivery of an asset. 2- Forward Contract –A contract between two people for the delivery of an asset at a negotiated price on a set date in the future. 3- Futures Contract –A contract similar to a forward contract, except there is an intermediary that creates a standardized contract. –Thus, the two parties do not have to negotiate the terms of the contract. The intermediary guarantees all trades & “provides” a secondary market for the speculation of Futures. –Not an actual sale! –Always a winner & a loser!

5. David KilgourLecture 95 What is an Option? Example: Desert land that contains gold deposit! –What if the cost of extraction > current price of gold? –Is it worthless? No if there is uncertainty about gold prices! The option to expand? The option to abandon? The option to default? Traded options? –Common stocks –Stock indices –Bonds –Commodities –FX

6. David KilgourLecture 96 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. European Call: Exercises only on one particular day. American Call: Exercised on OR before that day

7. David KilgourLecture 97 Option Value The value of an option at expiration is a function of the stock price and the exercise price. Example - Intel Option values given a exercise price of $85

8. David KilgourLecture 98 Call Option Value Call option value (to buyer) given a $85 exercise price. Share Price Call option value 85 105 $20

9. David KilgourLecture 99 Put Option Value Put option value (to buyer) given a $85 exercise price. Share Price Put option value 80 85 $5

10. David KilgourLecture 910 Call Option Value Call option payoff (to seller) given a $85 exercise price. Share Price Call option $ payoff 85

11. David KilgourLecture 911 Put Option Value Put option payoff (to seller) given a $85 exercise price. Share Price Put option $ payoff 85

12. David KilgourLecture 912 Financial Alchemy with Options - 1 Protective Put - Long stock and long put Buying a share of stock + Buying a put option on the stock Share Price Position Value Protective Put Long Put Long Stock By adding a put option on your investment in a stock you protect yourself against loss!

13. David KilgourLecture 913 Straddle - Long call and long put -Buying a call option + Buying a put option -Strategy for profiting from high volatility Share Price Position Value Straddle Financial Alchemy with Options - 2

14. David KilgourLecture 914 Option Value-Call Option Upper Limit Stock Price Lower Limit (Stock price - exercise price) or 0 whichever is higher Example: Option to buy Intel at £85! On exercise day if stock price<£85  you will not exercise the call! the option will be worthless! its value will be zero! if stock price>£85  Say £90! You will exercise the call! The value of the option will be £5! £90 - £85 = £5! When the stock is worthless the option is worthless! When the stock price becomes large the option price approaches the stock price less the PV of exercise price! The option price always exceeds the minimum value! If the option and the stock had the same price every one would rush to buy the option! So, the upper limit of the option price is the stock price!

15. David KilgourLecture 915 Option Value Components of the Option Price CallPut 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 discounted cash flows method is not helpful for options!

16. David KilgourLecture 916 Put - Call Parity Value of Put + Share Price = Value of Call + PV of Exercise Price Buy shareBuy Put Downside protection Bank depositBuy call £85

17. David KilgourLecture 917 Example: ABC is selling at £41 a share. A six month May 40 Call is selling for £4.00. If a May £0.50 dividend is expected and r=10%, what is the put price? Put - Call Parity Op = Oc + S - P - Carrying Cost + Div. Op = 4 + 40 - 41 - (.10x 40 x.50) +.50 Op = 3 - 2 +.5 Op = £1.50 Value of Put = Value of Call + PV of Strike Price - Share Price Put Price = Call Price + Strike Price - Share Price - Carrying Costs + Dividends Carrying Costs = Discount rate x Strike Price x time to maturity as fraction of year Assuming Dividends, we have: where