COMM122-2013-Lecture 12-Option Payoffs - 005

1、COMM122 - Lecture 121Corporate Finance II - Lecture 12Option Payoffs and Trading StrategiesCOMM122 - Lecture 122Option Example Consider a call option written on Royal Bank stock with an exercise price of $50, expiring on the third Friday of this May. The number of shares underlying one option is 100

2、. This option can not be exercised before expiry date. The current price of Royal Bank stock is $40.COMM122 - Lecture 123Option Trading Consider an European option and the following trades Long call Short call Long put Short put If we are long an option We have the right to exercise. We will exercis

3、e only if this results in a positive payoff. If we are short an option The holder of the option has the right to exercise against us. She will do so only if this results in a positive payoff to her.COMM122 - Lecture 124Option Payoff at Expiration Call Payoff at ExpirationCT = Max ST - K, 0WhereST is

4、 the value of the stock at expiry (time T)K is the exercise price.CT is the value of a call at expiry Put Payoff at ExpirationPT = Max K - ST , 0 Following previous example, COMM122 - Lecture 125Payoff Diagram: Long a Call201202040608010040204060Stock price ($)Option payoffs ($)Buy a callExercise pr

5、ice = $50500COMM122 - Lecture 126Payoff Diagram: Short a Call201202040608010040204060Stock price ($)Option payoffs ($)Sell a callExercise price = $5050COMM122 - Lecture 127Payoff Diagram: Call (With Premium)Exercise price = $50; Option premium = $10Sell a callBuy a call201202040608010040204060Stock

6、price ($)Option payoffs ($)5010 10COMM122 - Lecture 128Payoff Diagram: Put (With Premium)202040608010040204060Stock price ($)Option payoffs ($)Buy a putExercise price = $50; Option premium = $1010 10Sell a put50COMM122 - Lecture 129Option Hedging Strategies: Protective PutPayoff from a Protective Pu

7、t (Example)Protective Put: Buying a put option on a stock and the stock itselfSuppose Royal Bank stock price is currently at $40. The price for a put written on Royal Bank Stock with a strike price of $50 is $10. Suppose a protective put is constructed by buying one unit of stock and one put. Let ST

8、 denote the stock price at option maturity. Whats profit like for the protective put? Rang of Stock PriceProfit from StockProfit from PutTotal ProfitST = 30ST = 40ST = 50ST = 60ST = 70COMM122 - Lecture 1210Put-Call Parity Consider the following trading strategies:1. Buying a protective put (buying o

9、ne stock and a put)2. Buying a call (same exercise price and maturity as the put) and buying a zero coupon bond (principle same as the exercise price)COMM122 - Lecture 1211Protective Put Strategy ProfitsBuy a put with exercise price of $50 for $10Buy the stock at $40$40Protective Put strategy has do

10、wnside protection and upside potential$40$0-$40$50Value of stock at expiry-$10$60$70$10$20Option payoffs ($)COMM122 - Lecture 1212Value at Expiration for Strategy 1Buy a put with an exercise price of $50Buy the stockProtective Put payoff$50$0$50Value at expiryValue of stock at expiryCOMM122 - Lectur

11、e 1213Value at Expiration for Strategy 2Buy a call with an exercise price of $50Buy zero coupon bondTotal payoff of strategy 2$50$0$50Value at expiryValue of stock at expiryCOMM122 - Lecture 1214Put-Call ParityTwo strategies yield the same payoff!By no-arbitrage principle, the price of the two strat

12、egies must be the same, i.e.,This is known as the put-call parity!From the put-call parity we can show that writing a covered call (buying stock and short call) is the same as short a put and long a zero coupon bond.An important condition is the borrowing rate and the lending rate are the same.price

13、 exercise of PVcall of Priceput of Pricestock underlying of PriceCOMM122 - Lecture 1215Bounding the Value of an American CallConsider an American option with the exercise price $50. The current stock price is $60.What price must the call be sold for, at a minimum? What if the option price is now $5?

14、Can the option price be higher than the underlying stock price?Therefore, the lower bound value of an American call is the difference between the stock price and the exercise price, bounded by zero. This is also known as the intrinsic value of a call, max (S0 E, 0). The upper bound is the underlying

15、 stock price.COMM122 - Lecture 1216Market Value, Time Value and Intrinsic Value for an American CallThe value of a call option C0 must fall within max (S0 E, 0) C0 S0.Call STlossE$STTime valueIntrinsic valueMarket ValueIn-the-moneyOut-of-the-moneyCOMM122 - Lecture 1217Early Exercise of American Call

16、It never pays to exercise an American call option before the expiration date on a stock that does not pay dividend or whose price is adjusted for dividend payments.The reason is simple: a call option is worth more alive than dead!If an investor no longer wishes to hold the option, she/he could sell

17、the option rather than exercising it.COMM122 - Lecture 1218Some Big Losers in Derivatives MarketsCorporationDateInstrument/Strategy Loss ($b)Kashima Oil, JapanApr, 1994Currency Forwards1.45Orange County, CADec, 1994Reverse Repos1.81Barings Bank, U.K.Feb, 1995Stock Index Futures1.33Daiwa Bank, JapanSep, 1995US Treasury1.10LTCM, U.S.Aug, 1998Swaps etc.4.60.Most recently,Amar