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McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-0Chapter Outline22.1 Options22.2 Call Options22.3 Put Options22.4 Selling Options22.5 Reading The Wall Street Journal22.6 Combinations of Options22.7 Valuing Options22.8 An OptionPricing Formula22.9 Stocks and Bonds as Options22.10 Capital-Structure Policy and Options22.11 Mergers and Options22.12 Investment in Real Projects and Options22.13 Summary and ConclusionsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-122.1 OptionsMany corporate securities are similar to the stock options that are traded on organized exchanges.Almost every issue of corporate stocks and bonds has option features.In addition,capital structure and capital budgeting decisions can be viewed in terms of options.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-222.1 Options Contracts:PreliminariesAn option gives the holder the right,but not the obligation,to buy or sell a given quantity of an asset on(or perhaps before)a given date,at prices agreed upon today.Calls versus PutsCall options gives the holder the right,but not the obligation,to buy a given quantity of some asset at some time in the future,at prices agreed upon today.When exercising a call option,you“call in”the asset.Put options gives the holder the right,but not the obligation,to sell a given quantity of an asset at some time in the future,at prices agreed upon today.When exercising a put,you“put”the asset to someone.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-322.1 Options Contracts:PreliminariesExercising the OptionThe act of buying or selling the underlying asset through the option contract.Strike Price or Exercise PriceRefers to the fixed price in the option contract at which the holder can buy or sell the underlying asset.ExpiryThe maturity date of the option is referred to as the expiration date,or the expiry.European versus American optionsEuropean options can be exercised only at expiry.American options can be exercised at any time up to expiry.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-4Options Contracts:PreliminariesIn-the-MoneyThe exercise price is less than the spot price of the underlying asset.At-the-MoneyThe exercise price is equal to the spot price of the underlying asset.Out-of-the-MoneyThe exercise price is more than the spot price of the underlying asset.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-5Options Contracts:PreliminariesIntrinsic ValueThe difference between the exercise price of the option and the spot price of the underlying asset.Speculative ValueThe difference between the option premium and the intrinsic value of the option.Option Premium=Intrinsic ValueSpeculative Value+McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-622.2 Call OptionsCall options gives the holder the right,but not the obligation,to buy a given quantity of some asset on or before some time in the future,at prices agreed upon today.When exercising a call option,you“call in”the asset.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-7Basic Call Option Pricing Relationships at ExpiryAt expiry,an American call option is worth the same as a European option with the same characteristics.If the call is in-the-money,it is worth ST-E.If the call is out-of-the-money,it is worthless.CaT=CeT=MaxST-E,0WhereST is the value of the stock at expiry(time T)E is the exercise price.CaT is the value of an American call at expiryCeT is the value of a European call at expiryMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-8Call Option Payoffs-201009080706001020304050-40200-604060Stock price($)Option payoffs($)Buy a callExercise price=$50McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-9Call Option Payoffs-201009080706001020304050-40200-604060Stock price($)Option payoffs($)Write a callExercise price=$50McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-10Call Option Profits-201009080706001020304050-40200-604060Stock price($)Option profits($)Write a callBuy a callExercise price=$50;option premium=$10McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-1122.3 Put OptionsPut options gives the holder the right,but not the obligation,to sell a given quantity of an asset on or before some time in the future,at prices agreed upon today.When exercising a put,you“put”the asset to someone.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-12Basic Put Option Pricing Relationships at ExpiryAt expiry,an American put option is worth the same as a European option with the same characteristics.If the put is in-the-money,it is worth E-ST.If the put is out-of-the-money,it is worthless.PaT=PeT=MaxE-ST,0McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-13Put Option Payoffs-201009080706001020304050-40200-604060Stock price($)Option payoffs($)Buy a putExercise price=$50McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-14Put Option Payoffs-201009080706001020304050-40200-604060Option payoffs($)write a putExercise price=$50Stock price($)McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-15Put Option Profits-201009080706001020304050-40200-604060Stock price($)Option profits($)Buy a putWrite a putExercise price=$50;option premium=$1010-10McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-1622.4 Selling OptionsThe seller(or writer)of an option has an obligation.The purchaser of an option has an option.-201009080706001020304050-40200-604060Stock price($)Option profits($)Buy a putWrite a put10-10-201009080706001020304050-40200-604060Stock price($)Option profits($)Write a callBuy a callMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-1722.5 Reading The Wall Street JournalMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-1822.5 Reading The Wall Street JournalThis option has a strike price of$135;a recent price for the stock is$138.25 July is the expiration monthMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-1922.5 Reading The Wall Street JournalThis makes a call option with this exercise price in-the-money by$3.25=$138$135.Puts with this exercise price are out-of-the-money.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-2022.5 Reading The Wall Street JournalOn this day,2,365 call options with this exercise price were traded.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-2122.5 Reading The Wall Street JournalThe CALL option with a strike price of$135 is trading for$4.75.Since the option is on 100 shares of stock,buying this option would cost$475 plus commissions.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-2222.5 Reading The Wall Street JournalOn this day,2,431 put options with this exercise price were traded.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-2322.5 Reading The Wall Street JournalThe PUT option with a strike price of$135 is trading for$.8125.Since the option is on 100 shares of stock,buying this option would cost$81.25 plus commissions.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-2422.6 Combinations of OptionsPuts and calls can serve as the building blocks for more complex option contracts.If you understand this,you can become a financial engineer,tailoring the risk-return profile to meet your clients needs.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-25Protective Put Strategy:Buy a Put and Buy the Underlying Stock:Payoffs at ExpiryBuy a put with an exercise price of$50Buy the stockProtective Put strategy has downside protection and upside potential$50$0$50Value at expiryValue of stock at expiryMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-26Protective Put Strategy ProfitsBuy a put with exercise price of$50 for$10Buy the stock at$40$40Protective Put strategy has downside protection and upside potential$40$0-$40$50Value at expiryValue of stock at expiryMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-27Covered Call StrategySell a call with exercise price of$50 for$10Buy the stock at$40$40Covered call$40$0-$40$10-$30$30$50Value of stock at expiryValue at expiryMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-28Long Straddle:Buy a Call and a PutBuy a put with an exercise price of$50 for$10$40A Long Straddle only makes money if the stock price moves$20 away from$50.$40$0-$20$50Buy a call with an exercise price of$50 for$10-$10$30$60$30$70Value of stock at expiryValue at expiryMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-29Short Straddle:Sell a Call and a PutSell a put with exercise price of$50 for$10$40A Short Straddle only loses money if the stock price moves$20 away from$50.-$40$0-$30$50Sell a call with an exercise price of$50 for$10$10$20$60$30$70Value of stock at expiryValue at expiryMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-30Long Call SpreadSell a call with exercise price of$55 for$5$55long call spread$5$0$50Buy a call with an exercise price of$50 for$10-$10-$5$60Value of stock at expiryValue at expiryMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-31Put-Call ParitySell a put with an exercise price of$40Buy the stock at$40 financed with some debt:FV=$XBuy a call option with an exercise price of$40$0-$40$40-P0$40Buy the stock at$40-$40-P0In market equilibrium,it mast be the case that option prices are set such that:Otherwise,riskless portfolios with positive payoffs exist.Value of stock at expiryValue at expiryMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-3222.7 Valuing OptionsThe last section concerned itself with the value of an option at expiry.This section considers the value of an option prior to the expiration date.A much more interesting question.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-33Option Value DeterminantsCall Put1.Stock price+2.Exercise price +3.Interest rate+4.Volatility in the stock price+5.Expiration date+The value of a call option C0 must fall within max(S0 E,0)C0 MaxST-E,0ProfitlossESTMarket ValueIntrinsic valueST-ETime valueOut-of-the-moneyIn-the-moneySTThe value of a call option C0 must fall within max(S0 E,0)C0 S0.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-3522.8 An OptionPricing FormulaWe will start with a binomial option pricing formula to build our intuition.Then we will graduate to the normal approximation to the binomial for some real-world option valuation.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-36Binomial Option Pricing ModelSuppose a stock is worth$25 today and in one period will either be worth 15%more or 15%less.S0=$25 today and in one year S1is either$28.75 or$21.25.The risk-free rate is 5%.What is the value of an at-the-money call option?$25$21.25$28.75S1S0McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-37Binomial Option Pricing Model1.A call option on this stock with exercise price of$25 will have the following payoffs.2.We can replicate the payoffs of the call option.With a levered position in the stock.$25$21.25$28.75S1S0C1$3.75$0McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-38Binomial Option Pricing ModelBorrow the present value of$21.25 today and buy 1 share.The net payoff for this levered equity portfolio in one period is either$7.50 or$0.The levered equity portfolio has twice the options payoff so the portfolio is worth twice the call option value.$25$21.25$28.75S1S0debt-$21.25portfolio$7.50$0(-)=C1$3.75$0-$21.25McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-39Binomial Option Pricing Model The levered equity portfolio value today is todays value of one share less the present value of a$21.25 debt:$25$21.25$28.75S1S0debt-$21.25portfolio$7.50$0(-)=C1$3.75$0-$21.25McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-40Binomial Option Pricing ModelWe can value the option today as half of the value of the levered equity portfolio:$25$21.25$28.75S1S0debt-$21.25portfolio$7.50$0(-)=C1$3.75$0-$21.25McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-41If the interest rate is 5%,the call is worth:The Binomial Option Pricing Model$25$21.25$28.75S1S0debt-$21.25portfolio$7.50$0(-)=C1$3.75$0-$21.25McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-42If the interest rate is 5%,the call is worth:The Binomial Option Pricing Model$25$21.25$28.75S1S0debt-$21.25portfolio$7.50$0(-)=C1$3.75$0-$21.25$2.38C0McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-43Binomial Option Pricing Modelthe replicating portfolio intuition.Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.The most important lesson(so far)from the binomial option pricing model is:McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-44The Risk-Neutral Approach to ValuationWe could value V(0)as the value of the replicating portfolio.An equivalent method is risk-neutral valuationS(0),V(0)S(U),V(U)S(D),V(D)q1-qMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-45The Risk-Neutral Approach to ValuationS(0)is the value of the underlying asset today.S(0),V(0)S(U),V(U)S(D),V(D)S(U)and S(D)are the values of the asset in the next period following an up move and a down move,respectively.q1-qV(U)and V(D)are the values of the asset in the next period following an up move and a down move,respectively.q is the risk-neutral probability of an“up”move.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-46The Risk-Neutral Approach to ValuationThe key to finding q is to note that it is already impounded into an observable security price:the value of S(0):S(0),V(0)S(U),V(U)S(D),V(D)q1-qA minor bit of algebra yields:McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-47Example of the Risk-Neutral Valuation of a Call:$21.25,C(D)q1-qSuppose a stock is worth$25 today and in one period will either be worth 15%more or 15%less.The risk-free rate is 5%.What is the value of an at-the-money call option?The binomial tree would look like this:$25,C(0)$28.75,C(D)McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-48Example of the Risk-Neutral Valuation of a Call:$21.25,C(D)2/31/3 The next step would be to compute the risk neutral probabilities$25,C(0)$28.75,C(D)McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-49Example of the Risk-Neutral Valuation of a Call:$21.25,$02/31/3After that,find the value of the call in the up state and down state.$25,C(0)$28.75,$3.75McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-50Example of the Risk-Neutral Valuation of a Call:Finally,find the value of the call at time 0:$21.25,$02/31/3$25,C(0)$28.75,$3.75$25,$2.38McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-51This risk-neutral result is consistent with valuing the call using a replicating portfolio.Risk-Neutral Valuation and the Replicating PortfolioMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-52The Black-Scholes ModelThe Black-Scholes Model isWhereC0=the value of a European option at time t=0r=the risk-free interest rate.N(d)=Probability that a standardized,normally distributed,random variable will be less than or equal to d.The Black-Scholes Model allows us to value options in the real world just as we have done in the 2-state world.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-53The Black-Scholes ModelFind the value of a six-month call option on the Microsoft with an exercise price of$150The current value of a share of Microsoft is$160The interest rate available in the U.S.is r=5%.The option maturity is 6 months(half of a year).The volatility of the underlying asset is 30%per annum.Before we start,note that the intrinsic value of the option is$10our answer must be at least that amount.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-54The Black-Scholes ModelLets try our hand at using the model.If you have a calculator handy,follow along.Then,First calculate d1 and d2McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-55The Black-Scholes ModelN(d1)=N(0.52815)=0.7013N(d2)=N(0.31602)=0.62401McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-5722.9 Stocks and Bonds as OptionsLevered Equity is a Call Option.The underlying asset comprise the assets of the firm.The strike price is the payoff of the bond.If at the maturity of their debt,the assets of the firm are greater in value than the debt,the shareholders have an in-the-money call,they will pay the bondholders and“call in”the assets of the firm.If at the maturity of the debt the shareholders have an out-of-the-money call,they will not pay the bondholders(i.e.the shareholders will declare bankruptcy)and let the call expire.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-5822.9 Stocks and Bonds as OptionsLevered Equity is a Put Option.The underlying asset comprise the assets of the firm.The strike price is the payoff of the bond.If at the maturity of their debt,the assets of the firm are less in value than the debt,shareholders have an in-the-money put.They will put the firm to the bondholders.If at the maturity of the debt the shareholders have an out-of-the-money put,they will not exercise the option(i.e.NOT declare bankruptcy)and let the put expire.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-5922.9 Stocks and Bonds as OptionsIt all comes down to put-call parity.Value of a call on the firmValue of a put on the firmValue of a risk-free bondValue of the firm=+Stockholders position in terms of call optionsStockholders position in terms of put optionsMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-6022.10 Capital-Structure Policy and OptionsRecall some of the agency costs of debt:they can all be seen in terms of options.For example,recall the incentive shareholders in a levered firm have to take large risks.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-61Balance Sheet for a Company in DistressAssetsBVMVLiabilitiesBVMVCash$200$200LT bonds$300?Fixed Asset$400$0Equity$300?Total$600$200Total$600$200What happens if the firm is liquidated today?The bondholders get$200;the shareholders get nothing.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies,Inc.All rights reserved.22-62Selfish Strategy 1:Take Large Risks(Think of a Call Option)The GambleProbabilityPayoffWin Big10%$1,000Lose Big90%$0Cost of investment is$200(all the firms cash)Requi
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