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1Chapter 22 Options and Corporate Finance:Basic Concepts2Executive SummaryOptions are special contractual arrangements giving the owner the right to buy or sell an asset at a fixed price anytime on or before a given date.Stock options,the most familiar type,are options to buy and sell shares of common stock.Ever since 1973,stock options have been traded on organized exchanges.3Executive SummaryCorporate securities are very similar to the stock options that are traded on organized exchanges.Almost every issue of corporate bonds and stocks has option features.In addition,capital-structure decisions and capital-budgeting decisions can be viewed in terms of options.4Executive SummaryWe start this chapter with a description of different types of publicly traded options.We identify and discuss the factors that determine their values.We show how common stocks and bonds can be thought of as options on the underlying value of the firm.This leads to several new insights concerning corporate finance.5OptionsAn option is a contract giving its owner the right to buy or sell an asset at a fixed price on or before a given date.Options are a unique type of financial contract because they give the buyer the right,but not the obligation,to do something.The buyer uses the options only if it is advantageous to do so;otherwise the option can be thrown away.6OptionsSpecial vocabulary and important definitions:lExercising the OptionlStriking or Exercise PricelExpiration DatelAmerican and European Options7Call OptionsThe most common type of option is a call.A call option gives the owner the right to buy an asset at a fixed price during a particular time period.The most common calls traded on exchanges are options on stocks and bonds.Example-call on IBM stock8Call OptionsThe value of a call option at expiration depends on the value of the underlying stock at expiration.The call is in the money,out of the money,at the money.The payoff on the expiration date of a call option.9Call OptionsFigure 22.1 plots the value of the call at expiration against eh value of IBMs stock.It is referred to as the hockey-stick diagram of call-option values.Notice that the call can never have a negative value.It is a limited-liability instrument,which means that all the holder can lose is the initial amount of option fees.10Put OptionsA put option can be viewed as the opposite of a call.It gives the holder the right to sell the stock for a fixed exercise price.The payoff of the put option.11Selling OptionsAn investor who sells(or writes)a call on common stock promises to deliver shares of the common stock if required to do so by the call option holder.Notice the seller is obligated to do so.Why would the seller of a call place himself in such a precarious position?The answer is the seller is paid to take this risk.12Selling OptionsFigure 22.3:The payoffs to sellers of Calls and Puts,and to Buyers of Common Stock.Notice that buying the stock is the same as buying a call option on the stock with an exercise price of zero.Because the exercise price is zero,the call holder can buy the stock for nothing,which is really the same as owning it.13Reading the Wall Street JournalHow these options are quoted in media,such as Wall Street Journal?See the example of table 22.1.14Combinations of OptionsPuts and calls can serve as building blocks for more complex option contracts.The strategy of buying a put and buying the underlying stock is called a protective put.It is as if one is buying insurance for the stock.Figure 22.4 illustrates the payoff from buying a put option on a stock and simultaneously buying the stock.15Combinations of OptionsNote that the combination of buying a put and buying the underlying stock has the same shape in Figure 22.4 as the call purchase in Figure 22.1.16Combinations of OptionsNow,lets try the strategy of:l(leg A)Buying a calll(leg B)Buying a zero-coupon bond with a face value of$50 that matures on the same day that the option expires.lWhat does the graph of simultaneously buying both Leg A and Leg B of this strategy look like?It looks like the far right graph of Figure 22.5.17Combinations of OptionsThe far-right graph of Figure 22.5 looks exactly like the far-right graph of Figure 22.4.Thus,an investor gets the same payoff from the strategy of Figure 22.4,and the strategy of Figure 22.5,regardless of what happens to the price of the underlying stock.In other words,the investor gets the same payoff from the following two strategies:18Combinations of Options1.Buying a put and buying the underlying stock.2.Buying a call and buying a zero-coupon bond.If the above two strategies have the same payoffs,they must have the same cost.This leads to the interesting result that:19Combinations of OptionsPrice of underlying stock+Price of put=Price of call+Present value of exercise price,or,equivalently,20Combinations of OptionsThis relationship is known as put-call parity and is one of the most fundamental relationships concerning options.It is a very precise relationship.From the parity,you can replicate the purchase of a share of stock by buying a call,selling a put,and buying a zero-coupon bond.This is a synthetic stock.21Combinations of OptionsCovered-call StrategylBuy a stock and write the call on the stock simultaneously.This conservative strategy known as selling a covered call.22Valuing OptionsBounding the Value of a CalllLower Bound:An option can not sell below stock price exercise price.lStrategy:buy a call,exercise the call and sell stock at current market price.lUpper Bound:The upper boundary is the price of the underlying stock.lStrategy:buying the stock and selling the call.23Valuing OptionsThe factors Determining Call-Option ValueslExercise pricelExpiration DatelStock pricelKey factor:The variability of the underlying AssetlInterest Rate24Valuing OptionsFactors Determining Put-Option Values:lStock pricelExercise pricelInterest ratelExpiration datelVolatility of the underlying asset25Valuing OptionsSummary of Options values:Table 22.226An option-pricing FormulaThe value of an option is a function of five variables:lThe current price of the underlying assetlExercise pricelTime to expirationlVariance of the underlying stocklRisk-free interest rate27An option-pricing FormulaNPV approach can not be used to determine the price of an option because of the unknown risk level.Black and Scholes attacked the problem by pointing out that a strategy of borrowing to finance a stock purchase duplicates the risk of a call.Knowing the price of a stock already,one can determine the price of a call.28An option-pricing FormulaIf we let the future stock price be one of only two values,we are able to duplicate the call exactly.This model is called a two-state option model.29An option-pricing FormulaA Two-State Option ModelSuppose the current stock price is$50,and the stock will either be$60 or$40 at the end of the year.Imagine a call option on the stock with a one-year expiration date and a$50 exercise price.Investor can borrow at 10%.How to determine the price of the call?30An option-pricing FormulaConsider two strategies:l1.buy the calll2.buy one-half a share of stock;borrow$18.18.As you can see,the cash flows from the second strategy match the cash flows from the first strategy.We are duplicating the call with the second strategy.31An option-pricing FormulaSee the payoffs on page 626.The future payoff structure of the buy a call strategy is duplicated by the strategy of buy stock and borrow.That is,under either strategy,an investor would end up with$10 if the stock price rose and$0 if the stock price fell.These two strategies are equivalent.32An option-pricing FormulaIf two strategies always have the same cash flows at the end of the year,how must their initial costs be related?Same initial costs.Otherwise arbitrage happens.The costs of our strategy of buying stock and borrowing are:$6.82,so the price of the call is also$6.82.33An option-pricing FormulaDetermining the DeltaThe potential swing of the call price/the potential swing of the stock priceThe ratio is called the delta of the call.It means that the risk of buying one-half share of stock should be the same as the risk of buying one call.34An option-pricing FormulaDetermining the amount of borrowingHow did we know how much to borrow?Buying one-half share of stock brings us either$30 or$20 at expiration,which is exactly$20 more than the payoffs of$10 and$0,respectively,from the call.35An option-pricing FormulaRisk-Neutral ValuationWe found the exact value of the option without even knowing the probability that the stock would go up or down!The current stock price already balances the views of the optimists and the pessimists.The option reflects that balance because its value depends on the stock.36An option-pricing FormulaRisk Neutral ValuationThe insight provides us with another approach to valuing the call.If we dont need the probabilities of the two states to value the call,perhaps we can select any probabilities we want and still come up with the right answer.37An option-pricing FormulaA risk-neutral world occurs where the expected return on any asset is equal to the risk-free rate.In other words,this case occurs when investors demand no additional compensation beyond the risk-free rate,regardless of the risk of the asset in question.38An option-pricing FormulaRisk-neutral valuation allows us to value a call in the following two ways:l1.determine the cost of a strategy to duplicate the call.l2.calculate the probabilities of a rise and a fall under the assumption of risk-neutrality.39An option-pricing FormulaBlack-Scholes Model40An option-pricing FormulaBlack-Scholes modelExamples41Stocks and Bonds as Options42
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