第二十二章期權(quán)與公司理財(cái)：基本概念(共67頁(yè)).ppt

1、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 Option Pricing Formula22.9 Stocks and

2、 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 Options Many corporate securities are similar

3、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 r

4、ights reserved.22-222.1 Options Contracts: Preliminaries An 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 Puts Call options gives the holder the right, but not the

5、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 price

6、s 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: Preliminaries Exercising the Option The act of buying or selling the underlying asset through the option contr

7、act. Strike Price or Exercise Price Refers to the fixed price in the option contract at which the holder can buy or sell the underlying asset. Expiry The maturity date of the option is referred to as the expiration date, or the expiry. European versus American options European options can be exercis

8、ed 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: Preliminaries In-the-Money The exercise price is less than the spot price of the underlying asset. At-the-Money

9、The exercise price is equal to the spot price of the underlying asset. Out-of-the-Money The 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: Preliminaries Intrinsic Value T

10、he difference between the exercise price of the option and the spot price of the underlying asset. Speculative Value The 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 Comp

11、anies, Inc. All rights reserved.22-622.2 Call Options Call 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/IrwinCopy

12、right 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-7Basic Call Option Pricing Relationships at Expiry At 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-

13、money, it is worthless.CaT = CeT = MaxST - E, 0 WhereST 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 reserve

14、d.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 payo

15、ffs ($)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/Irw

16、inCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-1122.3 Put Options Put 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 a

17、sset to someone.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-12Basic Put Option Pricing Relationships at Expiry At 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

18、 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-Hi

19、ll/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 O

20、ption 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 h

21、as 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 Co

22、mpanies, Inc. All rights reserved.22-1722.5 Reading The Wall Street JournalOption/StrikeExp.Vol.LastVol.LastIBM130Oct364151075138130Jan112194209138135Jul23654243113/16138135Aug12319945138140Jul182614272138140Aug21936587-Put-Call-McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All

23、rights reserved.22-1822.5 Reading The Wall Street JournalOption/StrikeExp.Vol.LastVol.LastIBM130Oct364151075138130Jan112194209138135Jul23654243113/16138135Aug12319945138140Jul182614272138140Aug21936587-Put-Call-This option has a strike price of $135; a recent price for the stock is $138.25 July is t

24、he expiration monthMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-1922.5 Reading The Wall Street JournalOption/StrikeExp.Vol.LastVol.LastIBM130Oct364151075138130Jan112194209138135Jul23654243113/16138135Aug12319945138140Jul182614272138140Aug21936587-Put-Call

25、-This 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 JournalOption/StrikeExp.Vol.LastVol.LastIB

26、M130Oct364151075138130Jan112194209138135Jul23654243113/16138135Aug12319945138140Jul182614272138140Aug21936587-Put-Call-On 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 Wal

27、l Street JournalOption/StrikeExp.Vol.LastVol.LastIBM130Oct364151075138130Jan112194209138135Jul23654243113/16138135Aug12319945138140Jul182614272138140Aug21936587-Put-Call-The 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 wo

28、uld cost $475 plus commissions.McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-2222.5 Reading The Wall Street JournalOption/StrikeExp.Vol.LastVol.LastIBM130Oct364151075138130Jan112194209138135Jul23654243113/16138135Aug12319945138140Jul182614272138140Aug21936

29、587-Put-Call-On 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 JournalOption/StrikeExp.Vol.LastVol.LastIBM130Oct364151075138130Jan112194209138135Jul23654243113/1

30、6138135Aug12319945138140Jul182614272138140Aug21936587-Put-Call-The 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 rig

31、hts reserved.22-2422.6 Combinations of Options Puts 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-Hi

32、ll 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-

33、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 expi

34、ryMcGraw-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 McGr

35、aw-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

36、 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 ca

37、ll 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

38、 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 exer

39、cise price of $40$0-$40$40-P0rTXe40$40Buy the stock at $40040$C)40($rTXe-$40-P00C0PIn market equilibrium, it mast be the case that option prices are set such that:000SPXeCrTOtherwise, riskless portfolios with positive payoffs exist.Value of stock at expiryValue at expiryMcGraw-Hill/IrwinCopyright 20

40、02 by The McGraw-Hill Companies, Inc. All rights reserved.22-3222.7 Valuing Options The 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

41、 The McGraw-Hill Companies, Inc. All rights reserved.22-33Option Value DeterminantsCall PutStock price+ Exercise price +Interest rate + Volatility in the stock price+ +Expiration date+ +The value of a call option C0 must fall within max (S0 E, 0) C0 MaxST - E, 0ProfitlossESTMarket ValueIntrinsic val

42、ueST - 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 Option Pricing Formula We will start with a binomial option pricing formula to build

43、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 eit

44、her 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 Pr

45、icing ModelA call option on this stock with exercise price of $25 will have the following payoffs. 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.

46、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$21.25$

47、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:)1 (25.

48、21$25$fr$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:)1 (25.21$25$210f

49、rC$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 Model38. 2$24.2025$21)05. 1 (25.21$25$210C$25$21.25$28.75S1S0

50、debt- $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 Model38. 2$24.2025$21)05. 1 (25.21$25$210C$25$21.25$28.75S1S0debt- $21.25portfolio

51、$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 ModelMany derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the der

52、ivative 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 equivale

53、nt method is risk-neutral valuationS(0), V(0)S(U), V(U)S(D), V(D)q1- q)1 ()()1 ()()0(frDVqUVqVMcGraw-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(

54、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/IrwinCo

55、pyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-46The Risk-Neutral Approach to Valuation The 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- q)1 ()()1 ()()0(frDVqUVqV)1 ()()1 ()()0(

56、frDSqUSqSA minor bit of algebra yields:)()()()0()1 (DSUSDSSrqfMcGraw-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

57、 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)15. 1 (25$75.28$)15.1 (25$25.21$McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-48Example of the Risk-Neutral V

58、aluation 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)()()()0()1 (DSUSDSSrqf3250. 7$5$25.21$75.28$25.21$25$)05. 1 (qMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-49Example of the Risk-Neutra

59、l 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, $3.7525$75.28$)(UC0 ,75.28$25max$)(DCMcGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-50Example of the Risk-Neutral Valuation of a Call

60、:Finally, find the value of the call at time 0:$21.25, $02/31/3$25,C(0)$28.75,$3.75)1 ()()1 ()()0(frDCqUCqC)05. 1 (0$)31 (75. 3$32)0(C38. 2$)05. 1 (50. 2$)0(C$25,$2.38McGraw-Hill/IrwinCopyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved.22-51This risk-neutral result is consistent wi