第二十二章 期權與公司理財：基本概念

1、McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-0 Chapter Outline 22.1 Options 22.2 Call Options 22.3 Put Options 22.4 Selling Options 22.5 Reading The Wall Street Journal 22.6 Combinations of Options 22.7 Valuing Options 22.8 An Option Pricing Formula 22.

2、9 Stocks and Bonds as Options 22.10 Capital-Structure Policy and Options 22.11 Mergers and Options 22.12 Investment in Real Projects and Options 22.13 Summary and Conclusions McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-1 22.1 Options Many corporate sec

3、urities 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/Irwin Copyright 2002 by The McGraw-Hill

4、 Companies, Inc. All rights reserved. 22-2 22.1 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

5、 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

6、 in the future, at prices agreed upon today. When exercising a put, you “put” the asset to someone. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-3 22.1 Options Contracts: Preliminaries Exercising the Option The act of buying or selling the underlying as

7、set through the option contract. 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 Eur

8、opean options can be exercised only at expiry. American options can be exercised at any time up to expiry. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-4 Options Contracts: Preliminaries In-the-Money The exercise price is less than the spot price of the

9、 underlying asset. At-the-Money 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/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-5 Options Contra

10、cts: Preliminaries Intrinsic Value The 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 Value Speculative Value + McGraw-Hill/I

11、rwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-6 22.2 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,

12、you “call in” the asset. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-7 Basic 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-mone

13、y, it is worth ST - E. If the call is out-of-the-money, it is worthless. CaT = CeT = MaxST - E, 0 Where ST is the value of the stock at expiry (time T) E is the exercise price. CaT is the value of an American call at expiry CeT is the value of a European call at expiry McGraw-Hill/Irwin Copyright 20

14、02 by The McGraw-Hill Companies, Inc. All rights reserved. 22-8 Call Option Payoffs -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option payoffs ($) Buy a call Exercise price = $50 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-9 Call Opti

15、on Payoffs -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option payoffs ($) Write a call Exercise price = $50 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-10 Call Option Profits -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price (

16、$) Option profits ($) Write a call Buy a call Exercise price = $50; option premium = $10 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-11 22.3 Put Options Put options gives the holder the right, but not the obligation, to sell a given quantity of an asse

17、t 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/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-12 Basic Put Option Pricing Relationships at Expiry At expiry, an American put optio

18、n 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, 0 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-13 Put Option

19、Payoffs -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option payoffs ($) Buy a put Exercise price = $50 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-14 Put Option Payoffs -20 1009080706001020304050 -40 20 0 -60 40 60 Option payoffs ($) w

20、rite a put Exercise price = $50 Stock price ($) McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-15 Put Option Profits -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option profits ($) Buy a put Write a put Exercise price = $50; option premiu

21、m = $10 10 -10 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-16 22.4 Selling Options The seller (or writer) of an option has an obligation. The purchaser of an option has an option. -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option pro

22、fits ($) Buy a put Write a put 10 -10 -20 1009080706001020304050 -40 20 0 -60 40 60 Stock price ($) Option profits ($) Write a call Buy a call McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-17 22.5 Reading The Wall Street Journal Option/StrikeExp.Vol.Last

23、Vol.Last IBM130Oct364151075 138130Jan112194209 138135Jul23654243113/16 138135Aug12319945 138140Jul182614272 138140Aug21936587 -Put-Call- McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-18 22.5 Reading The Wall Street Journal Option/StrikeExp.Vol.LastVol.La

24、st IBM130Oct364151075 138130Jan112194209 138135Jul23654243113/16 138135Aug12319945 138140Jul182614272 138140Aug21936587 -Put-Call- This option has a strike price of $135; a recent price for the stock is $138.25 July is the expiration month McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companie

25、s, Inc. All rights reserved. 22-19 22.5 Reading The Wall Street Journal Option/StrikeExp.Vol.LastVol.Last IBM130Oct364151075 138130Jan112194209 138135Jul23654243113/16 138135Aug12319945 138140Jul182614272 138140Aug21936587 -Put-Call- This makes a call option with this exercise price in-the- money by

26、 $3.25 = $138 $135. Puts with this exercise price are out-of-the-money. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-20 22.5 Reading The Wall Street Journal Option/StrikeExp.Vol.LastVol.Last IBM130Oct364151075 138130Jan112194209 138135Jul23654243113/16

27、138135Aug12319945 138140Jul182614272 138140Aug21936587 -Put-Call- On this day, 2,365 call options with this exercise price were traded. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-21 22.5 Reading The Wall Street Journal Option/StrikeExp.Vol.LastVol.Las

28、t IBM130Oct364151075 138130Jan112194209 138135Jul23654243113/16 138135Aug12319945 138140Jul182614272 138140Aug21936587 -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 would cost $475 plus commissions. McGraw-

29、Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-22 22.5 Reading The Wall Street Journal Option/StrikeExp.Vol.LastVol.Last IBM130Oct364151075 138130Jan112194209 138135Jul23654243113/16 138135Aug12319945 138140Jul182614272 138140Aug21936587 -Put-Call- On this day,

30、2,431 put options with this exercise price were traded. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-23 22.5 Reading The Wall Street Journal Option/StrikeExp.Vol.LastVol.Last IBM130Oct364151075 138130Jan112194209 138135Jul23654243113/16 138135Aug1231994

31、5 138140Jul182614272 138140Aug21936587 -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/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserv

32、ed. 22-24 22.6 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/Irwin Copyright 2002 by The McGraw-Hill Com

33、panies, Inc. All rights reserved. 22-25 Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiry Buy a put with an exercise price of $50 Buy the stock Protective Put strategy has downside protection and upside potential $50 $0 $50 Value at expiry Value of stock at expiry Mc

34、Graw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-26 Protective Put Strategy Profits Buy a put with exercise price of $50 for $10 Buy the stock at $40 $40 Protective Put strategy has downside protection and upside potential $40 $0 -$40 $50 Value at expiry Valu

35、e of stock at expiry McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-27 Covered Call Strategy Sell a call with exercise price of $50 for $10 Buy the stock at $40 $40 Covered call $40 $0 -$40 $10 -$30 $30$50 Value of stock at expiry Value at expiry McGraw-H

36、ill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-28 Long Straddle: Buy a Call and a Put Buy a put with an exercise price of $50 for $10 $40 A Long Straddle only makes money if the stock price moves $20 away from $50. $40 $0 -$20 $50 Buy a call with an exercise pric

37、e of $50 for $10 -$10 $30 $60$30$70 Value of stock at expiry Value at expiry McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-29 Short Straddle: Sell a Call and a Put Sell a put with exercise price of $50 for $10 $40 A Short Straddle only loses money if the

38、 stock price moves $20 away from $50. -$40 $0 -$30 $50 Sell a call with an exercise price of $50 for $10 $10 $20 $60$30$70 Value of stock at expiry Value at expiry McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-30 Long Call Spread Sell a call with exercis

39、e price of $55 for $5 $55 long call spread $5 $0 $50 Buy a call with an exercise price of $50 for $10 -$10 -$5 $60 Value of stock at expiry Value at expiry McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-31 Put-Call Parity Sell a put with an exercise price

40、 of $40 Buy the stock at $40 financed with some debt: FV = $X Buy a call option with an exercise price of $40 $0 -$40 $40-P0 rT Xe 40$ $40 Buy the stock at $40 0 40$C )40($ rT Xe -$40-P0 0 C 0 P In market equilibrium, it mast be the case that option prices are set such that: 000 SPXeC rT Otherwise,

41、riskless portfolios with positive payoffs exist. Value of stock at expiry Value at expiry McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-32 22.7 Valuing Options The last section concerned itself with the value of an option at expiry. This section consider

42、s the value of an option prior to the expiration date. A much more interesting question. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-33 Option Value Determinants Call Put 1. Stock price+ 2. Exercise price + 3. Interest rate + 4. Volatility in the stock

43、 price+ + 5. Expiration date+ + The value of a call option C0 must fall within max (S0 E, 0) C0 MaxST - E, 0 Profit loss E ST Market Value Intrinsic value ST - E Time value Out-of-the-moneyIn-the-money ST The value of a call option C0 must fall within max (S0 E, 0) C0 S0. McGraw-Hill/Irwin Copyright

44、 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-35 22.8 An Option Pricing Formula We 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/Irwin C

45、opyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-36 Binomial Option Pricing Model Suppose 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

46、value of an at-the-money call option? $25 $21.25 $28.75 S1S0 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-37 Binomial Option Pricing Model 1. A call option on this stock with exercise price of $25 will have the following payoffs. 2. We can replicate the

47、 payoffs of the call option. With a levered position in the stock. $25 $21.25 $28.75 S1S0C1 $3.75 $0 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-38 Binomial Option Pricing Model Borrow the present value of $21.25 today and buy 1 share. The net payoff f

48、or 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 $28.75 S1S0debt - $21.25 portfolio $7.50 $0 ( - ) = = = C1 $3.75 $0- $21.25 McGraw-Hill/Irwin Copyright 20

49、02 by The McGraw-Hill Companies, Inc. All rights reserved. 22-39 Binomial Option Pricing Model The levered equity portfolio value today is todays value of one share less the present value of a $21.25 debt: )1 ( 25.21$ 25$ f r $25 $21.25 $28.75 S1S0debt - $21.25 portfolio $7.50 $0 ( - ) = = = C1 $3.7

50、5 $0- $21.25 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-40 Binomial Option Pricing Model We can value the option today as half of the value of the levered equity portfolio: )1 ( 25.21$ 25$ 2 1 0 f r C $25 $21.25 $28.75 S1S0debt - $21.25 portfolio $7.5

51、0 $0 ( - ) = = = C1 $3.75 $0- $21.25 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-41 If the interest rate is 5%, the call is worth: The Binomial Option Pricing Model 38. 2$24.2025$ 2 1 )05. 1 ( 25.21$ 25$ 2 1 0 C $25 $21.25 $28.75 S1S0debt - $21.25 port

52、folio $7.50 $0 ( - ) = = = C1 $3.75 $0- $21.25 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-42 If the interest rate is 5%, the call is worth: The Binomial Option Pricing Model 38. 2$24.2025$ 2 1 )05. 1 ( 25.21$ 25$ 2 1 0 C $25 $21.25 $28.75 S1S0debt - $

53、21.25 portfolio $7.50 $0 ( - ) = = = C1 $3.75 $0- $21.25 $2.38 C0 McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-43 Binomial Option Pricing Model Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios

54、have the same payoffs as the derivative securities. The most important lesson (so far) from the binomial option pricing model is: McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-44 The Risk-Neutral Approach to Valuation We could value V(0) as the value of

55、the replicating portfolio. An equivalent method is risk-neutral valuation S(0), V(0) S(U), V(U) S(D), V(D) q 1- q )1 ( )()1 ()( )0( f r DVqUVq V McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-45 The Risk-Neutral Approach to Valuation S(0) is the value of

56、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. q 1- q V(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 t

57、he risk-neutral probability of an “up” move. McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-46 The 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),

58、V(0) S(U), V(U) S(D), V(D) q 1- q )1 ( )()1 ()( )0( f r DVqUVq V )1 ( )()1 ()( )0( f r DSqUSq S A minor bit of algebra yields: )()( )()0()1 ( DSUS DSSr q f McGraw-Hill/Irwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-47 Example of the Risk-Neutral Valuation of a Call:

59、$21.25,C(D) q 1- q Suppose 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) )15. 1 (25$75.28$ )15.1 (25$25.21$ McGraw-Hill/I

60、rwin Copyright 2002 by The McGraw-Hill Companies, Inc. All rights reserved. 22-48 Example of the Risk-Neutral Valuation of a Call: $21.25,C(D) 2/3 1/3 The next step would be to compute the risk neutral probabilities $25,C(0) $28.75,C(D) )()( )()0()1 ( DSUS DSSr q f 32 50 . 7 $ 5$ 25.21$75.28$ 25.21$