公司理財chap022課件

1、Options and Corporate Finance,公司理財chap022,Key Concepts and Skills,Understand option terminology Be able to determine option payoffs and profits Understand the major determinants of option prices Understand and apply put-call parity Be able to determine option prices using the binomial and Black-Scho

2、les models,公司理財chap022,Chapter Outline,22.1 Options 22.2 Call Options 22.3 Put Options 22.4 Selling Options 22.5 Option Quotes 22.6 Combinations of Options 22.7 Valuing Options 22.8 An Option Pricing Formula 22.9 Stocks and Bonds as Options 22.10 Options and Corporate Decisions: Some Applications 22

3、.11 Investment in Real Projects and Options,公司理財chap022,22.1 Options,An option gives the holder the right, but not the obligation, to buy or sell a given quantity of an asset on (or before) a given date, at prices agreed upon today. Exercising the Option The act of buying or selling the underlying a

4、sset 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 (Expiration Date) The maturity date of the option,公司理財chap022,Options,European versus American options European options can be exercised only at expiry

5、. American options can be exercised at any time up to expiry. In-the-Money Exercising the option would result in a positive payoff. At-the-Money Exercising the option would result in a zero payoff (i.e., exercise price equal to spot price). Out-of-the-Money Exercising the option would result in a ne

6、gative payoff.,公司理財chap022,22.2 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, you “call in” the asset.,公司理財chap022,Call Option Prici

7、ng 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-money, it is worthless: C = MaxST E, 0 Where ST is the value of the stock at expiry (time T) E is the exercis

8、e price. C is the value of the call option at expiry,公司理財chap022,Call Option Payoffs,20,120,20,40,60,80,100,40,20,40,60,Stock price ($),Option payoffs ($),Buy a call,Exercise price = $50,50,公司理財chap022,Call Option Profits,Exercise price = $50; option premium = $10,Buy a call,50,10,10,公司理財chap022,22.

9、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 asset to someone.,公司理財chap022,Put Option Pricing at Expiry,At expiry, an American

10、 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. P = MaxE ST, 0,公司理財chap022,Put Option Payoffs,20,0,20,40,60,80,100,40,20,0,40,60,Stock price ($),Option payoffs ($),Buy a p

11、ut,Exercise price = $50,50,50,公司理財chap022,Put Option Profits,20,20,40,60,80,100,40,20,40,60,Stock price ($),Option payoffs ($),Buy a put,Exercise price = $50; option premium = $10,10,10,50,公司理財chap022,Option Value,Intrinsic Value Call: MaxST E, 0 Put: MaxE ST , 0 Speculative Value The difference bet

12、ween the option premium and the intrinsic value of the option.,公司理財chap022,22.4 Selling Options,The seller (or writer) of an option has an obligation. The seller receives the option premium in exchange.,公司理財chap022,Call Option Payoffs,20,120,20,40,60,80,100,40,20,40,60,Stock price ($),Option payoffs

13、 ($),Sell a call,Exercise price = $50,50,公司理財chap022,Put Option Payoffs,20,0,20,40,60,80,100,40,20,0,40,50,Stock price ($),Option payoffs ($),Sell a put,Exercise price = $50,50,公司理財chap022,Option Diagrams Revisited,Exercise price = $50; option premium = $10,Sell a call,Buy a call,50,60,40,100,40,40,

14、Stock price ($),Option payoffs ($),Buy a put,Sell a put,10,10,Buy a call,Sell a put,Buy a put,Sell a call,公司理財chap022,22.5 Option Quotes,公司理財chap022,Option Quotes,This option has a strike price of $135;,a recent price for the stock is $138.25;,July is the expiration month.,公司理財chap022,Option Quotes,

15、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.,公司理財chap022,Option Quotes,On this day, 2,365 call options with this exercise price were traded.,公司理財chap022,Option Quotes,The CALL option with a strike price of $1

16、35 is trading for $4.75.,Since the option is on 100 shares of stock, buying this option would cost $475 plus commissions.,公司理財chap022,Option Quotes,On this day, 2,431 put options with this exercise price were traded.,公司理財chap022,Option Quotes,The PUT option with a strike price of $135 is trading for

17、 $.8125.,Since the option is on 100 shares of stock, buying this option would cost $81.25 plus commissions.,公司理財chap022,22.6 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, tailori

18、ng the risk-return pro meet your clients needs.,公司理財chap022,Protective Put Strategy (Payoffs),Buy a put with an exercise price of $50,Buy the stock,Protective Put payoffs,$50,$0,$50,Value at expiry,Value of stock at expiry,公司理財chap022,Protective Put Strategy (Profits),Buy a put with exercise price o

19、f $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,Value of stock at expiry,-$10,公司理財chap022,Covered Call Strategy,Sell a call with exercise price of $50 for $10,Buy the stock at $40,$40,Covered Call strategy,$0

20、,-$40,$50,Value at expiry,Value of stock at expiry,公司理財chap022,Long Straddle,30,40,60,70,30,40,Stock price ($),Option payoffs ($),Buy a put with exercise price of $50 for $10,Buy a call with exercise price of $50 for $10,A Long Straddle only makes money if the stock price moves $20 away from $50.,$5

21、0,公司理財chap022,Short Straddle,30,30,40,60,70,40,Stock price ($),Option payoffs ($),$50,This Short Straddle only loses money if the stock price moves $20 away from $50.,Sell a put with exercise price of $50 for $10,Sell a call with an exercise price of $50 for $10,公司理財chap022,Put-Call Parity: p0 + S0

22、= c0 + E/(1+ r)T,25,25,Stock price ($),Option payoffs ($),Consider the payoffs from holding a portfolio consisting of a call with a strike price of $25 and a bond with a future value of $25.,Call,Portfolio payoff,公司理財chap022,Put-Call Parity,25,25,Stock price ($),Option payoffs ($),Consider the payof

23、fs from holding a portfolio consisting of a share of stock and a put with a $25 strike.,Portfolio value today = p0 + S0,Portfolio payoff,公司理財chap022,Put-Call Parity,Since these portfolios have identical payoffs, they must have the same value today: hence Put-Call Parity: c0 + E/(1+r)T = p0 + S0,公司理財

24、chap022,22.7 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.,公司理財chap022,American Call,C0 must fall within max (S0 E, 0) C0 S0.,25,Option payoffs ($)

25、,Call,ST,loss,E,Profit,ST,Time value,Intrinsic value,In-the-money,Out-of-the-money,公司理財chap022,Option Value Determinants,Call Put Stock 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 S0. The

26、precise position will depend on these factors.,公司理財chap022,22.8 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.,公司理財chap022,Binomial Option P

27、ricing 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 value of an at-the-money call option?,$25,S0,公司理財chap022,Binomial Option Pricing Model,A call

28、 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,$28.75,S1,S0,C1,$3.75,$0,公司理財chap022,Binomial Option Pricing Model,Borrow the present value of $21.25 today and buy 1 sha

29、re. 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,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,( ) =,=,=,C1,$3.75,$0, $21.25,公司理財chap02

30、2,Binomial Option Pricing Model,The value today of the levered equity portfolio is todays value of one share less the present value of a $21.25 debt:,$25,$21.25,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,( ) =,=,=,C1,$3.75,$0, $21.25,公司理財chap022,Binomial Option Pricing Model,We can value the call

31、option today as half of the value of the levered equity portfolio:,$25,$21.25,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,( ) =,=,=,C1,$3.75,$0, $21.25,公司理財chap022,If the interest rate is 5%, the call is worth:,Binomial Option Pricing Model,$25,$21.25,$28.75,S1,S0,debt, $21.25,portfolio,$7.50,$0,(

32、) =,=,=,C1,$3.75,$0, $21.25,公司理財chap022,Binomial Option Pricing Model,the 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 fa

33、r) from the binomial option pricing model is:,公司理財chap022,Delta,This practice of the construction of a riskless hedge is called delta hedging. The delta of a call option is positive. Recall from the example:,The delta of a put option is negative.,公司理財chap022,Delta,Determining the Amount of Borrowing

34、: Value of a call = Stock price Delta Amount borrowed $2.38 = $25 Amount borrowed Amount borrowed = $10.12,公司理財chap022,The Risk-Neutral Approach,We could value the option, V(0), as the value of the replicating portfolio. An equivalent method is risk-neutral valuation:,S(0), V(0),S(U), V(U),S(D), V(D

35、),q,1- q,公司理財chap022,The Risk-Neutral Approach,S(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.,q,1- q,V(U) and V(D) are the values of the option in the n

36、ext period following an up move and a down move, respectively.,q is the risk-neutral probability of an “up” move.,公司理財chap022,The Risk-Neutral Approach,The key to finding q is to note that it is already impounded into an observable security price: the value of S(0):,A minor bit of algebra yields:,公司

37、理財chap022,Example of Risk-Neutral Valuation,$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(U),公司理財

38、chap022,Example of Risk-Neutral Valuation,$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(U),公司理財chap022,Example of Risk-Neutral Valuation,$21.25, $0,2/3,1/3,After that, find the value of the call in the up state and down state.,$25,C(0),$28.75,

39、 $3.75,公司理財chap022,Example of Risk-Neutral Valuation,Finally, find the value of the call at time 0:,$25,$2.38,公司理財chap022,This risk-neutral result is consistent with valuing the call using a replicating portfolio.,Risk-Neutral Valuation and the Replicating Portfolio,公司理財chap022,The Black-Scholes Mod

40、el,Where C0 = the value of a European option at time t = 0,r = 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

41、2-state world.,公司理財chap022,The Black-Scholes Model,Find the value of a six-month call option on Microsoft with an exercise price of $150. The current value of a share of Microsoft is $160. The interest rate available in the U.S. is r = 5%. The option maturity is 6 months (half of a year). The volati

42、lity 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.,公司理財chap022,The Black-Scholes Model,Lets try our hand at using the model. If you have a calculator handy, follow along.,Then,First calculate d1 a

43、nd d2,公司理財chap022,The Black-Scholes Model,N(d1) = N(0.52815) = 0.7013 N(d2) = N(0.31602) = 0.62401,公司理財chap022,22.9 Stocks and Bonds as Options,Levered equity is a call option. The underlying asset comprises the assets of the firm. The strike price is the payoff of the bond. If at the maturity of th

44、eir 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.

45、the shareholders will declare bankruptcy) and let the call expire.,公司理財chap022,Stocks and Bonds as Options,Levered equity is a put option. The underlying asset comprises 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 l

46、ess 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.,公司理財chap022,Stocks and B

47、onds as Options,It all comes down to put-call parity.,Stockholders position in terms of call options,Stockholders position in terms of put options,公司理財chap022,Mergers and Diversification,Diversification is a frequently mentioned reason for mergers. Diversification reduces risk and, therefore, volati

48、lity. Decreasing volatility decreases the value of an option. Assume diversification is the only benefit to a merger: Since equity can be viewed as a call option, should the merger increase or decrease the value of the equity? Since risky debt can be viewed as risk-free debt minus a put option, what

49、 happens to the value of the risky debt? Overall, what has happened with the merger and is it a good decision in view of the goal of stockholder wealth maximization?,公司理財chap022,Example,Consider the following two merger candidates. The merger is for diversification purposes only with no synergies in

50、volved. Risk-free rate is 4%.,公司理財chap022,Example,Use the Black and Scholes OPM (or an options calculator) to compute the value of the equity. Value of the debt = value of assets value of equity,公司理財chap022,Example,The asset return standard deviation for the combined firm is 30% Market value assets

51、(combined) = 40 + 15 = 55 Face value debt (combined) = 18 + 7 = 25,Total MV of equity of separate firms = 25.72 + 9.88 = 35.60 Wealth transfer from stockholders to bondholders = 35.60 34.18 = 1.42 (exact increase in MV of debt),公司理財chap022,M&A Conclusions,Mergers for diversification only transfer we

52、alth from the stockholders to the bondholders. The standard deviation of returns on the assets is reduced, thereby reducing the option value of the equity. If managements goal is to maximize stockholder wealth, then mergers for reasons of diversification should not occur.,公司理財chap022,Options and Cap

53、ital Budgeting,Stockholders may prefer low NPV projects to high NPV projects if the firm is highly leveraged and the low NPV project increases volatility. Consider a company with the following characteristics: MV assets = 40 million Face Value debt = 25 million Debt maturity = 5 years Asset return s

54、tandard deviation = 40% Risk-free rate = 4%,公司理財chap022,Example: Low NPV,Current market value of equity = $22.706 million Current market value of debt = $17.294 million,公司理財chap022,Example: Low NPV,Which project should management take? Even though project B has a lower NPV, it is better for stockhol

55、ders. The firm has a relatively high amount of leverage: With project A, the bondholders share in the NPV because it reduces the risk of bankruptcy. With project B, the stockholders actually appropriate additional wealth from the bondholders for a larger gain in value.,公司理財chap022,Example: Negative NPV,We have seen that stockholders might prefer a low NPV to a high one, but would they ever prefer a negative NPV? Under certain circumstances,