1、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 OptionPricing Formula 22.9 Stocks and Bonds as Options 22.10 Capital-Structure Policy and Options 22.11 Mergers and Opti 。

2、ons 22.12 Investment in Real Projects and Options 22.13 Summary and Conclusions,22.1 Options,Many 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 cap 。

3、ital budgeting decisions can be viewed in terms of options.,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 。

4、 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 a 。

5、sset at some time in the future, at prices agreed upon today. When exercising a put, you “put” the asset to someone.,22.1 Options Contracts: Preliminaries,Exercising the Option The act of buying or selling the underlying asset through the option contract. Strike Price or Exercise Price Refers to the 。

6、 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 exercised only at expiry. American options can be exerci 。

7、sed at any time up to expiry.,Options Contracts: Preliminaries,In-the-Money The exercise price is less than the spot price of the 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 t 。

8、he underlying asset.,Options Contracts: 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 Valu 。

9、e,Speculative Value,+,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.,Basic Call Option Pricing Relation 。

10、ships 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. CaT = CeT = MaxST - E, 0 Where ST is the value of the stock at expiry (time T) E 。

11、 is the exercise price. CaT is the value of an American call at expiry CeT is the value of a European call at expiry,Call Option Payoffs,-20,100,90,80,70,60,0,10,20,30,40,50,-40,20,0,-60,40,60,Stock price ($),Option payoffs ($),Buy a call,Exercise price = $50,Call Option Payoffs,Write a call,Exercis 。

12、e price = $50,Call Option Profits,Write a call,Buy a call,Exercise price = $50;
option premium = $10,22.3 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 exercisin 。

13、g a put, you “put” the asset to someone.,Basic 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 E - ST. If the put is out-of-the-money, it is worthless. PaT = PeT 。

14、 = MaxE - ST, 0,Put Option Payoffs,-20,100,90,80,70,60,0,10,20,30,40,50,-40,20,0,-60,40,60,Stock price ($),Option payoffs ($),Buy a put,Exercise price = $50,Put Option Payoffs,-20,100,90,80,70,60,0,10,20,30,40,50,-40,20,0,-60,40,60,Option payoffs ($),write a put,Exercise price = $50,Stock price ($), 。

15、Put Option Profits,-20,100,90,80,70,60,0,10,20,30,40,50,-40,20,0,-60,40,60,Stock price ($),Option profits ($),Buy a put,Write a put,Exercise price = $50;
option premium = $10,10,-10,22.4 Selling Options,The seller (or writer) of an option has an obligation.,The purchaser of an option has an option., 。

16、22.5 Reading The Wall Street Journal,22.5 Reading The Wall Street Journal,This option has a strike price of $135;
,a recent price for the stock is $138.25,July is the expiration month,22.5 Reading The Wall Street Journal,This makes a call option with this exercise price in-the-money by $3.25 = $138 $ 。

17、135.,Puts with this exercise price are out-of-the-money.,22.5 Reading The Wall Street Journal,On this day, 2,365 call options with this exercise price were traded.,22.5 Reading The Wall Street Journal,The CALL option with a strike price of $135 is trading for $4.75.,Since the option is on 100 shares 。

18、 of stock, buying this option would cost $475 plus commissions.,22.5 Reading The Wall Street Journal,On this day, 2,431 put options with this exercise price were traded.,22.5 Reading The Wall Street Journal,The PUT option with a strike price of $135 is trading for $.8125.,Since the option is on 100。

19、shares of stock, buying this option would cost $81.25 plus commissions.,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。

20、needs.,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,Protective Put Strategy Profits,Buy 。

21、 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,Value of stock at expiry,Covered Call Strategy,Sell a call with exercise price of $50 for $10,Buy the stock at $40,$40,Covered call, 。

22、$40,$0,-$40,$10,-$30,$30,$50,Value of stock at expiry,Value at expiry,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 price of $50 for $10, 。

23、-$10,$30,$60,$30,$70,Value of stock at expiry,Value at expiry,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 stock price moves $20 away from $50.,-$40,$0,-$30,$50,Sell a call with an exercise price of $50 for $10,$10,$ 。

24、20,$60,$30,$70,Value of stock at expiry,Value at expiry,Long Call Spread,Sell a call with exercise 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,Put-Call Parity,Sell a put with an exercise pri 。

25、ce 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,$40,Buy the stock at $40,-$40-P0,In market equilibrium, it mast be the case that option prices are set such that:,Otherwise, riskless portfolios with positive payoffs exist. 。

26、,Value of stock at expiry,Value at expiry,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.,Option Value Determinants,Call Put Stock price+ Exerci 。

27、se 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 precise position will depend on these factors.,Market Value, Time Value and Intrinsic Value for an American Call,CaT MaxST - E, 0,Profit,loss,E,ST,Ma 。

28、rket Value,Intrinsic value,ST - E,Time value,Out-of-the-money,In-the-money,ST,The value of a call option C0 must fall within max (S0 E, 0) C0 S0.,22.8 An OptionPricing Formula,We will start with a binomial option pricing formula to build our intuition.,Then we will graduate to the normal approximati 。

29、on to the binomial for some real-world option valuation.,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 value of an at-the- 。

30、money call option?,$25,$21.25,$28.75,S1,S0,Binomial Option Pricing Model,A 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,$28.75,S1,S0,C1,$3.75,$0,Binomial Option。

31、Pricing Model,Borrow 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,$28.75,S1,S0,debt, 。

32、- $21.25,portfolio,$7.50,$0,( - ) =,=,=,C1,$3.75,$0,- $21.25,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:,$25,$21.25,$28.75,S1,S0,debt,- $21.25,portfolio,$7.50,$0,( - ) =,=,=,C1,$3.75,$0,- $21.25,Binomial 。

33、 Option Pricing Model,We can value the 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,If the interest rate is 5%, the call is worth:,The Binomial Option Pricing Model,$25,$21.25,$28.75,S1,S0 。

34、,debt,- $21.25,portfolio,$7.50,$0,( - ) =,=,=,C1,$3.75,$0,- $21.25,If the interest rate is 5%, the call is worth:,The Binomial Option Pricing Model,$25,$21.25,$28.75,S1,S0,debt,- $21.25,portfolio,$7.50,$0,( - ) =,=,=,C1,$3.75,$0,- $21.25,Binomial Option Pricing Model,the replicating portfolio intuit 。

35、ion.,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:,The Risk-Neutral Approach to Valuation,We could value V( 。

36、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),q,1- q,The Risk-Neutral Approach to Valuation,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 t 。

37、he 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 the risk-neutral probability of an “up” move.,The Risk-Neutral Approach to Valuation,The key to finding q is 。

38、 to note that it is already impounded into an observable security price: the value of S(0):,A minor bit of algebra yields:,Example of the Risk-Neutral Valuation of a Call:,$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 。

39、 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),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),Example of the Risk-N 。

40、eutral Valuation of a Call:,$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, $3.75,Example of the Risk-Neutral Valuation of a Call:,Finally, find the value of the call at time 0:,$25,$2.38,This risk-neutral result is consistent with valuing t 。

41、he call using a replicating portfolio.,Risk-Neutral Valuation and the Replicating Portfolio,The Black-Scholes Model,The Black-Scholes Model is,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 。

42、 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.,The Black-Scholes Model,Find the value of a six-month call option on the Microsoft with an exercise price of $150 The current value of a share of 。

43、 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 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.,The Black-Schol 。

44、es Model,Lets try our hand at using the model. If you have a calculator handy, follow along.,Then,First calculate d1 and d2,The Black-Scholes Model,N(d1) = N(0.52815) = 0.7013 N(d2) = N(0.31602) = 0.62401,Assume S = $50, X = $45, T = 6 months, r = 10%, and = 28%, calculate the value of a call and a。

45、put.,From a standard normal probability table, look up N(d1) = 0.812 and N(d2) = 0.754 (or use Excels “normsdist” function),Another Black-Scholes Example,22.9 Stocks and Bonds as Options,Levered Equity is a Call Option. The underlying asset comprise the assets of the firm. The strike price is the pa 。

46、yoff 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 。

47、, they will not pay the bondholders (i.e. the shareholders will declare bankruptcy) and let the call expire.,22.9 Stocks and Bonds as Options,Levered 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。

48、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 pu 。

49、t expire.,22.9 Stocks and Bonds as Options,It all comes down to put-call parity.,Stockholders position in terms of call options,Stockholders position in terms of put options,22.10 Capital-Structure Policy and Options,Recall some of the agency costs of debt: they can all be seen in terms of options.。

50、For example, recall the incentive shareholders in a levered firm have to take large risks.,Balance Sheet for a Company in Distress,AssetsBVMVLiabilitiesBVMV Cash$200$200LT bonds$300? Fixed Asset$400$0Equity$300? Total$600$200Total$600$200 What happens if the firm is liquidated today?,The bondholders 。

51、 get $200;
the shareholders get nothing.,Selfish Strategy 1: Take Large Risks (Think of a Call Option),The GambleProbabilityPayoff Win Big10%$1,000 Lose Big90%$0 Cost of investment is $200 (all the firms cash) Required return is 50% Expected CF from the Gamble = $1000 0.10 + $0 = $100,Selfish Stockh 。

52、olders Accept Negative NPV Project with Large Risks,Expected cash flow from the Gamble To Bondholders = $300 0.10 + $0 = $30 To Stockholders = ($1000 - $300) 0.10 + $0 = $70 PV of Bonds Without the Gamble = $200 PV of Stocks Without the Gamble = $0 PV of Bonds With the Gamble = $30 / 1.5 = $20 PV of 。

53、 Stocks With the Gamble = $70 / 1.5 = $47,The stocks are worth more with the high risk project because the call option that the shareholders of the levered firm hold is worth more when the volatility is increased.,22.11 Mergers and Options,This is an area rich with optionality, both in the structuri 。

54、ng of the deals and in their execution.,22.12 Investment in Real Projects & Options,Classic NPV calculations typically ignore the flexibility that real-world firms typically have. The next chapter will take up this point.,22.13 Summary and Conclusions,The most familiar options are puts and calls. Pu 。

55、t options give the holder the right to sell stock at a set price for a given amount of time. Call options give the holder the right to buy stock at a set price for a given amount of time. Put-Call parity,22.13 Summary and Conclusions,The value of a stock option depends on six factors: 1. Current pri 。

【第二十二章|第二十二章 期权与公司理财：基本概念(PPT 67页)】56、ce of underlying stock. 2. Dividend yield of the underlying stock. 3. Strike price specified in the option contract. 4. Risk-free interest rate over the life of the contract. 5. Time remaining until the option contract expires. 6. Price volatility of the underlying stock. Much of corporate financial theory can be presented in terms of options. Common stock in a levered firm can be viewed as a call option on the assets of the firm. Real projects often have hidden option that enhance value 。

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标题：第二十二章|第二十二章 期权与公司理财：基本概念(PPT 67页)