Presentation on theme: "Chapter Outline 22.1 Options 22.2 Call Options 22.3 Put Options"— Presentation transcript:
0Options and Corporate Finance: Basic Concepts CHAPTER22Options and Corporate Finance: Basic Concepts
1Chapter Outline 22.1 Options 22.2 Call Options 22.3 Put Options 22.4 Selling Options22.5 Reading The Wall Street Journal22.6 Combinations of Options22.7 Valuing Options22.8 An Option‑Pricing Formula22.9 Stocks and Bonds as Options22.10 Capital-Structure Policy and Options22.11 Mergers and Options22.12 Investment in Real Projects and Options22.13 Summary and Conclusions
222.1 OptionsMany 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 capital budgeting decisions can be viewed in terms of options.
322.1 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 PutsCall options 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 asset at some time in the future, at prices agreed upon today. When exercising a put, you “put” the asset to someone.
422.1 Options Contracts: Preliminaries Exercising the OptionThe act of buying or selling the underlying asset through the option contract.Strike Price or Exercise PriceRefers to the fixed price in the option contract at which the holder can buy or sell the underlying asset.ExpiryThe maturity date of the option is referred to as the expiration date, or the expiry.European versus American optionsEuropean options can be exercised only at expiry.American options can be exercised at any time up to expiry.
5Options Contracts: Preliminaries In-the-MoneyThe exercise price is less than the spot price of the underlying asset.At-the-MoneyThe exercise price is equal to the spot price of the underlying asset.Out-of-the-MoneyThe exercise price is more than the spot price of the underlying asset.
6Options Contracts: Preliminaries Intrinsic ValueThe difference between the exercise price of the option and the spot price of the underlying asset.Speculative ValueThe difference between the option premium and the intrinsic value of the option.Option Premium=Intrinsic ValueSpeculative Value+
722.2 Call OptionsCall 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.
8Basic 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-money, it is worthless:C = Max[ST – E, 0]WhereST is the value of the stock at expiry (time T)E is the exercise price.C is the value of the call option at expiry
1222.3 Put OptionsPut 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.
13Basic 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.P = Max[E – ST, 0]
14Put Option Payoffs Exercise price = $50 Buy a put 60 50 40 20Buy a put2040608010050Stock price ($)–20Exercise price = $50–40
15Put Option Payoffs Exercise price = $50 Sell a put 40 20Sell a put2040608010050Stock price ($)–20Exercise price = $50–40–50
1722.4 Selling OptionsThe seller (or writer) of an option has an obligation.The purchaser of an option has an option.40Buy a callOption payoffs ($)Buy a putSell a call10Sell a putStock price ($)50Buy a call4060100–10Buy a putSell a putExercise price = $50; option premium = $10Sell a call–40
1922.5 Reading The Wall Street Journal This option has a strike price of $135;a recent price for the stock is $138.25July is the expiration month
2022.5 Reading The Wall Street Journal This makes a call option with this exercise price in-the-money by $3.25 = $138¼ – $135.Puts with this exercise price are out-of-the-money.
2122.5 Reading The Wall Street Journal On this day, 2,365 call options with this exercise price were traded.
2222.5 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 of stock, buying this option would cost $475 plus commissions.
2322.5 Reading The Wall Street Journal On this day, 2,431 put options with this exercise price were traded.
2422.5 Reading The Wall Street Journal The PUT option with a strike price of $135 is trading for $.8125.Since the option is on 100 shares of stock, buying this option would cost $81.25 plus commissions.
2522.6 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 client’s needs.
26Value of stock at expiry Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at ExpiryProtective Put payoffsValue at expiry$50Buy the stockBuy a put with an exercise price of $50$0Value of stock at expiry$50
27Protective Put Strategy Profits Value at expiryBuy the stock at $40$40Protective Put strategy has downside protection and upside potential$0-$10$40$50Buy a put with exercise price of $50 for $10Value of stock at expiry-$40
28Value of stock at expiry Covered Call StrategyValue at expiryBuy the stock at $40$10Covered Call strategy$0Value of stock at expiry$40$50Sell a call with exercise price of $50 for $10-$30-$40
29Long Straddle: Buy a Call and a Put 40Buy a call with exercise price of $50 for $10Option payoffs ($)30Stock price ($)40603070Buy a put with exercise price of $50 for $10–20$50A Long Straddle only makes money if the stock price moves $20 away from $50.
30Long Straddle: Buy a Call and a Put This Short Straddle only loses money if the stock price moves $20 away from $50.Option payoffs ($)20Sell a put with exercise price of$50 for $10Stock price ($)30406070$50–30Sell a call with anexercise price of $50 for $10–40
31Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T Portfolio value today = c0 +(1+ r)TEPortfolio payoffCallOption payoffs ($)bond2525Stock price ($)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 $25.
32Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T Portfolio payoffPortfolio value today = p0 + S0Option payoffs ($)25Stock price ($)25Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike.
33Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T 25Stock price ($)Option payoffs ($)Portfolio value today = p0 + S0Portfolio value today(1+ r)TE= c0 +Since these portfolios have identical payoffs, they must have the same value today: hencePut-Call Parity: c0 + E/(1+r)T = p0 + S0
3422.7 Valuing OptionsThe last section concerned itself with the value of an option at expiry.This section considers the value of an option prior to the expiration date.A much more interesting question.
35Option Value Determinants Call PutStock price –Exercise price –Interest rate –Volatility in the stock priceExpiration dateThe value of a call option C0 must fall withinmax (S0 – E, 0) < C0 < S0.The precise position will depend on these factors.
36Market Value, Time Value and Intrinsic Value for an American Call ProfitSTCallOption payoffs ($)25Market ValueTime valueIntrinsic valueSTEOut-of-the-moneyIn-the-moneylossThe value of a call option C0 must fall within max (S0 – E, 0) < C0 < S0.
3722.8 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.
38Binomial 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 $ The risk-free rate is 5%. What is the value of an at-the-money call option?S0$21.25 = $25×(1 –.15)$28.75 = $25×(1.15)S1$25
39Binomial 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.S0S1C1$28.75$3.75$25$21.25$0
40Binomial Option 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 option’s payoff so the portfolio is worth twice the call option value.S0( – ) =S1debtportfolioC1$28.75– $21.25=$7.50$3.75$25$21.25– $21.25=$0$0
41Binomial Option Pricing Model The value today of the levered equity portfolio is today’s value of one share less the present value of a $21.25 debt:S0( – ) =S1debtportfolioC1$28.75– $21.25=$7.50$3.75$25$21.25– $21.25=$0$0
42Binomial Option Pricing Model We can value the call option today as half of the value of the levered equity portfolio:S0( – ) =S1debtportfolioC1$28.75– $21.25=$7.50$3.75$25$21.25– $21.25=$0$0
43The Binomial Option Pricing Model If the interest rate is 5%, the call is worth:$2.38C0S0( – ) =S1debtportfolioC1$28.75– $21.25=$7.50$3.75$25$21.25– $21.25=$0$0
44Binomial Option Pricing Model the replicating portfolio intuition.The most important lesson (so far) from the binomial option pricing model is:Many derivative securities can be valued by valuing portfolios of primitive securities when those portfolios have the same payoffs as the derivative securities.
45Delta and the Hedge Ratio 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:D =Swing of callSwing of stockThe delta of a put option is negative.
46Delta Determining the Amount of Borrowing: Value of a call = Stock price × Delta – Amount borrowed$2.38 = $25 × ½ – Amount borrowedAmount borrowed = $10.12
47The Risk-Neutral Approach to Valuation We could value V(0) as the value of the replicating portfolio. An equivalent method is risk-neutral valuationS(U), V(U)qS(0), V(0)1- qS(D), V(D))1(frDVqU+-=
48The Risk-Neutral Approach to Valuation S(U), V(U)qq is the risk-neutral probability of an “up” move.S(0), V(0)1- qS(0) is the value of the underlying asset today.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.V(U) and V(D) are the values of the asset in the next period following an up move and a down move, respectively.
49The Risk-Neutral Approach to Valuation S(0), V(0)S(U), V(U)S(D), V(D)q1- q)1(frDVqU+-=The key to finding q is to note that it is already impounded into an observable security price: the value of S(0):)1(frDSqU+-=A minor bit of algebra yields:
50Example of the Risk-Neutral Valuation of a Call: 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:$21.25,C(D)q1- q$25,C(0)$28.75,C(D))15.1(25$7528=21-
51Example of the Risk-Neutral Valuation of a Call: The next step would be to compute the risk neutral probabilities)(1DSUrqf-+=3250.7$525217528)051(=-q$28.75,C(D)2/3$25,C(0)1/3$21.25,C(D)
52Example of the Risk-Neutral Valuation of a Call: After that, find the value of the call in the up state and down state.25$75.28)(-=UC$28.75, $3.752/3$25,C(0)],75.28$25max[$)(-=DC1/3$21.25, $0
53Example of the Risk-Neutral Valuation of a Call: Finally, find the value of the call at time 0:)1(frDCqU+-=)05.1($3752+=C$21.25, $02/31/3$25,C(0)$28.75,$3.7538.2$)051(50=C$25,$2.38
54Risk-Neutral Valuation and the Replicating Portfolio This risk-neutral result is consistent with valuing the call using a replicating portfolio.The replicating portfolio consists of buying one share of stock today and borrowing the present value of $ The payoffs to the portfolio are twice those of the call, therefore the portfolio is worth twice as much as a call. Since we can value the portfolio, we can value the call.
55The Black-Scholes Model The Black-Scholes Model is)N(21dEeSCrT-=WhereC0 = the value of a European option at time t = 0r = the risk-free interest rate.TσrESds)2(/ln(1+=N(d) = Probability that a standardized, normally distributed, random variable will be less than or equal to d.Tds-=12The Black-Scholes Model allows us to value options in the real world just as we have done in the 2-state world.
56The Black-Scholes Model Find the value of a six-month call option on the Microsoft with an exercise price of $150The current value of a share of Microsoft is $160The 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 $10—our answer must be at least that amount.
57The Black-Scholes Model Let’s try our hand at using the model. If you have a calculator handy, follow along.First calculate d1 and d2TσrESds)5.(/ln(21+=5282.530).)(05(.150/160ln(21=+dThen,31602.5305281512=-Tds
59Another Black-Scholes Example Assume S = $50, X = $45, T = 6 months, r = 10%,and = 28%, calculate the value of a call and a put.()884.502821045ln1=÷øöçèæ+-d686.50288842=-dFrom a standard normal probability table, look up N(d1) = and N(d2) = (or use Excel’s “normsdist” function)32.8$)754(4581250105=-eC125.1$4550328)(10=+-eP
6022.9 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 payoff 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, they will not pay the bondholders (i.e. the shareholders will declare bankruptcy) and let the call expire.
6122.9 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 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 put expire.
6222.9 Stocks and Bonds as Options It all comes down to put-call parity.c0 = S0 + p0 –(1+ r)TEValue of a call on the firmValue of a put on the firmValue of a risk-free bondValue of the firm=+–Stockholder’s position in terms of call optionsStockholder’s position in terms of put options
6322.10 Capital-Structure Policy and Options Recall some of the agency costs of debt: they can all be seen in terms of options.For example, recall the incentive shareholders in a levered firm have to take large risks.
64Balance Sheet for a Company in Distress Assets BV MV Liabilities BV MVCash $200 $200 LT bonds $300Fixed Asset $400 $0 Equity $300Total $600 $200 Total $600 $200What happens if the firm is liquidated today?$200$0The bondholders get $200; the shareholders get nothing.
65Selfish Strategy 1: Take Large Risks The Gamble Probability PayoffWin Big 10% $1,000Lose Big 90% $0Cost of investment is $200 (all the firm’s cash)Required return is 50%Expected CF from the Gamble = $1000 × $0 = $100NPV = –$200 +$100(1.10)NPV = –$133
66Selfish Stockholders Accept Negative NPV Project with Large Risks Expected CF from the GambleTo Bondholders = $300 × $0 = $30To Stockholders = ($1000 – $300) × $0 = $70PV of Bonds Without the Gamble = $200PV of Stocks Without the Gamble = $0$20 =$30(1.50)PV of Bonds With the Gamble:$47 =$70(1.50)PV of Stocks With the Gamble: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 of the firm is increased.
6722.11 Mergers and OptionsThis is an area rich with optionality, both in the structuring of the deals and in their execution.In the first half of 2000, General Mills was attempting to acquire the Pillsbury division of Diageo PLC.The structure of the deal was Diageo’s stockholders received 141 million shares of General Mills stock (then valued at $42.55) plus contingent value rights of $4.55 per share.
6822.11 Mergers and OptionsThe contingent value rights paid the difference between $42.55 and General Mills’ stock price in one year up to a maximum of $4.55.Cash payment to newly issued shares$4.55$38$0$42.55Value of General Mills in 1 year
6922.11 Mergers and OptionsThe contingent value plan can be viewed in terms of puts:Each newly issued share of General Mills given to Diageo’s shareholders came with a put option with an exercise price of $42.55.But the shareholders of Diageo sold a put with an exercise price of $38
7022.11 Mergers and Options Cash payment to newly issued shares Own a putStrike $42.55$42.55– $38.00$4.55$42.55$0Sell a putStrike $38$42.55Value of General Mills in 1 year$38–$38
7122.11 Mergers and Options Value of General Mills in 1 year Value of a shareValue of a share plus cash payment$42.55$4.55$0Value of General Mills in 1 year$38$42.55
7222.12 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.
7322.13 Summary and Conclusions The most familiar options are puts and calls.Put 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 parityc0–(1+ r)TE= S0 + p0
7422.13 Summary and Conclusions The value of a stock option depends on six factors:1. Current price 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.