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CHAPTER. 22. Options and Corporate Finance: Basic Concepts. 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 22.9 Stocks and Bonds as Options

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    1. CHAPTER 22 Options and Corporate Finance: Basic Concepts

    2. 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 22.9 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 Chapter Outline

    3. 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 capital budgeting decisions can be viewed in terms of options. 22.1 Options

    4. 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 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.

    5. 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 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 exercised at any time up to expiry.

    6. 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 the underlying asset.

    7. Option Premium Intrinsic Value Speculative Value + = 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.

    8. 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. 22.2 Call Options

    9. Basic Call Option Pricing Relationshipsat 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] Where ST 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

    10. Call Option Payoffs Buy a call 60 40 Option payoffs ($) 20 80 120 20 40 60 100 50 Stock price ($) –20 Exercise price = $50 –40

    11. Call Option Payoffs 60 40 Option payoffs ($) 20 80 120 20 40 60 100 50 Stock price ($) –20 Exercise price = $50 Sell a call –40

    12. 60 40 Option payoffs ($) 20 80 120 20 40 60 100 Stock price ($) –20 –40 Call Option Profits Buy a call 10 50 –10 Exercise price = $50; option premium = $10 Sell a call

    13. 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. 22.3 Put Options

    14. Basic Put Option Pricing Relationshipsat 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]

    15. Put Option Payoffs 60 50 40 Option payoffs ($) 20 Buy a put 0 80 0 20 40 60 100 50 Stock price ($) –20 Exercise price = $50 –40

    16. Put Option Payoffs 40 Option payoffs ($) 20 Sell a put 0 80 0 20 40 60 100 50 Stock price ($) –20 Exercise price = $50 –40 –50

    17. Put Option Profits 60 40 Option payoffs ($) 20 Sell a put 10 Stock price ($) 80 50 20 40 60 100 –10 Buy a put –20 Exercise price = $50; option premium = $10 –40

    18. 22.4 Selling Options The seller (or writer) of an option has an obligation. The purchaser of an option has an option. Buy a call 40 Option payoffs ($) Buy a put Sell a call Sell a put 10 Stock price ($) 50 40 60 100 Buy a call –10 Buy a put Sell a put Exercise price = $50; option premium = $10 Sell a call –40

    19. 22.5 Reading The WallStreet Journal

    20. 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

    21. 22.5 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.

    22. 22.5 Reading The Wall Street Journal On this day, 2,365 call options with thisexercise price were traded.

    23. 22.5 Reading The Wall Street Journal The CALL option with a strike priceof $135 is trading for $4.75. Since the option is on 100 shares of stock, buying this option would cost $475 plus commissions.

    24. 22.5 Reading The Wall Street Journal On this day, 2,431 put options with thisexercise price were traded.

    25. 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 shares of stock, buying this option would cost $81.25 plus commissions.

    26. 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. 22.6 Combinations of Options

    27. Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiry Protective Put payoffs Value at expiry $50 Buy the stock Buy a put with an exercise price of $50 $0 Value of stock at expiry $50

    28. Protective Put Strategy Profits Value at expiry Buy the stock at $40 $40 Protective Put strategy has downside protection and upside potential $0 -$10 $40 $50 Buy a put with exercise price of $50 for $10 Value of stock at expiry -$40

    29. $10 -$30 Covered Call Strategy Value at expiry Buy the stock at $40 Covered Call strategy $0 Value of stock at expiry $40 $50 Sell a call with exercise price of $50 for $10 -$40

    30. –20 Long Straddle: Buy a Call and a Put Buy a call with exercise price of $50 for $10 40 Option payoffs ($) 30 Stock price ($) 40 60 30 70 Buy a put with exercise price of $50 for $10 $50 A Long Straddle only makes money if the stock price moves $20 away from $50.

    31. 20 Long Straddle: Buy a Call and a Put This Short Straddle only loses money if the stock price moves $20 away from $50. Option payoffs ($) Sell a put with exercise price of $50 for $10 Stock price ($) 30 70 40 60 $50 –30 Sell a call with an exercise price of $50 for $10 –40

    32. E Portfolio value today = c0 + (1+ r)T bond Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T Portfolio payoff Call Option payoffs ($) 25 Stock price ($) 25 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.

    33. Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T Portfolio payoff Portfolio value today = p0 + S0 Option payoffs ($) 25 Stock price ($) 25 Consider the payoffs from holding a portfolio consisting of a share of stock and a put with a $25 strike.

    34. Portfolio value today Portfolio value today = p0 + S0 E = c0 + Option payoffs ($) Option payoffs ($) (1+ r)T 25 25 Stock price ($) Stock price ($) 25 25 Put-Call Parity: p0 + S0 = c0 + E/(1+ r)T Since these portfolios have identical payoffs, they must have the same value today: hence Put-Call Parity: c0 + E/(1+r)T = p0 + S0

    35. 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. 22.7 Valuing Options

    36. 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 precise position will depend on these factors.

    37. Market Value Market Value, Time Value and Intrinsic Valuefor an American Call Profit ST Call Option payoffs ($) 25 Time value Intrinsic value ST E Out-of-the-money In-the-money loss The value of a call option C0 must fall within max (S0 – E, 0) <C0<S0.

    38. 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. 22.8 An Option‑Pricing Formula

    39. S1 $28.75 = $25×(1.15) $21.25 = $25×(1 –.15) 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-money call option? S0 $25

    40. 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. S0 S1 C1 $28.75 $3.75 $25 $21.25 $0

    41. Binomial 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 S1 debt portfolio C1 ( – ) = – $21.25 $7.50 $28.75 = $3.75 $25 – $21.25 $21.25 $0 = $0

    42. Binomial 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 S1 debt portfolio C1 ( – ) = – $21.25 $7.50 $28.75 = $3.75 $25 – $21.25 $21.25 $0 = $0

    43. Binomial Option Pricing Model We can value the call option todayas half of the value of thelevered equity portfolio: S0 S1 debt portfolio C1 ( – ) = – $21.25 $7.50 $28.75 = $3.75 $25 – $21.25 $21.25 $0 = $0

    44. C0 $2.38 The Binomial Option Pricing Model If the interest rate is 5%, the call is worth: S0 S1 debt portfolio C1 ( – ) = – $21.25 $7.50 $28.75 = $3.75 $25 – $21.25 $21.25 $0 = $0

    45. Binomial Option Pricing Model The most important lesson (so far) from the binomial option pricing model is: 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.

    46. Swing of call D = Swing of stock Delta 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: The delta of a put option is negative.

    47. Delta • Determining the Amount of Borrowing: Value of a call = Stock price ×Delta – Amount borrowed $2.38 = $25 × ½ – Amount borrowed Amount borrowed = $10.12

    48. ´ + - ´ q V ( U ) ( 1 q ) V ( D ) = V ( 0 ) + ( 1 r ) f The Risk-Neutral Approach to Valuation S(U), V(U) We could value V(0) as the value of the replicating portfolio. An equivalent method is risk-neutral valuation q S(0), V(0) 1- q S(D), V(D)

    49. The Risk-Neutral Approach to Valuation S(U), V(U) S(0) is the value of the underlying asset today. q q is the risk-neutral probability of an “up” move. S(0), V(0) 1- q 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.

    50. S(U), V(U) q ´ + - ´ q V ( U ) ( 1 q ) V ( D ) = V ( 0 ) S(0), V(0) + ( 1 r ) f 1- q S(D), V(D) ´ + - ´ q S ( U ) ( 1 q ) S ( D ) = S ( 0 ) + ( 1 r ) f 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): A minor bit of algebra yields: