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Corporate Finance Ross  Westerfield  Jaffe

Chapter Twenty Two. 22. Options and Corporate Finance: Basic Concepts. Corporate Finance Ross  Westerfield  Jaffe. Sixth Edition. Prepared by Gady Jacoby University of Manitoba and Sebouh Aintablian American University of Beirut. 22.1 Options 22.2 Call Options 22.3 Put Options

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Corporate Finance Ross  Westerfield  Jaffe

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  1. Chapter Twenty Two 22 Options and Corporate Finance: Basic Concepts Corporate Finance Ross Westerfield  Jaffe Sixth Edition Prepared by Gady Jacoby University of Manitoba and Sebouh Aintablian American University of Beirut

  2. 22.1 Options 22.2 Call Options 22.3 Put Options 22.4 Selling Options 22.5 Stock Option Quotations 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. 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 Value Speculative Value + =

  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 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. CaT = CeT= Max[ST -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

  10. Call Option Payoffs 60 40 Buy a call 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Exercise price = $50

  11. 60 40 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Call Option Payoffs Write a call Exercise price = $50

  12. 60 40 20 0 0 10 20 30 40 50 60 70 80 90 100 Option profits ($) Stock price ($) -20 -40 -60 Call Option Profits Buy a call Write a call Exercise price = $50; option premium = $10

  13. Put options give 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 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= Max[E - ST, 0]

  15. Put Option Payoffs 60 40 Buy a put 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 -60 Exercise price = $50

  16. Put Option Payoffs 60 40 20 0 Option payoffs ($) 0 10 20 30 40 50 60 70 80 90 100 Stock price ($) -20 -40 write a put -60 Exercise price = $50

  17. Put Option Profits 60 Option profits ($) 40 20 Write a put 10 0 0 10 20 30 40 50 60 70 80 90 100 -10 Buy a put Stock price ($) -20 -40 -60 Exercise price = $50; option premium = $10

  18. The seller (or writer) of an option has an obligation. The purchaser of an option has an option. 60 60 40 Option profits ($) 40 Buy a call 20 20 Write a put 0 0 10 20 30 40 50 60 70 80 90 100 Option profits ($) 10 0 Stock price ($) 0 10 20 30 40 50 60 70 80 90 100 -20 -10 Buy a put Stock price ($) -20 -40 Write a call -40 -60 -60 22.4 Selling Options

  19. 22.5 Stock Option Quotations

  20. 22.5 Stock Option Quotations A recent price for the stock is $9.35 This option has a strike price of $8; June is the expiration month

  21. 22.5 Stock Option Quotations This makes a call option with this exercise price in-the-money by $1.35 = $9.35 – $8. Puts with this exercise price are out-of-the-money.

  22. 22.5 Stock Option Quotations On this day, 15 call options with this exercise price were traded.

  23. 22.5 Stock Option Quotations The holder of this CALL option can sell it for $1.95. Since the option is on 100 shares of stock, selling this option would yield $195.

  24. 22.5 Stock Option Quotations Buying this CALL option costs $2.10. Since the option is on 100 shares of stock, buying this option would cost $210.

  25. 22.5 Stock Option Quotations On this day, there were 660 call options with this exercise outstanding in the market.

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

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

  30. Long Straddle: Buy a Call and a Put Value at expiry Buy a call with an exercise price of $50 for $10 $40 $30 $0 -$10 Buy a put with an exercise price of $50 for $10 -$20 $30 $40 $50 $60 $70 Value of stock at expiry A Long Straddle only makes money if the stock price moves $20 away from $50.

  31. Short Straddle: Sell a Call and a Put Value at expiry A Short Straddle only loses money if the stock price moves $20 away from $50. $20 Sell a put with exercise price of $50 for $10 $10 $0 Value of stock at expiry $30 $40 $50 $60 $70 -$30 Sell a call with an exercise price of $50 for $10 -$40

  32. Long Call Spread Value at expiry Buy a call with an exercise price of $50 for $10 $5 long call spread $0 -$5 -$10 Value of stock at expiry $50 $60 $55 Sell a call with exercise price of $55 for $5

  33. Put-Call Parity In market equilibrium, it mast be the case that option prices are set such that: Otherwise, riskless portfolios with positive payoffs exist. Buy the stock at $40 Value at expiry Buy the stock at $40 financed with some debt: FV = $X Buy a call option with an exercise price of $40 Sell a put with an exercise price of $40 $0 Value of stock at expiry $40 -[$40-P0] $40-P0 -$40

  34. 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

  35. 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.

  36. Market Value, Time Value, and Intrinsic Value for an American Call CaT> Max[ST - E, 0] The value of a call option C0 must fall within max (S0 – E, 0) <C0<S0. Profit ST ST - E Market Value Time value Intrinsic value ST E loss Out-of-the-money In-the-money

  37. 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

  38. 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 S1 is either $28.75 or $21.25. The risk-free rate is 5%. What is the value of an at-the-money call option? S0 S1 $28.75 $25 $21.25

  39. 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

  40. Binomial Option Pricing Model Borrow the present value of $21.25 today and buy one 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

  41. Binomial Option Pricing Model The levered equity portfolio value today 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

  42. Binomial Option Pricing Model We can value the option today as half of the value of the levered equity portfolio: S0 S1 debt portfolio C1 ( - ) = - $21.25 $7.50 $28.75 = $3.75 $25 - $21.25 $21.25 $0 = $0

  43. 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

  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 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.

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

  47. The Risk-Neutral Approach to Valuation S(0) is the value of the underlying asset today. S(U), V(U) 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.

  48. S(U), V(U) q S(0), V(0) 1- q S(D), V(D) 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:

  49. Example 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: $28.75,C(D) q $25,C(0) 1- q $21.25,C(D)

  50. Example of the Risk-Neutral Valuation of a Call: The next step would be to compute the risk neutral probabilities $28.75,C(D) 2/3 $25,C(0) 1/3 $21.25,C(D)

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