Содержание
- 2. 22.1 Options Many corporate securities are similar to the stock options that are traded on organized
- 3. 22.1 Options Contracts: Preliminaries An option gives the holder the right, but not the obligation, to
- 4. 22.1 Options Contracts: Preliminaries Exercising the Option The act of buying or selling the underlying asset
- 5. Options Contracts: Preliminaries In-the-Money The exercise price is less than the spot price of the underlying
- 6. Options Contracts: Preliminaries Intrinsic Value The difference between the exercise price of the option and the
- 7. 22.2 Call Options Call options gives the holder the right, but not the obligation, to buy
- 8. Basic Call Option Pricing Relationships at Expiry At expiry, an American call option is worth the
- 9. Call Option Payoffs -20 100 90 80 70 60 0 10 20 30 40 50 -40
- 10. Call Option Payoffs Write a call Exercise price = $50
- 11. Call Option Profits Write a call Buy a call Exercise price = $50; option premium =
- 12. 22.3 Put Options Put options give the holder the right, but not the obligation, to sell
- 13. Basic Put Option Pricing Relationships at Expiry At expiry, an American put option is worth the
- 14. Put Option Payoffs -20 100 90 80 70 60 0 10 20 30 40 50 -40
- 15. Put Option Payoffs -20 100 90 80 70 60 0 10 20 30 40 50 -40
- 16. Put Option Profits -20 100 90 80 70 60 0 10 20 30 40 50 -40
- 17. 22.4 Selling Options The seller (or writer) of an option has an obligation. The purchaser of
- 18. 22.5 Stock Option Quotations
- 19. 22.5 Stock Option Quotations This option has a strike price of $8; A recent price for
- 20. 22.5 Stock Option Quotations This makes a call option with this exercise price in-the-money by $1.35
- 21. 22.5 Stock Option Quotations On this day, 15 call options with this exercise price were traded.
- 22. 22.5 Stock Option Quotations The holder of this CALL option can sell it for $1.95. Since
- 23. 22.5 Stock Option Quotations Buying this CALL option costs $2.10. Since the option is on 100
- 24. 22.5 Stock Option Quotations On this day, there were 660 call options with this exercise outstanding
- 25. 22.6 Combinations of Options Puts and calls can serve as the building blocks for more complex
- 26. Protective Put Strategy: Buy a Put and Buy the Underlying Stock: Payoffs at Expiry Buy a
- 27. Protective Put Strategy Profits Buy a put with exercise price of $50 for $10 Buy the
- 28. Covered Call Strategy Sell a call with exercise price of $50 for $10 Buy the stock
- 29. Long Straddle: Buy a Call and a Put Buy a put with an exercise price of
- 30. Short Straddle: Sell a Call and a Put Sell a put with exercise price of $50
- 31. Long Call Spread Sell a call with exercise price of $55 for $5 $55 long call
- 32. Put-Call Parity Sell a put with an exercise price of $40 Buy the stock at $40
- 33. 22.7 Valuing Options The last section concerned itself with the value of an option at expiry.
- 34. Option Value Determinants Call Put Stock price + – Exercise price – + Interest rate +
- 35. Market Value, Time Value, and Intrinsic Value for an American Call CaT > Max[ST - E,
- 36. 22.8 An Option‑Pricing Formula We will start with a binomial option pricing formula to build our
- 37. Binomial Option Pricing Model Suppose a stock is worth $25 today and in one period will
- 38. Binomial Option Pricing Model A call option on this stock with exercise price of $25 will
- 39. Binomial Option Pricing Model Borrow the present value of $21.25 today and buy one share. The
- 40. Binomial Option Pricing Model The levered equity portfolio value today is today’s value of one share
- 41. Binomial Option Pricing Model We can value the option today as half of the value of
- 42. The Binomial Option Pricing Model If the interest rate is 5%, the call is worth: $25
- 43. The Binomial Option Pricing Model If the interest rate is 5%, the call is worth: $25
- 44. Binomial Option Pricing Model the replicating portfolio intuition. Many derivative securities can be valued by valuing
- 45. The Risk-Neutral Approach to Valuation We could value V(0) as the value of the replicating portfolio.
- 46. The Risk-Neutral Approach to Valuation S(0) is the value of the underlying asset today. S(0), V(0)
- 47. The Risk-Neutral Approach to Valuation The key to finding q is to note that it is
- 48. Example of the Risk-Neutral Valuation of a Call: Suppose a stock is worth $25 today and
- 49. Example of the Risk-Neutral Valuation of a Call: The next step would be to compute the
- 50. Example of the Risk-Neutral Valuation of a Call: After that, find the value of the call
- 51. Example of the Risk-Neutral Valuation of a Call: Finally, find the value of the call at
- 52. Risk-Neutral Valuation and the Replicating Portfolio This risk-neutral result is consistent with valuing the call using
- 53. The Black-Scholes Model The Black-Scholes Model is Where C0 = the value of a European option
- 54. The Black-Scholes Model Find the value of a six-month call option on Microsoft with an exercise
- 55. The Black-Scholes Model Let’s try our hand at using the model. If you have a calculator
- 56. The Black-Scholes Model N(d1) = N(0.52815) = 0.7013 N(d2) = N(0.31602) = 0.62401
- 57. Assume S = $50, X = $45, T = 6 months, r = 10%, and σ
- 58. 22.9 Stocks and Bonds as Options Levered Equity is a Call Option. The underlying asset comprises
- 59. 22.9 Stocks and Bonds as Options Levered Equity is a Put Option. The underlying asset comprise
- 60. 22.9 Stocks and Bonds as Options It all comes down to put-call parity. Stockholder’s position in
- 61. 22.10 Capital-Structure Policy and Options Recall some of the agency costs of debt: they can all
- 62. Balance Sheet for a Company in Distress Assets BV MV Liabilities BV MV Cash $200 $200
- 63. Selfish Strategy 1: Take Large Risks (Think of a Call Option) The Gamble Probability Payoff Win
- 64. Selfish Stockholders Accept Negative NPV Project with Large Risks Expected cash flow from the Gamble To
- 65. 22.11 Mergers and Options This is an area rich with optionality, both in the structuring of
- 66. 22.12 Investment in Real Projects & Options Classic NPV calculations typically ignore the flexibility that real-world
- 67. 22.13 Summary and Conclusions The most familiar options are puts and calls. Put options give the
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