Lower bound = adjusted intrinsic value:
C > S0 - PV (X) - PV (D)
(D=dividend)
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Figure 21.2 Range of Possible Call Option Values
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Early Exercise: Puts
• American puts are worth more than European puts, all else equal.
• The possibility of early exercise has value because:
– The value of the stock cannot fall below zero. – Once the firm is bankrupt, it is optimal to
• Call value cannot be negative. The option payoff is zero at worst, and highly positive at best.
• Call value cannot exceed the stock value.
• Value of the call must be greater than the value of levered equity.
30
30
18.18
3C
0
0
3C = $18.18 C = $6.06
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CHAPTER 21
Option Valuation
McGraw-Hill/Irwin
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Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.
• The right to exercise an American call early is valueless as long as the stock pays no dividends until the option expires.
• The value of American and European calls is therefore identical.
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21-11
Binomial Option Pricing: Text Example
120
10
100
Байду номын сангаас
C
90
0
Stock Price
Call Option Value X = 110
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• The call gains value as the stock price rises. Since the price can rise infinitely, the call is “worth more alive than dead.”
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• Time value - the difference between the option price and the intrinsic value
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21-3
Figure 21.1 Call Option Value before Expiration
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21-4
Table 21.1 Determinants of Call Option Values
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21-5
Restrictions on Option Value: Call
Repay loan - 90 - 90
Net Payoff
0 30
30
0 Payoff Structure is exactly 3 times the Call
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Binomial Option Pricing: Text Example
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Option Values
• Intrinsic value - profit that could be made if the option was immediately exercised – Call: stock price - exercise price – Put: exercise price - stock price
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21-7
Figure 21.3 Call Option Value as a Function of the Current Stock Price
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21-8
Early Exercise: Calls
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Binomial Option Pricing: Text Example
Alternative Portfolio
Buy 1 share of stock at $100
Borrow $81.82 (10% Rate) 18.18
Net outlay $18.18
Payoff
Value of Stock 90 120
exercise the American put immediately because of the time value of money.
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21-10
Figure 21.4 Put Option Values as a Function of the Current Stock Price