文档介绍：Options on Stock Indices, Currencies, and Futures Chapter 13
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
European Options on Stocks Providing a Dividend Yield
We get the same probability distribution for the stock price at time T in each of the following cases:
1. The stock starts at price S0 and provides a dividend yield = q
2. The stock starts at price S0e–q T and provides no e
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
European Options on Stocks Providing Dividend Yield continued
We can value European options by reducing the stock price to S0e–q T and then behaving as though there is no dividend
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Extension of Chapter 8 Results (Equations to )
Lower Bound for calls:
Lower Bound for puts
Put Call Parity
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Extension of Chapter 12 Results (Equations and )
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
The Binomial Model
S0u
ƒu
S0d
ƒd
S0
ƒ
p
(1 – p )
f=e-rT[pfu+(1-p)fd ]
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
The Binomial Model continued
In a risk-neutral world the stock price grows at r-q rather than at r when there is a dividend yield at rate q
The probability, p, of an up movement must therefore satisfy
pS0u+(1-p)S0d=S0e (r-q)T
so that
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Index Options
Option contracts are on 100 times the index
The most popular underlying indices are
the Dow Jones Industrial (European) DJX
the S&P 100 (American) OEX
the S&P 500 (European) SPX
Contracts are settled in cash
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Index Option Example
Consider a call option on an index with a strike price of 560
Suppose 1 contract is exerc