文档介绍：Volatility Smiles Chapter 15
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Put-Call Parity Arguments
Put-call parity p +S0e-qT = c +X e–r T holds regardless of the assumptions made about the stock price distribution
It follows that
pmkt-pbs=cmkt-cbs
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Implied Volatilities
The implied volatility calculated from a European call option should be the same as that calculated from a European put option when both have the same strike price and maturity
The same is approximately true of American options
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Volatility Smile
A volatility smile shows the variation of the implied volatility with the strike price
The volatility smile should be the same whether calculated from call options or put options
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
The Volatility Smile for Foreign Currency Options (Figure , page 332)
Implied
Volatility
Strike
Price
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Implied Distribution for Foreign Currency Options
The implied distribution is as shown in Figure , page 332
Both tails are heavier than the lognormal distribution
It is also “more peaked than the lognormal distribution
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
The Volatility Smile for Equity Options (Figure , page 334)
Implied
Volatility
Strike
Price
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Implied Distribution for Equity Options
The implied distribution is as shown in Figure , page 335
The right tail is less heavy and the left tail is heavier than the lognormal distribution
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Other Volatility Smiles?
What is the volatility smile if
True distri