文档介绍：Interest Rate Derivatives: The Standard Market Models Chapter 22
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Why Interest Rate Derivatives are Much More Difficult to Value Than Stock Options
We are dealing with the whole term structure of interest rates; not a single variable
The probabilistic behavior of an individual interest rate is plicated than that of a stock price
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Why Interest Rate Derivatives are Much More Difficult to Value Than Stock Options
Volatilities of different points on the term structure are different
Interest rates are used for discounting as well as for defining the payoff
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Main Approaches to Pricing Interest Rate Options
Use a variant of Black’s model
Use a no-arbitrage (yield curve based) model
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Black’s Model & Its Extensions
Black’s model is similar to the Black-Scholes model used for valuing stock options
It assumes that the value of an interest rate, a bond price, or some other variable at a particular time T in the future has a lognormal distribution
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Black’s Model & Its Extensions (continued)
The mean of the probability distribution is the forward value of the variable
The standard deviation of the probability distribution of the log of the variable is
where s is the volatility
The expected payoff is discounted at the T-maturity rate observed today
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Black’s Model (Eqn and , p 509)
K : strike price
F0 : forward value of variable
T : option maturity
s : volatility
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
The Black’s Model: Payoff Later Than Variable