文档介绍：Interest Rate Derivatives: More Advanced Models Chapter 24
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
The Two-Factor Hull-White Model (Equation , page 571)
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Analytic Results
Bond prices and European options on zero-coupon bonds can be calculated analytically when f(r) = r
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Options on Coupon-Bearing Bonds
We cannot use the same procedure for options on coupon-bearing bonds as we do in the case of one-factor models
If we make the approximate assumption that the coupon-bearing bond price is lognormal, we can use Black’s model
The appropriate volatility is calculated from the volatilities of and correlations between the underlying zero-coupon bond prices
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Volatility Structures
In the one-factor Ho-Lee or Hull-White model the forward rate are either constant or decline exponentially. All forward rates are instantaneously perfectly correlated
In the two-factor model many different forward rate . patterns and correlation structures can be obtained
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Example Giving Humped Volatility Structure (Figure , page 572) a=1, b=, s1=, s2=, r=
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Transformation of the General Model
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Transformation of the General Model continued
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Attractive Features of the Model
It is Markov so that a bining 3-dimensional tree can be constructed
The volatility structure is stationary
Volatility and correlation patterns similar to th