Lévy-Based Interest Rate Derivatives: Change of Time Method and PIDEs
نویسنده
چکیده
In this paper, we show how to calculate the price of zerocoupon bonds for many Gaussian and Lévy one-factor and multi-factor models of r(t) using change of time method. These models include, in particular, Ornshtein-Uhlenbeck (1930), Vasicek (1977), Cox-Ingersoll-Ross (1985), continuous-time GARCH, Ho-Lee (1986), Hull-White (1990) and HeathJarrrow-Morton (1992) models and their various combinations. We also derive partial integro-differential equations (PIDEs) for the values of swaps, caps, floors and options on them, swaptions, captions and floortions, respectively. We apply the change of time method to price the interest rate derivatives for the interest rates r(t) described by various stochastic differential equations driven by α-stable Lévy processes.
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