The LIBOR market (LM) model (Brace, Gatarek, and Musiela [8],
Miltersen, Sandmann, Sondermann [21], and Jamshidian [18]) is a HeathJarrow-Morton
model (Heath, Jarrow, and Morton [15]) specified to be an
interest rate version of the celebrated Black-Scholes model of stock price, and
is the most popular among practitioners and researchers. However, a statistical
test (Kusuda [19]) rejected the LM model, and suggested that the deterministic
volatility in the LIBOR market model should be replaced with a stochastic
one and/or that a jump process should be introduced into the LM model. This
paper presents a stochastic volatility jump-diffusion LM model using a general
equilibrium security market model of Kusuda [19]. Approximate general
equilibrium pricing formulas for caplet and swaption are derived exploiting the
forward martingale measure approach (Jamshidian [17]) and a Fourier transform
method (Heston [16], Bates [4], and Duffie, Pan, and Singleton [13]).
A Stochastic Volatility Jump-Diffusion LIBOR Market Model and General Equilibrium Pricing of Interest Rate Derivatives
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