Journal of Computational Finance

Risk.net

Robust and accurate Monte Carlo simulation of (cross-) Gammas for Bermudan swaptions in the LIBOR market model

Ralf Korn and Qian Liang

ABSTRACT

We present two new efficient methods for the Monte Carlo computation of the (cross-) Gammas of a Bermudan swaption in the LIBOR market model. One approach is a combination of the finite difference method with pathwise Deltas whose efficiency benefits from an innovative new version of the adjoint method. In contrast to this method, which incorporates a bias, our second method is based on the pure pathwise method and a robust, accurate unbiased simulation. Numerical examples show the perfectly calculated Gamma matrices of Bermudan swaptions.

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