An exact and efficient method for computing cross-Gammas of Bermudan swaptions and cancelable swaps under the Libor market model

Dan Zhu and Mark S. Joshi

Journal of Computational Finance

Abstract: ABSTRACT We introduce a new simulation algorithm for computing the Hessians of Bermudan swaptions and cancelable swaps. The resulting pathwise estimates are unbiased and;accurate. Given the exercise strategy, the pathwise angularities are removed by a;sequence of measure changes. The change of measure at each exercise time is chosen to;be optimal in terms of minimizing the variance of the likelihood ratio terms. Numerical;results for the Hessian of cancelable swaps are presented to demonstrate the speed;and efficacy of the method.

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