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

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.