An Exact and Efficient Method for Computing Cross-Gammas of Bermudan Swaptions and Cancellable Swaps Under the Libor Market Model

Abstract

We introduce a new simulation algorithm for computing the Hessians of Bermudan swaptions and cancellable 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 are presented for computing the Hessian of cancellable swaps, to demonstrate the time and efficacy of the method.

Keywords: Monte Carlo, Bermudan Swaption, Cancellable Swap, Greek, Gamma matrix, Automatic-differentiation