  This paper describes a fast and stable algorithm for evaluating Bermudan
swaption under the two factor Hull-White model. We discretize the calculation
of the expected value in the evaluation of Bermudan swaption by numerical
integration, and Gaussian kernel sums appears in it. The fast Gauss transform
can be applied to these Gaussian kernel sums, and it reduces computational
complexity from $O(N^2)$ to $O(N)$ as grid points number $N$ of numerical
integration. We also propose to stabilize the computation under the condition
that the correlation is close to $-1$ by introducing the grid rotation.
Numerical experiments using actual market data show that our method reduces the
computation time significantly compared to the method without the fast Gauss
transform. They also show that the method of the grid rotation contributes to
computational stability in the situations where the correlation is close to
$-1$ and time step is short.
