  We propose a fast and accurate numerical method for pricing European
swaptions in multi-factor Gaussian term structure models. Our method can be
used to accelerate the calibration of such models to the volatility surface.
The pricing of an interest rate option in such a model involves evaluating a
multi-dimensional integral of the payoff of the claim on a domain where the
payoff is positive. In our method, we approximate the exercise boundary of the
state space by a hyperplane tangent to the maximum probability point on the
boundary and simplify the multi-dimensional integration into an analytical
form. The maximum probability point can be determined using the gradient
descent method. We demonstrate that our method is superior to previous methods
by comparing the results to the price obtained by numerical integration.
