This paper shows that Singleton and Umantsev’s method for swaption pricing in affine models can be simplified and extended to other models. Two alternative methods for approximating the option exercise boundary are introduced: one based on the multivariate Taylor series expansion, and the other based on duration‐matched zero‐coupon bond approximation. Applied to affine models and quadratic‐Gaussian models, these methods are found to give accurate swaption prices.