In this thesis, we will analyze swaptions whose short term interest rates are assumed to follow some affine models with dimension of factors more than two, so called multiple-factor interest rate models. Considering there is generally no analytical swaption price, we attempt to approximate it, and our discussion will focus on one of these approximation method proposed by Collin-Dufresne and Goldstein. I implement and develop this method by providing an accurate measure of approximation errors. Besides, there are several of my innovation and research recommendations on my last chapter with respect to other methods to price swaptions.