Quantitative Finance

A swaption is a sort of fixed-income derivatives in finance, which are widely traded in financial markets. Thus, swaption pricing is a hot topic in financial mathematics. 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 no analytical solution for such a swaption price , we attempt to approximate it, and our discussion will focus on one of these approximation method proposed by Collin-Dufresne and Goldstein. We will discuss the situations where the underlying interest rate models are Gaussian and CIR2++ respectively and develop this method by providing an accurate measure of approximation errors. Besides, other swaption pricing methods in literatures that provide different insights into swaption other than CDG approximation are discussed, as well as analytical solutions under one-factor interest rate models if exist.