| The first part of this thesis is concerned with actively traded interest rate derivatives-swaptions and caps. Traditional pricing methods such as term structure models entail model risk. To address this issue, a basis function approach combining economic theory (in the form of arbitrage-free term structure models) and modern nonparametric regression techniques is introduced. This provides a more robust approach to pricing caps and swaptions than the traditional approach involving the LIBOR market model or other term structure models and calibration. Both simulation and empirical results are provided. Our methods can be applied to hedging interest rate risk, managing model risk, developing trading strategies and other areas in fixed income research.; Whereas the first part of this thesis addresses valuation of actively traded interest rate derivatives, the second part is concerned with exotic American-style interest rate derivatives such as callable bonds, Bermudan swaptions and other instruments with early exercise characteristics. The neuro-dynamic programming approach, consisting of simulation and regression, provides a promising method to price complex American-style options. However, how to choose basis functions for the regression component of this approach has been relatively unexplored in the option valuation literature. Our work provides some guidelines for choosing suitable basis functions that are computationally tractable and spatially adaptive. Numerical studies on nondefaultable callable bonds with notice, corporate callable bonds and Bermudan swaptions show that the methods we propose work well in pricing these American-style interest rate derivatives. |
