| This dissertation consists of three essays in interest rate derivative pricing. In the first essay, a model is developed for pricing interest rate options. Our model prices interest rate claims in the Heath-Jarrow-Morton (1992) paradigm. Analytical solutions are available for European options and efficient algorithms exist for the pricing of American claims. The volatility for the forward rate is humped, which is consistent with empirical evidence. The structure of volatilities is captured without using time varying parameters. Hence, the volatility structure is stationary. The dynamics of our term structure are driven by three state Markovain system. We developed an efficient lattice based algorithms for pricing American claims by extending Li, Ritchken and Sankarausbramanian's model in two-dimensional scheme.; Our purpose in essay 2 and essay 3 is to perform empirical tests of the new models using caplets and swaptions data respectively. We show that our models which incorporate the volatility hump of forward rates produce significantly better out-of-sample results than models that do not account for the hump. |
