| It is well known that interest rate market is an important part of the financial market, and many models have been proposed to fit the market. In this research, we study numerical methods for interest rate derivatives under several models. We consider pricing American put options on zero-coupon bonds under a single factor model of short-term rate, and valuing caps under Lognormal Forward-LIBOR Model (LFM). Monte Carlo method is illustrated for pricing caps, European options on coupon-bearing bonds and swaptions under one-factor LFM. Also, the performance of a short rate model (CIR model) and the one-factor LFM for pricing interest rate derivatives is compared. Calibration experiments indicate that the LFM with zero correlations is closer to the real market than the CIR model, and the LFM with nonzero correlations is even better than the LFM with zero correlations in fitting the market data. In addition, we observe that caps have lower prices under the one-factor LFM than under the CIR model from numerical experiments. European options on coupon-bearing bonds under these two models are found possessing similar price behavior.;Finally, we develop a PDE approach similar to that of Heston (1993) for pricing three-period caps under the one-factor LFM, and establish numerical schemes for solving the PDEs. This PDE approach is applicable when the underlying forward rates are correlated, and can be applied to evaluate caplets and caps under the one-factor LFM with stochastic volatility. |
