Pricing and risk management of fixed income securities and their derivatives

This thesis is a collection of two essays that explore issues related to the pricing and the risk management of fixed income securities and derivatives in US markets. In the context of the pricing of derivatives, the arbitrage-free pricing approach is adopted. For the issue of risk management, the estimation of Value-at-Risk is presented.; In the first essay, this thesis provides a new methodology for pricing the fixed income derivatives using the arbitrage-free Heath-Jarrow-Morton model (hereafter HJM model). While, most previous empirical implementations of HJM model like that by Amin and Morton (1994) are focused on one-factor model only, the essay attempts to extend the test to a two-factor model that could further capture the subtleties of the forward rate process. The two-factor Poisson-Gaussian version of HJM model derived by Das (1999) that incorporates a jump component as the second state variables is used to value the actively traded Eurodollar futures call option under the jump diffusion lattice. The one-factor and two-factor models are compared with five volatility functions to evaluate the degree of pricing improvement by the inclusion of one more state variable.; The essay also addresses the critical issues on the volatility structure of forward rates that affect the pricing performance of option under the HJM framework. Three new volatility specifications are constructed to estimate the traded options. The first volatility function is the humped & curvature adjusted model that allows for humped shape in volatility structure and better adjustment to the curvature of the term structure. The second is the humped & proportional model that exhibits humped volatility feature and is proportional to the forward rate. The third function is the linear exponential model that is extended from Vasicek's exponential model. They are compared with two other volatility structures developed by previous researchers on their pricing performances. The alternative models are examined from the perspectives of in-sample fit, out-of-sample pricing and hedging.; The second essay develops an approach for estimating the Value-at-Risk (hereafter VaR) with jumps using the Monte Carlo simulation method. It is by far the first paper to estimate VaR using the HJM model. The paper takes the framework of the Poisson Gaussian version of HJM model (hereafter, HJM jump-diffusion model) from Das (1999). The model is incorporated with a jump component to capture the kurtosis effect in the daily price changes. As a result, the HJM jump-diffusion model allows for the fat tailed and skewed distribution of return in most financial markets. The simulation process is expedited by using variance reduction method. The model is used for calculating the VaR of a portfolio consisting of the fixed income derivatives. The accuracy of the VaR estimates is examined statistically at the VaR at confidence level of both 95 and 99 percent.