Lai, Kwok Tung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 64-66). / Abstracts in English and Chinese. / Abstract --- p.i / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.9 / Chapter 3 --- Preliminary Analysis of Data --- p.17 / Chapter 3.1 --- Data --- p.17 / Chapter 3.2 --- Preliminary Analysis of Unspanned Stochastic Volatility --- p.20 / Chapter 4 --- A Jump-Diffusion Model for Federal Funds Target Rate --- p.23 / Chapter 4.1 --- Model Specification --- p.23 / Chapter 4.2 --- Estimation Result --- p.31 / Chapter 5 --- Pricing and Hedging Performance of Interest Rate Derivatives --- p.34 / Chapter 5.1 --- Pricing Performance of Interest Rate Cap --- p.34 / Chapter 5.2 --- Hedging Performance of Interest Rate Caplet --- p.38 / Chapter 5.3 --- Hedging Performance of Interest Rate Straddle --- p.42 / Chapter 6 --- Conclusion --- p.49 / Figures --- p.51 / Tables --- p.55 / Bibliography --- p.64

This thesis comprises three essays that explore several theoretical and empirical features of affine term structure models. In the first essay, we focus on the ability of continuous-time affine term structure models to capture time variability in the second conditional moment. Using data on US Treasury yields, we conclude that affine term structure models are much better at extracting time-series volatility from the cross-section of yields than argued in the literature. These models have nonetheless difficulty capturing volatility dynamics at the short end of the maturity spectrum, perhaps indicating some form of segmentation between long-maturity and short-maturity bonds. These results are robust to the choice of sample period, interpolation method and estimation method. In the second essay, we propose the use of the unscented Kalman filter technique for the estimation of affine term structure models using non-linear instruments. We focus on swap rates and show that the unscented Kalman filter leads to important reductions in bias and gains in precision. The use of the unscented Kalman filter results in substantial improvements in out-of-sample forecasts. Our findings suggest that the unscented Kalman filter may prove to be a good approach for a number of problems in fixed income pricing in which the relationship between the state vector and the observations is nonlinear, such as the estimation of term structure models using interest rate derivatives or coupon bonds, and the estimation of quadratic term structure models. The third essay provides a tractable framework for pricing defaultable securities with recovery risk. Pricing solutions are explored for a large family of discrete-time affine processes and a five-factor Gaussian model is estimated on BBB and B Standard and Poor's yield indices. This rich econometric setup allows the model to simultaneously capture two important stylized facts of defaultable securities: The positive correlation between the loss given default and the intensity of default, and the negative correlation between the intensity of default and the risk-free interest rate.

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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. / 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. / by Ze-To Yau Man. / Source: Dissertation Abstracts International, Volume: 62-09, Section: A, page: 3138. / Supervisors: Jia He; Ying-foon Chow. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (p. 145-151). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest dissertations and theses, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.