Pricing fixed income securities with a class of Markov regime switching processes

Markov regime switch models have been used in time series analysis to describe cyclical structural breaks in the economic data. Most of the works so far in this area are in the discrete time framework. This dissertation is a collection of papers on a class of continuous time Markov regime switching processes and their applications in pricing fixed income securities. The probabilistic properties including the backward equation and the characteristic functions are discussed for the regime switch mean reverting process. The advantage of the continuous time regime-switching processes in the setting of fixed income pricing is their analytical tractability. The exponential affine bond pricing structures are essentially preserved. The first application of these processes is to model the cyclical behavior of the interest rate. The bond pricing and the bond option pricing are discussed for this model class. As a discrete time approximation to the process, a regime switching AR(1) model is estimated for the monthly one month risk free interest rate data from January, 1970 to December, 1997. An improved non-linear filtration estimation based on the continuous time model is done for the coupon bond price data in the same period, using quasi-maximum likelihood method. The continuous time Markov regime switching processes are then used in pricing the bonds exposed to credit risks. Both rating transitions and spread innovations, under the recovery of market value assumption, justify the dynamics of credit spreads. This includes, as special cases, the pure Markov chain credit spread model and the default intensity based credit spread model. Two approaches, the correlated Brownian motions and the hidden Markov chain model, are suggested to describe the effect of the change of treasury interest rates on the credit spreads. In the more general settings, where analytically tractable solutions are not obtainable, finite difference schemes are discussed for the resulting system of partial differential equations of bond pricing. Finally, as a supplementary issue, this dissertation suggests a transformation and uses statistical analysis to improve the B-spline based estimation of the implied yield curve.