Pricing and Evaluating a Bond Portfolio Using a Regime Switching Markov Model

We apply a regime switching Markov chain model to determine bond prices. Our work builds upon the work of Thomas, Allen amp; Morkel-Kingsbury (2002) and Jarrow, Lando amp; Turnbull (1997). The interest rate process and credit rating migration process are considered. Our aim is to study the price evolution of a portfolio of defaultable bonds. We are interested in determining the density process to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) a year ahead. Whereas Thomas et al. describe a model under the pricing measure only, our model takes into consideration both the physical and pricing measures. We also describe the whole (risk free) forward rate curve, with appropriate conditions for the absence of arbitrage, while Thomas et al. describe the spot rate process. Most bond models make use of zero coupon bond prices. By using bond stripping we are able to discover zero coupon bond prices for bonds of different ratings. We use a mathematical programming approach to strip coupons and minimise squared error, subject to no arbitrage constraints