The CIR Pricing Model Of Default-risky Bonds With Liquidity Risk

In this thesis, we consider defaultable bonds market, in which the intensity of default time is driven by a continuous-time Markov chain. At first, under the assumption that recovery rate at default is zero, we obtain a semi-martingale decomposition of the process of the defaultable bond, from which one could see three different parts―default, interest-rate and credit-quality. Second, we consider the price process of a defaultable bond in the illiquid market. We introduce a new process to describe the liquidity spread. This new process not only can capture such empirical regularities of liquidity spreads as jumps and changes in its reference level during the business cycle, but also can preserve the non-negativity of the liquidity spreads under some condition on jump sizes. Then we also obtain an semi-martingale decomposition of the process of the defaultable bond in this illiquid market. Finally, using the previous results, the valuation model is extended to the case that the recovery rate is not zero at default. We also obtained the semi-martingale representations of bond price for both liquidity and illiquidity defaultable zero-coupon bonds.