Pricing Defaultable Bonds With Multiscale Intensity Models

Based on the research of the stochastic volatility models by the formers, thispaper studies the multi-scale intensity model for the defaultable bonds.As the defaultable bonds are exposed to both interest rate risk and default risk,this paper characterizes the interest rate through Vasicek model. For the default risk,we make the following two tasks: 1.Establish single-scale model for the intensityof default, and derive the formula to price a defaultable bond by using Feynman-Kac theorem and asymptotic estimation. The simulation results show that single-scaleintensity model is applicable for short-term bonds. 2. .Establish multi-scale model forthe intensity of default by adding a slow diffusion process to the intensity function,and derive the approximate formula for the defaultable bond based on the work of 1.Finally, we do the empirical analysis for the multi-scale intensity model in connectionwith Chinese bond market. We use Treasury yield data as the risk-free rate of interestto estimate the parameters in the Vasicek model. We demonstrate the calibration of thecorporate yield curve on companies with different credit rating, and gain parametersby performing least-squares estimation respectively.In addition, the parameters arecompared for their practical significance.