Intensity based Model for CDS Spread with Time-Changed Levy Process

In credit default swap (CDS) pricing, it is important to nd both exible and tractable models. In this paper, by setting up a time-changed Levy process subordinated by Ornstein-Uhlenbeck we present an intensity based model for the CDS spread. We apply a stochastic volatility model driven by in nite activity Levy processes that is consistent with phenomenon observed in underlying asset. Some typical Levy process, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance are investigated. The asset value processes of these models are able to t any valid CDS curve that would possibly be of both nite variations. Furthermore, we obtain a closed form formula for its survival function in terms of characteristic function of the time-changed Levy where the default is triggered by a predetermined barrier. This pricing formula is well calibrated on the CDS market by an intelligent global optimization search algorithm that improves the calibration quality of the tted models.