Credit Default Swaps Calibration and Option Pricing with the SSRD Stochastic Intensity and Interest-Rate Model

In the present paper we introduce a two-dimensional shifted square-root diffusion (SSRD) model for interest rate derivatives and single-name credit derivatives, in a stochastic intensity framework. The SSRD is the unique model, to the best of our knowledge, allowing for an automatic calibration of the term structure of interest rates and of credit default swaps (CDS’s). Moreover, the model retains free dynamics parameters that can be used to calibrate option data, such as caps for the interest rate market and options on CDS’s in the credit market. The calibrations to the interest-rate market and to the credit market can be kept separate, thus realizing a superposition that is of practical value. We discuss the impact of interest-rate and default-intensity correlation on calibration and pricing, and test it by means of Monte Carlo simulation. We use a variant of Jamshidian’s decomposition to derive an analytical formula for CDS options under CIR++ stochastic intensity. Finally, we develop an analytical approximation based on a Gaussian dependence mapping for some basic credit derivatives terms involving correlated CIR processes. JEL classification code: G13. AMS classification codes: 60H10, 60J60, 60J75, 91B70