A Comparison between the stochastic intensity SSRD Model and the Market Model for CDS Options Pricing ∗

In this paper we investigate implied volatility patterns in the Shifted Square Root Diffusion (SSRD) model as functions of the model parameters. We begin by recalling the Credit Default Swap (CDS) options market model that is consistent with a market Black-like formula, thus introducing a notion of implied volatility for CDS options. We examine implied volatilies coming from SSRD prices and characterize the qualitative behavior of implied volatilities as functions of the SSRD model parameters. We introduce an analytical approximation for the SSRD implied volatility that follows the same patterns in the model parameters and that can be used to have a first rough estimate of the implied volatility following a calibration. We compute numerically the CDS-rate volatility smile for the adopted SSRD model. We find a decreasing pattern of SSRD implied volatilities in the interest-rate/intensity correlation. We check whether it is possible to assume zero correlation after the option maturity in computing the option price and provide an upper bound for the Monte Carlo standard error in cases where this is not possible. JEL classification code: G13. AMS classification codes: 60H10, 60J60, 60J75, 91B70 ∗Presented at the third Bachelier Conference, Chicago, July 21-24, 2004. We are grateful to Aurélien Alfonsi for helpful comments and suggestions