CDS Option Valuation with Double-Exponential Jumps

Abstract

We demonstrate how the Double-Exponential Jump-Diffusion (DEJD) process can be used to value iTraxx CDS options based on historical returns of the underlying CDS index. In the first step we find Maximum Likelihood estimates for the volatility of the normal component of returns and the Poisson frequencies and mean sizes of upward and downward exponential jumps. In results similar to Ramezani and Zeng’s (2006) application of DEJD to equities, we find that the DEJD provides a better fit than either a normal or single-jump specification. We take the additional step of using parameter estimates as inputs to the semi-closed European option pricing formula proposed by Kou (2002) under DEJD. We compare the model and market option prices across strikes and find that both the level and shape of the implied volatility smile match closely. Our findings suggest that the DEJD provides a realistic description of the joint role of positive and negative economic surprises in credit markets. In addition, the use of Maximum Likelihood with the option pricing model is a practical way to analyse divergence between realised and market-implied distributions of credit returns, and can be used to check pricing.