CDS Option Valuation under Double-Exponential Jump-Diffusion (DEJD)

This study combines the empirical estimation of a Double-Exponential Jump-Diffusion (DEJD) process for a CDS index and the use of estimated parameters to price options on the index. In the first step we find Maximum Likelihood estimates for the diffusion volatility, the Poisson jump frequencies, and the mean sizes of up and down exponential jumps in the iTraxx Investment Grade index.In the second step we use the parameter estimates as inputs to the Kou (2002) pricing formula for European options under the DEJD.We estimate a rolling parameter time-series to generate the time series of option prices, then compare implied volatilities across strikes to the market-implied volatilities. While the empirical parameters produce realistic at-the-money implied volatilities, the model generates negative call-minus-put skews, which is at odds with positive volatility skews in the market. The large and persistent differences suggest the presence of risk premiums relating to large upward CDS jumps.The study develops a practical parametric approach to analyse the divergence between realised and market-implied distributions of CDS returns, and can be used to check pricing in illiquid markets