Pricing CDS Index Options in a Nonlinear Filtering Model

We derive practical formulas for forward starting index CDS spreads in the filtering model of Frey and Schmidt (2009). We also outline a novel approach for estimating the parameters in the filtering models by using time-series data of index CDS spreads and classical maximum-likelihood algorithms. The calibration-approach incorporates the Kushner-Stratonovich SDE for the dynamics of the filtering probabilities. The convenient formula for the forward starting index-CDS is a prerequisite for our estimation algorithm. Furthermore, a systematic study is performed in order to understand the impact of various model parameters on credit index options (and on the index itself).