CDS INDEX OPTIONS UNDER INCOMPLETE INFORMATION

Abstract

We derive practical formulas for CDS index spreads in a credit risk model under incomplete information. The factor process driving the default intensities is not directly observable, and the filtering model of Frey & Schmidt (2012) is used as our setup. In this framework we find a computationally tractable expressions for the payoff of a CDS index option which naturally includes the so-called armageddon correction. A lower bound for the price of the CDS index option is derived and we provide explicit conditions on the strike spread for which this inequality becomes an equality. The bound is computationally feasible and do not depend the noise parameters in the filtering model. We outline how to explicitly compute the quantities involved in the lower bound for the price of the credit index option as well as implement and calibrate this model to market data. A numerical study is performed where we show that the lower bound in our model can be several hundred percent bigger compared with models which assume that the CDS index spreads follows a log-normal process. Also a systematic study is performed in order to understand the impact of various model parameters on CDS index options (and on the index itself).