Two Generic Frameworks for Credit Index Volatility Products and Their Application to Credit Index Options
by Taoufik Bounhar of Société Générale, and
October 14, 2008
Abstract: The extension of the single-name CDS option to the index case requires a careful analysis of the index "spread" -- including the joint distribution of the index spread and the index loss. We first introduce an index spread that is closer to the single-name case, called CDS-like spread. We then compare it to the spread quoted in the market, in terms of forward, change of probability measure, treatment of convexity, etc. These frameworks are not sufficient to deal with the index loss in the option payoff. To cope with this, we use the ad hoc spread adjustment designed for the option by Pedersen  ; alternatively, we suggest to work conditionally on the spread to capture the loss distribution. Our methodologies can be used with any dynamics for the index spreads introduced, but the variety of these dynamics is not explored here -- we essentially stick to the lognormal distribution as an example.
Keywords: credit index, index option, spread, volatility.