Arbitrage-free pricing of Credit Index Options. The no-armageddon pricing measure and the role of correlation after the subprime crisis

In this work we consider three problems of the standard market approach to pricing of credit index options: the definition of the index spread is not valid in general, the usually considered payoff leads to a pricing which is not always defined, and the candidate numeraire one would use to define a pricing measure is not strictly positive, which would lead to a non-equivalent pricing measure. We give a general mathematical solution to the three problems, based on a novel way of modelling the flow of information through the definition of a new subfiltration. Using this subfiltration, we take into account consistently the possibility of default of all names in the portfolio, that is neglected in the standard market approach. We show that, while the related mispricing can be negligible for standard options in normal market conditions, it can become highly relevant for different options or in stressed market conditions. In particular, we show on 2007 market data that after the subprime credit crisis the mispricing of the market formula compared to the no arbitrage formula we propose has become financially relevant even for the liquid Crossover Index Options. ∗Corresponding Author. We thank Tomasz Bielecki, Paolo Longato and Lutz Schloegl for helpful comments and discussion. Tomasz Bielecki also signalled us that a related work on credit index options is being developed independently in Armstrong and Rutkowski (2007) This paper expresses the views of its authors and does not represent the opinion of Banca IMI or FitchRatings, and neither organization is responsible for any use which maybe made of its contents.