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

摘要

In this work we consider three problems of the standard market approach topricing of credit index options: the definition of the index spread is notvalid in general, the usually considered payoff leads to a pricing which is notalways defined, and the candidate numeraire one would use to define a pricingmeasure is not strictly positive, which would lead to a non-equivalent pricingmeasure. We give a general mathematical solution to the three problems, based on anovel way of modeling the flow of information through the definition of a newsubfiltration. Using this subfiltration, we take into account consistently thepossibility of default of all names in the portfolio, that is neglected in thestandard market approach. We show that, while the related mispricing can benegligible for standard options in normal market conditions, it can becomehighly relevant for different options or in stressed market conditions. In particular, we show on 2007 market data that after the subprime creditcrisis the mispricing of the market formula compared to the no arbitrageformula we propose has become financially relevant even for the liquidCrossover Index Options.