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

TL;DR

This paper introduces a mathematically rigorous approach to credit index option pricing that accounts for default risk and correlation, addressing limitations of the standard market approach especially in stressed market conditions.

Contribution

It proposes a novel subfiltration framework for arbitrage-free pricing of credit index options, incorporating default risk and correlation effects neglected previously.

Findings

The new pricing model aligns with market data post-2007 crisis.

Mispricing in standard models becomes significant in stressed markets.

The approach improves pricing accuracy for liquid credit index options.

Abstract

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 modeling 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.