Credit Models and the crisis: The importance of systemic risk and extreme scenarios in valuation

We present three examples of credit products whose valuation poses challenging modeling problems related to armageddon scenarios and extreme losses, analyzing their behaviour pre- and in-crisis.

The products are Credit Index Options (CIOs), Collateralized Debt Obligations (CDOs), and Credit Valuation Adjustment (CVA) related products. We show that poor mathematical treatment of possibly vanishing numeraires in CIOs and lack of modes in the tail of the loss distribution in CDOs may lead to inaccurate valuation, both pre- and especially in crisis. We also consider the limits of copula models in trying to represent systemic risk in credit intensity models. We finally enlarge the picture and comment on a number of common biases in the public perception of modeling in relationship with the crisis.