On Risk Neutral Pricing of CDOs

by Roy Mashal of the Columbia Business School

April 1, 2002

Abstract:  The aim of this paper is to explain the risks that are associated with the standard application of risk-neutral pricing for multi-name credit derivatives and especially to CDOs. Until the recent years CDOs were priced using rating based models, i.e. the rating companies rate the different tranches of the structure and the tranches were priced based on the spread of comparable rated bonds. This pricing method has two important shortcomings. First it is not applicable to the equity tranches, as these are not rated. Second, it ignores market data of the underlying portfolio; it resembles pricing a credit default swap based on the rating of the name. As a result, in recent years there is a strong tendency to develop new models that are based on risk-neutral pricing. Many market participants that are trying to develop such models have observed that the market prices are very different than the prices that are the outcome of their new models.

The problem with the standard application of risk-neutral pricing to multiname credit derivatives is that the risk-neutral measure for each underlying has a considerable component that reflects non-default risks. When pricing a multi-name instrument these non-default parts of the risk-neutral measure accumulate almost linearly. There is no economic reasoning for this rapid accumulation and that makes the disparity between the model prices and the market ones. We illustrate the main idea in a series of examples and give, mainly for illustration purposes, an alternative model that overcomes this problem.

JEL Classification: G11, G12, G13.

Keywords: Credit risk, credit derivatives, portfolio models, CDO.

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