An Implied Loss Model

by Martijn van der Voort of Abn Amro Bank & Erasmus University Rotterdam

May 11, 2006

Abstract: In this paper we present a model which is, by construction, consistent with observed market quotes for standard CDO tranches. The model is closely related to implied tree methods which can be used for valuing exotic equity derivatives consistent with observed market quotes for vanilla European call and put options. Rather than modelling default events for each name in the basket, the total basket loss is modelled directly and calibrated to CDO prices by construction.

The proposed model has multiple important uses. First, the model can be used as a tool for avoiding arbitrage opportunities when pricing standard CDO tranches. This is a problem which is hard to solve when using the market standard Base Correlation approach in combination with interpolation and extrapolation rules. As a result the proposed model can be used to determine an arbitrage free distribution for portfolio losses for all maturities, which can subsequently be used as input to the more complex HJM type models which have recently become popular. Second, it provides us with a straightforward method for valuing Forward Starting CDOs, FDOs, consistently with observed market quotes on CDO tranches.

A number of tests have been performed which have shown that the model performs well for pricing FDOs, when compared to a number of different factor copula models. Moreover, even under the assumption of heterogeneity of the basket in terms of recovery rates, the performance of the model is still impressive.

Apart from performance tests, some additional tests have been presented in this paper, which show that the limited amount of market data still leads to a large amount of uncertainty in FDO prices.

Finally forward Base Correlation skews implied by the model are considered and these are found to be rather stable.

JEL Classification: G13.

Keywords: Credit Derivatives, CDOs, Forward Starting CDOs, Dependence Modelling, Base Correlation, Factor Copula.

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