Valuation of forward-starting CDOs

Abstract

A forward-starting collateralized debt obligation (FCDO) is a single tranche CDO with a specified premium starting at a specified future time. Pricing and hedging FCDOs have become an active research topic. We develop a generic method for pricing FCDOs, which is applicable to any model based on the conditional independence framework. The method converts the pricing of an FCDO to an equivalent synthetic CDO pricing problem. The value of the FCDO can then be computed by the well-developed methods for pricing the equivalent synthetic one. We illustrate our method by the market-standard Gaussian factor copula model. Numerical results demonstrate the accuracy and efficiency of our method.

Keywords:

• credit derivatives
• forward-starting CDOs
• conditional independence
• Gaussian factor copula

2000 AMS Subject Classifications :

• 91B28
• 65C20
• 65C50

Acknowledgements

The authors thank Alex Kreinin for proposing this interesting topic, for several very informative discussions that lead to the development of our method, and for his helpful comments on earlier drafts of the paper. This research was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

Notes

There are two different ways to interpret the relationship between tranche loss and pool loss of FCDOs. Since the pool loss before T does not affect the tranche loss, the tranche loss is a function of the pool loss after T only with attachment point a and detachment point b. If we interpret the tranche loss as a function of the pool loss from time 0, then the tranche has attachment point (a+L _T ) and detachment point (b+L _T ).

It is important to note here that our approach is quite general in the sense that any other method based on the conditional independence framework for pricing synthetic CDOs could be used instead of the Gaussian factor copula model to price the equivalent synthetic CDO.

While preparing this paper, we learned that De Prisco and Kreinin 6 developed a similar method to price FCDOs and Andersen applied a similar approach to numerically test the correlation of losses across time in FCDOs in his recent paper 1, although the method is not explained in detail there.