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A New Framework for Dynamic Credit Portfolio Loss Modelling

by Jakob Sidenius of the Royal Bank of Scotland,
Vladimir Piterbarg of Barclays Capital, and
Leif Andersen of Banc of America Securities

June 18, 2006

Abstract: We present the SPA framework, a novel approach to the modeling of the dynamics of portfolio default losses. In this framework, models are specified by a two layer process. The first layer models the dynamics of portfolio loss distributions in the absence of information about default times. This background process can be explicitly calibrated to the full grid of marginal loss distributions as implied by initial CDO tranche values indexed on maturity, as well as to the prices of suitable options. We give sufficient conditions for consistent dynamics. The second layer models the loss process itself as a Markov process conditioned on the path taken by the background process. The choice of loss process is non-unique. We present a number of choices, and discuss their advantages and disadvantages. Several concrete model examples are given, and valuation in the new framework is described in detail. Among the specific securities for which algorithms are presented are CDO tranche options and leveraged super-senior tranches.

Keywords: Dynamic model of CDOs, dynamic copula, conditional Markov process, options on tranches, option on CDO tranche, portfolio loss, SPA model, leveraged super-senior.

Published in: International Journal of Theoretical and Applied Finance, Vol. 11, No. 2 (March 2008), pp. 163-197.

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