Analytic Improvement of the Saddle-point Approximation and Spread Risk Attribution in a Portfolio of Tranches

by Damian Taras of Dresdner Kleinwort Wasserstein,
Christopher Cloke-Browne of Dresdner Kleinwort Wasserstein, and
Evan Kalimtgis of Dresdner Kleinwort Wasserstein

August 4, 2005

Abstract: The saddle-point approximation has rapidly become an established technique for the evaluation of portfolio loss distributions and risk measures such as Value-at-Risk. In this paper, Damian Taras, Chistopher Cloke-Brown and Evan Kalimtgis describe an improved version of the saddle-point approximation which, in contrast to the original version, retains accuracy over the whole distribution. The key applications of the approach are the evaluation of portfolio risk measures and the pricing of structured credit instruments. The next step in the risk management of a portfolio of tranches is to consider movements of the loss distributions, due to spread risk. It is shown how spread risk measures may be evaluated for such a portfolio and a consistent procedure for the attribution of spread risk to names inside tranches is described for the first time. The existence of this procedure has wide-ranging implications for the management and hedging of structured credit portfolios.

Keywords: Saddle-point approximation, Structured credit, Risk attribution.

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