Analytical Value-At-Risk with Jumps and Credit Risk

by Darrell Duffie of Stanford University, and
Jun Pan of Stanford University

November 29, 1999

Abstract: This paper provides an analytical method for computing value at risk, and other risk measures, for portfolios that may include options and other derivatives, with defaultable counterparties or borrowers. The risk setting is that of a classical multi-factor jump-diffusion for default intensities and asset returns, under which between-jump returns are correlated Brownian motions, with return jumps at Poisson arrivals that are jointly normally distributed. This allows for fat-tailed and skewed return distributions.

JEL Classification: G10.

AMS Classification: 90A09.

Keywords: Value-at-risk, credit risk, jump risk, analytical VaR, delta-gamma approximation.

Published in: Finance and Stochastics, Vol. 5, No. 2, (April 2001), pp. 155-180.

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