Finance and Stochastics

, Volume 5, Issue 2, pp 155–180 | Cite as

Analytical value-at-risk with jumps and credit risk

  • Darrell Duffie
  • Jun Pan
Original Paper


This paper provides an analytical approximation 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.

Key words: Value-at-risk, credit risk, jump risk, analytical VaR, delta-gamma approximation 
JEL Classification: G10 
Mathematics Subject Classification (1991): 90A09 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Darrell Duffie
    • 1
  • Jun Pan
    • 2
  1. 1.Graduate School of Business, Stanford University, Stanford, CA 94305, USA (e-mail: US
  2. 2.MIT Sloan School of Management, Cambridge, MA 02142, USA (e-mail: US

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