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Analytical value-at-risk with jumps and credit risk


  • Jun Pan

    () (MIT Sloan School of Management, Cambridge, MA 02142, USA Manuscript)

  • Darrell Duffie

    () (Graduate School of Business, Stanford University, Stanford, CA 94305, USA)


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.

Suggested Citation

  • Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
  • Handle: RePEc:spr:finsto:v:5:y:2001:i:2:p:155-180
    Note: received: January 2000; final version received: May 2000

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    More about this item


    Value-at-risk; credit risk; jump risk; analytical VaR; delta-gamma approximation;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)


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