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A new Fourier transform algorithm for value-at-risk


  • Claudio Albanese
  • Ken Jackson
  • Petter Wiberg


In this paper, we introduce a new Fourier method for computing value-at-risk for a portfolio with derivatives and for return models with fat tails. The new method does not assume that the characteristic function for the return model is known explicitly. We define a class of admissible models for returns and present statistical evidence that supports our approach. We discuss the details of the algorithm. The paper concludes with two applications of value-at-risk. Both examples illustrate the effect that changes in the models for portfolio value and for risk factor returns have on the value-at-risk surface.

Suggested Citation

  • Claudio Albanese & Ken Jackson & Petter Wiberg, 2004. "A new Fourier transform algorithm for value-at-risk," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 328-338.
  • Handle: RePEc:taf:quantf:v:4:y:2004:i:3:p:328-338 DOI: 10.1088/1469-7688/4/3/008

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    References listed on IDEAS

    1. John E. Angus, 1999. "A note on pricing Asian derivatives with continuous geometric averaging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 845-858, October.
    2. Min Dai, 2003. "One-state variable binomial models for European-/American-style geometric Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 288-295.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Jean-Pierre Fouque & Chuan-Hsiang Han, 2003. "Pricing Asian options with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(5), pages 353-362.
    5. Klaus Sandmann & J. Aase Nielsen, 2002. "Pricing of Asian exchange rate options under stochastic interest rates as a sum of options," Finance and Stochastics, Springer, vol. 6(3), pages 355-370.
    6. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
    7. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    8. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
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    Cited by:

    1. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters,in: The Risks of Financial Institutions, pages 513-548 National Bureau of Economic Research, Inc.
    2. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, Elsevier.
    3. Alessandro Ramponi, 2012. "Computing Quantiles in Regime-Switching Jump-Diffusions with Application to Optimal Risk Management: a Fourier Transform Approach," Papers 1207.6759,
    4. Chen, Rongda & Yu, Lean, 2013. "A novel nonlinear value-at-risk method for modeling risk of option portfolio with multivariate mixture of normal distributions," Economic Modelling, Elsevier, vol. 35(C), pages 796-804.

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