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On a Transform Method for the Efficient Computation of Conditional VaR (and VaR) with Application to Loss Models with Jumps and Stochastic Volatility

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  • Alessandro Ramponi

Abstract

In this paper we consider Fourier transform techniques to efficiently compute the Value-at-Risk and the Conditional Value-at-Risk of an arbitrary loss random variable, characterized by having a computable generalized characteristic function. We exploit the property of these risk measures of being the solution of an elementary optimization problem of convex type in one dimension for which Fast and Fractional Fourier transform can be implemented. An application to univariate loss models driven by L\'{e}vy or stochastic volatility risk factors dynamic is finally reported.

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  • Alessandro Ramponi, 2014. "On a Transform Method for the Efficient Computation of Conditional VaR (and VaR) with Application to Loss Models with Jumps and Stochastic Volatility," Papers 1407.1072, arXiv.org.
  • Handle: RePEc:arx:papers:1407.1072
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    File URL: http://arxiv.org/pdf/1407.1072
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    References listed on IDEAS

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    1. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    2. Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
    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. Naik, Vasanttilak, 1993. "Option Valuation and Hedging Strategies with Jumps in the Volatility of Asset Returns," Journal of Finance, American Finance Association, vol. 48(5), pages 1969-1984, December.
    5. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    6. G. Bormetti & V. Cazzola & G. Livan & G. Montagna & O. Nicrosini, 2009. "A Generalized Fourier Transform Approach to Risk Measures," Papers 0909.3978, arXiv.org, revised May 2012.
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