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Efficient Simulation of Value at Risk with Heavy-Tailed Risk Factors

Author

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  • Cheng-Der Fuh

    (Graduate Institute of Statistics, National Central University, Jhong-Li, 32001 Taiwan, Republic of China)

  • Inchi Hu

    (Department of ISOM, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Ya-Hui Hsu

    (Global Statistics and Data Management, Abbott Laboratories, Abbott Park, Illinois 60064)

  • Ren-Her Wang

    (Department of Banking and Finance, Tamkang University, New Taipei City, 25137 Taiwan, Republic of China)

Abstract

Simulation of small probabilities has important applications in many disciplines. The probabilities considered in value-at-risk (VaR) are moderately small. However, the variance reduction techniques developed in the literature for VaR computation are based on large-deviations methods, which are good for very small probabilities. Modeling heavy-tailed risk factors using multivariate t distributions, we develop a new method for VaR computation. We show that the proposed method minimizes the variance of the importance-sampling estimator exactly, whereas previous methods produce approximations to the exact solution. Thus, the proposed method consistently outperforms existing methods derived from large deviations theory under various settings. The results are confirmed by a simulation study.

Suggested Citation

  • Cheng-Der Fuh & Inchi Hu & Ya-Hui Hsu & Ren-Her Wang, 2011. "Efficient Simulation of Value at Risk with Heavy-Tailed Risk Factors," Operations Research, INFORMS, vol. 59(6), pages 1395-1406, December.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:6:p:1395-1406
    DOI: 10.1287/opre.1110.0993
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    References listed on IDEAS

    as
    1. Winfried G. Hallerbach, 1999. "Decomposing Portfolio Value-at-Risk: A General Analysis," Tinbergen Institute Discussion Papers 99-034/2, Tinbergen Institute.
    2. Cheng-Der Fuh, 2004. "Efficient importance sampling for events of moderate deviations with applications," Biometrika, Biometrika Trust, vol. 91(2), pages 471-490, June.
    3. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269, July.
    4. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
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    Citations

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    Cited by:

    1. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy, 2018. "Ex-ante real estate Value at Risk calculation method," Annals of Operations Research, Springer, vol. 262(2), pages 257-285, March.
    2. Cheng-Der Fuh & Chuan-Ju Wang, 2017. "Efficient Exponential Tilting for Portfolio Credit Risk," Papers 1711.03744, arXiv.org, revised Apr 2019.
    3. Huei-Wen Teng & Cheng-Der Fuh & Chun-Chieh Chen, 2016. "On an automatic and optimal importance sampling approach with applications in finance," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1259-1271, August.
    4. Cheng-Der Fuh & Yanwei Jia & Steven Kou, 2023. "A General Framework for Importance Sampling with Latent Markov Processes," Papers 2311.12330, arXiv.org.
    5. Huei-Wen Teng, 2023. "Importance Sampling for Calculating the Value-at-Risk and Expected Shortfall of the Quadratic Portfolio with t-Distributed Risk Factors," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1125-1154, October.
    6. Cheng-Der Fuh & Huei-Wen Teng & Ren-Her Wang, 2018. "Efficient Simulation of Value-at-Risk Under a Jump Diffusion Model: A New Method for Moderate Deviation Events," Computational Economics, Springer;Society for Computational Economics, vol. 51(4), pages 973-990, April.

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