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Efficient Simulation of Value-at-Risk Under a Jump Diffusion Model: A New Method for Moderate Deviation Events

Author

Listed:
  • Cheng-Der Fuh

    (National Central University)

  • Huei-Wen Teng

    (National Chiao Tung University)

  • Ren-Her Wang

    (Tamkang University)

Abstract

Importance sampling is a powerful variance reduction technique for rare event simulation, and can be applied to evaluate a portfolio’s Value-at-Risk (VaR). By adding a jump term in the geometric Brownian motion, the jump diffusion model can be used to describe abnormal changes in asset prices when there is a serious event in the market. In this paper, we propose an importance sampling algorithm to compute the portfolio’s VaR under a multi-variate jump diffusion model. To be more precise, an efficient computational procedure is developed for estimating the portfolio loss probability for those assets with jump risks. And the tilting measure can be separated for the diffusion and the jump part under the assumption of independence. The simulation results show that the efficiency of importance sampling improves over the naive Monte Carlo simulation from 9 to 277 times under various situations.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:51:y:2018:i:4:d:10.1007_s10614-017-9654-z
    DOI: 10.1007/s10614-017-9654-z
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    References listed on IDEAS

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    1. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    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. 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.
    5. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    6. Naik, Vasanttilak & Lee, Moon, 1990. "General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 493-521.
    7. 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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