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Efficient Randomized Quasi-Monte Carlo Methods For Portfolio Market Risk

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  • Halis Sak
  • .Ismail Bac{s}ou{g}lu

Abstract

We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance reduction methods for Monte Carlo simulation of portfolio market risk, there is no paper discussing combining the randomized quasi-Monte Carlo method with variance reduction techniques. In this paper, we combine the randomized quasi-Monte Carlo method with importance sampling and stratified importance sampling. Numerical results for realistic portfolio examples suggest that replacing pseudorandom numbers (Monte Carlo) with quasi-random sequences (quasi-Monte Carlo) in the simulations increases the robustness of the estimates once we reduce the effective dimension and the non-smoothness of the integrands.

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  • Halis Sak & .Ismail Bac{s}ou{g}lu, 2015. "Efficient Randomized Quasi-Monte Carlo Methods For Portfolio Market Risk," Papers 1510.01593, arXiv.org.
    • Handle: RePEc:arx:papers:1510.01593
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    References listed on IDEAS

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    1. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
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    3. Sak, Halis & Hörmann, Wolfgang & Leydold, Josef, 2010. "Efficient risk simulations for linear asset portfolios in the t-copula model," European Journal of Operational Research, Elsevier, vol. 202(3), pages 802-809, May.
    4. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    5. 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.
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    Cited by:

    1. Yu-Ying Tzeng & Paul M. Beaumont & Giray Ökten, 2018. "Time Series Simulation with Randomized Quasi-Monte Carlo Methods: An Application to Value at Risk and Expected Shortfall," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 55-77, June.

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