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Time Series Simulation with Randomized Quasi-Monte Carlo Methods: An Application to Value at Risk and Expected Shortfall

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  • Yu-Ying Tzeng

    (Florida State University)

  • Paul M. Beaumont

    (Florida State University)

  • Giray Ökten

    (Florida State University)

Abstract

Quasi-Monte Carlo methods are designed to produce efficient estimates of simulated values but the error statistics of these estimates are difficult to compute. Randomized quasi-Monte Carlo methods have been developed to address this shortcoming. In this paper we compare quasi-Monte Carlo and randomized quasi-Monte Carlo techniques for simulating time series. We use randomized quasi-Monte Carlo to compute value-at-risk and expected shortfall measures for a stock portfolio whose returns follow a highly nonlinear Markov switching stochastic volatility model which does not admit analytical solutions for the returns distribution. Quasi-Monte Carlo methods are more accurate but do not allow the computation of reliable confidence intervals about risk measures. We find that randomized quasi-Monte Carlo methods maintain many of the advantages of quasi-Monte Carlo while also providing the ability to produce reliable confidence intervals of the simulated risk measures. However, the advantages in speed of convergence of randomized quasi-Monte Carlo diminish as the forecast horizon increases.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9661-0
    DOI: 10.1007/s10614-017-9661-0
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    References listed on IDEAS

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    1. Carvalho, Carlos M. & Lopes, Hedibert F., 2007. "Simulation-based sequential analysis of Markov switching stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4526-4542, May.
    2. S. Ninomiya & S. Tezuka, 1996. "Toward real-time pricing of complex financial derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 1-20.
    3. Okten, Giray & Eastman, Warren, 2004. "Randomized quasi-Monte Carlo methods in pricing securities," Journal of Economic Dynamics and Control, Elsevier, vol. 28(12), pages 2399-2426, December.
    4. Halis Sak & .Ismail Bac{s}ou{g}lu, 2015. "Efficient Randomized Quasi-Monte Carlo Methods For Portfolio Market Risk," Papers 1510.01593, arXiv.org.
    5. Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, vol. 42(6), pages 926-938, June.
    6. Xing Jin & Allen X. Zhang, 2006. "Reclaiming Quasi-Monte Carlo Efficiency in Portfolio Value-at-Risk Simulation Through Fourier Transform," Management Science, INFORMS, vol. 52(6), pages 925-938, June.
    7. François M. Longin, 1999. "Optimal margin level in futures markets: Extreme price movements," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(2), pages 127-152, April.
    8. So, Mike K P & Lam, K & Li, W K, 1998. "A Stochastic Volatility Model with Markov Switching," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 244-253, April.
    9. 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.
    10. Klaus Göggelmann & Peter Winker & Martin Schellhorn & Wolfgang Franz, 2000. "Quasi-Monte Carlo methods in stochastic simulations: An application to policy simulations using a disequilibrium model of the West German economy 1960-1994," Empirical Economics, Springer, vol. 25(2), pages 247-259.
    11. Jenny Li & Peter Winker, 2003. "Time Series Simulation with Quasi Monte Carlo Methods," Computational Economics, Springer;Society for Computational Economics, vol. 21(1), pages 23-43, February.
    12. Linlin Xu & Giray Ökten, 2015. "High-performance financial simulation using randomized quasi-Monte Carlo methods," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1425-1436, August.
    13. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
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