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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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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.

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Notes

  1. So et al. (1998) filter their returns data to eliminate a small negative persistence term in the mean equation (6) induced by the market crash at the end of the estimation period. For the purposes of our simulations, we treat the conditional mean returns as constant.

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Acknowledgements

We thank Dr. Ahmet Göncü for his helpful comments.

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Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, FL, 32306-4510, USA

    Yu-Ying Tzeng & Giray Ökten

  2. Department of Economics, Florida State University, Tallahassee, FL, 32306-2180, USA

    Paul M. Beaumont

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  1. Yu-Ying Tzeng
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  2. Paul M. Beaumont
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  3. Giray Ökten
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Correspondence to Paul M. Beaumont.

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Tzeng, YY., Beaumont, P.M. & Ökten, G. Time Series Simulation with Randomized Quasi-Monte Carlo Methods: An Application to Value at Risk and Expected Shortfall. Comput Econ 52, 55–77 (2018). https://doi.org/10.1007/s10614-017-9661-0

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