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

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 randomi...

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Bibliographic Details
Published inComputational economics Vol. 52; no. 1; pp. 55 - 77
Main Authors Tzeng, Yu-Ying, Beaumont, Paul M., Ökten, Giray
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2018
Springer Nature B.V
Subjects
Behavioral/Experimental Economics
Computer Appl. in Social and Behavioral Sciences
Computer simulation
Confidence intervals
Convergence
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Economics and Finance
Markov chains
Math Applications in Computer Science
Monte Carlo simulation
Operations Research/Decision Theory
Production methods
Randomization
Risk levels
Simulation
Time series
Volatility
Randomized Quasi-Monte Carlo
Time series simulation
Quasi-Monte Carlo
Expected shortfall
Value-at-risk
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Summary: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.
ISSN:0927-7099
1572-9974
DOI:10.1007/s10614-017-9661-0