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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| Published in | Computational economics Vol. 52; no. 1; pp. 55 - 77 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.06.2018
Springer Nature B.V |
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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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| AbstractList | 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. |
| Author | Ökten, Giray Beaumont, Paul M. Tzeng, Yu-Ying |
| Author_xml | – sequence: 1 givenname: Yu-Ying surname: Tzeng fullname: Tzeng, Yu-Ying organization: Department of Mathematics, Florida State University – sequence: 2 givenname: Paul M. surname: Beaumont fullname: Beaumont, Paul M. email: beaumont@fsu.edu organization: Department of Economics, Florida State University – sequence: 3 givenname: Giray surname: Ökten fullname: Ökten, Giray organization: Department of Mathematics, Florida State University |
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| CitedBy_id | crossref_primary_10_3390_math10142413 crossref_primary_10_3390_su11143892 |
| Cites_doi | 10.1016/j.jco.2008.10.001 10.21314/JCF.1997.005 10.1016/0377-0427(94)00054-5 10.1137/0713071 10.1016/0377-0427(85)90035-4 10.1007/978-1-4614-7789-1_2 10.1515/mcma.1996.2.4.295 10.1145/272991.272995 10.1016/j.jedc.2003.11.003 10.1287/mnsc.42.6.926 10.1287/mnsc.1060.0505 10.1214/aos/1032526964 10.1016/j.csda.2006.07.019 10.1016/j.jco.2006.03.003 10.1137/S0036142994277468 10.1007/s001819900015 10.3905/jpm.1995.409541 10.1016/S0165-1889(97)00028-6 10.1002/(SICI)1096-9934(199904)19:2<127::AID-FUT1>3.0.CO;2-M 10.1080/13504869600000001 10.1007/s10614-013-9409-4 10.1090/S0025-5718-99-01019-4 10.1006/jcom.1998.0489 10.1214/aos/1031594731 10.1016/j.jco.2008.11.003 10.1023/A:1022289509702 10.1016/S0895-7177(00)00178-3 10.1006/jcom.1997.0463 10.3905/jfi.1997.408198 10.1016/0377-0427(90)90172-V 10.1080/14697688.2015.1032549 10.1137/1.9781611970081 10.3905/jod.1997.407985 10.1109/3CA.2010.5533637 10.1142/9789812709677_0069 10.1080/07350015.1998.10524758 |
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| Keywords | Randomized Quasi-Monte Carlo Time series simulation Quasi-Monte Carlo Expected shortfall Value-at-risk |
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| SubjectTerms | 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 |
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| Title | Time Series Simulation with Randomized Quasi-Monte Carlo Methods: An Application to Value at Risk and Expected Shortfall |
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