IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v52y2018i1d10.1007_s10614-017-9661-0.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10614-017-9661-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10614-017-9661-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Halis Sak & .Ismail Bac{s}ou{g}lu, 2015. "Efficient Randomized Quasi-Monte Carlo Methods For Portfolio Market Risk," Papers 1510.01593, arXiv.org.
    9. 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.
    10. Spassimir H. Paskov & Joseph F. Traub, 1995. "Faster Valuation of Financial Derivatives," Working Papers 95-03-034, Santa Fe Institute.
    11. 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.
    12. 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.
    13. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lu-Tao Zhao & Li-Na Liu & Zi-Jie Wang & Ling-Yun He, 2019. "Forecasting Oil Price Volatility in the Era of Big Data: A Text Mining for VaR Approach," Sustainability, MDPI, vol. 11(14), pages 1-20, July.
    2. Yingchao Zou & Kaijian He, 2022. "Forecasting Crude Oil Risk Using a Multivariate Multiscale Convolutional Neural Network Model," Mathematics, MDPI, vol. 10(14), pages 1-11, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Xiaoqun Wang & Ken Seng Tan, 2013. "Pricing and Hedging with Discontinuous Functions: Quasi-Monte Carlo Methods and Dimension Reduction," Management Science, INFORMS, vol. 59(2), pages 376-389, July.
    3. Tan, Ken Seng & Boyle, Phelim P., 2000. "Applications of randomized low discrepancy sequences to the valuation of complex securities," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1747-1782, October.
    4. Xiaoqun Wang & Ian H. Sloan, 2011. "Quasi-Monte Carlo Methods in Financial Engineering: An Equivalence Principle and Dimension Reduction," Operations Research, INFORMS, vol. 59(1), pages 80-95, February.
    5. Fredrik Åkesson & John P. Lehoczky, 2000. "Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities," Management Science, INFORMS, vol. 46(9), pages 1171-1187, September.
    6. Phelim P. Boyle & Adam W. Kolkiewicz & Ken Seng Tan, 2013. "Pricing Bermudan options using low-discrepancy mesh methods," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 841-860, May.
    7. Aintablian, Sebouh & Khoury, Wissam El, 2017. "A simulation on the presence of competing bidders in mergers and acquisitions," Finance Research Letters, Elsevier, vol. 22(C), pages 233-243.
    8. Eichler Andreas & Leobacher Gunther & Zellinger Heidrun, 2011. "Calibration of financial models using quasi-Monte Carlo," Monte Carlo Methods and Applications, De Gruyter, vol. 17(2), pages 99-131, January.
    9. Xiaoqun Wang, 2006. "On the Effects of Dimension Reduction Techniques on Some High-Dimensional Problems in Finance," Operations Research, INFORMS, vol. 54(6), pages 1063-1078, December.
    10. 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.
    11. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
    12. Dag Kolsrud, 2008. "Stochastic Ceteris Paribus Simulations," Computational Economics, Springer;Society for Computational Economics, vol. 31(1), pages 21-43, February.
    13. Martin B. Haugh & Leonid Kogan, 2004. "Pricing American Options: A Duality Approach," Operations Research, INFORMS, vol. 52(2), pages 258-270, April.
    14. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
    15. Boyle, Phelim & Imai, Junichi & Tan, Ken Seng, 2008. "Computation of optimal portfolios using simulation-based dimension reduction," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 327-338, December.
    16. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
    17. Beveridge, Christopher & Joshi, Mark & Tang, Robert, 2013. "Practical policy iteration: Generic methods for obtaining rapid and tight bounds for Bermudan exotic derivatives using Monte Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1342-1361.
    18. David Heath & Eckhard Platen, 2002. "A variance reduction technique based on integral representations," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 362-369.
    19. Jacob Lundgren & Yuri Shpolyanskiy, 2017. "Approaches to Asian Option Pricing with Discrete Dividends," Papers 1702.00994, arXiv.org, revised Mar 2021.
    20. Raimova, Gulnora, 2011. "Variance reduction methods at the pricing of weather options," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 21(1), pages 3-15.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:compec:v:52:y:2018:i:1:d:10.1007_s10614-017-9661-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.