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An empirical application of stochastic volatility models


  • Ronald J. Mahieu

    (Erasmus University, Rotterdam)

  • Peter C. Schotman

    (Maastricht University, PO Box 616, 6200 MD Maastricht, The Netherlands)


This paper studies the empirical performance of stochastic volatility models for twenty years of weekly exchange rate data for four major currencies. We concentrate on the effects of the distribution of the exchange rate innovations for both parameter estimates and for estimates of the latent volatility series. The density of the log of squared exchange rate innovations is modelled as a flexible mixture of normals. We use three different estimation techniques: quasi-maximum likelihood, simulated EM, and a Bayesian procedure. The estimated models are applied for pricing currency options. The major findings of the paper are that: (1) explicitly incorporating fat-tailed innovations increases the estimates of the persistence of volatility dynamics; (2) the estimation error of the volatility time series is very large; (3) this in turn causes standard errors on calculated option prices to be so large that these prices are rarely significantly different from a model with constant volatility. © 1998 John Wiley & Sons, Ltd.

Suggested Citation

  • Ronald J. Mahieu & Peter C. Schotman, 1998. "An empirical application of stochastic volatility models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(4), pages 333-360.
  • Handle: RePEc:jae:japmet:v:13:y:1998:i:4:p:333-360

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    References listed on IDEAS

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    Cited by:

    1. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    2. Salima El Kolei, 2013. "Parametric estimation of hidden stochastic model by contrast minimization and deconvolution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 1031-1081, November.
    3. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    4. Pascale VALERY (HEC-Montreal) & Jean-Marie Dufour (University of Montreal), 2004. "A simple estimation method and finite-sample inference for a stochastic volatility model," Econometric Society 2004 North American Summer Meetings 153, Econometric Society.
    5. Athanasia Gavala & Nikolay Gospodinov & Deming Jiang, 2006. "Forecasting volatility," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(6), pages 381-400.
    6. Yu, Jun & Yang, Zhenlin & Zhang, Xibin, 2006. "A class of nonlinear stochastic volatility models and its implications for pricing currency options," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2218-2231, December.
    7. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
    8. Bauwens, Luc & Lubrano, Michel, 2002. "Bayesian option pricing using asymmetric GARCH models," Journal of Empirical Finance, Elsevier, vol. 9(3), pages 321-342, August.
    9. Hardiyanto, A.V., 2007. "Daily Rp/USD stochastic volatility and the policy implication lesson," Journal of Asian Economics, Elsevier, vol. 18(1), pages 237-256, February.
    10. Dinghai Xu, 2009. "The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey," Working Papers 0904, University of Waterloo, Department of Economics, revised Sep 2009.
    11. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    12. Damiano Brigo & Bernard Hanzon, 2008. "On three filtering problems arising in mathematical finance," Papers 0812.4050,
    13. Dominik Bertsche & Robin Braun, 2017. "Identification of Structural Vector Autoregressions by Stochastic Volatility," Working Paper Series of the Department of Economics, University of Konstanz 2017-11, Department of Economics, University of Konstanz.
    14. Feldmann, David & Härdle, Wolfgang K. & Hafner, Christian M. & Hoffmann, Marc & Lepskii, Oleg V. & Tsybakov, Alexandre B., 1998. "Flexible stochastic volatility structures for high frequency financial data," SFB 373 Discussion Papers 1998,34, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    15. Dinghai Xu & John Knight, 2013. "Stochastic volatility model under a discrete mixture-of-normal specification," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 37(2), pages 216-239, April.
    16. Yasuhiro Omori & Siddhartha Chib & Neil Shephard & Jouchi Nakajima, 2004. "Stochastic volatility with leverage: fast likelihood inference," Economics Papers 2004-W19, Economics Group, Nuffield College, University of Oxford.
    17. Brigo, Damiano & Hanzon, Bernard, 1998. "On some filtering problems arising in mathematical finance," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 53-64, May.
    18. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    19. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
    20. Ronald Mahieu & Rob Bauer, 1998. "A Bayesian analysis of stock return volatility and trading volume," Applied Financial Economics, Taylor & Francis Journals, vol. 8(6), pages 671-687.
    21. Ibrahim Chowdhury & Lucio Sarno, 2004. "Time-Varying Volatility in the Foreign Exchange Market: New Evidence on its Persistence and on Currency Spillovers," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 31(5-6), pages 759-793.
    22. Salima El Kolei, 2012. "Parametric estimation of hidden stochastic model by contrast minimization and deconvolution: application to the Stochastic Volatility Model," Papers 1202.2559,, revised Mar 2013.
    23. Shirley J. Huang & Qianqiu Liu & Jun Yu, 2007. "Realized Daily Variance of S&P 500 Cash Index: A Revaluation of Stylized Facts," Annals of Economics and Finance, Society for AEF, vol. 8(1), pages 33-56, May.
    24. Anna Pajor, 2009. "A Note on Option Pricing with the Use of Discrete-Time Stochastic Volatility Processes," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 1(1), pages 71-81, March.

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