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Stochastic volatility and the distribution of exchange rate news

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  • Ronald Mahieu
  • Peter Schotman

Abstract

This paper studies the empirical performance of stochastic volatility models for twenty years of weekly exchange rate data. We concentrate on the effects of the distribution of the exchange rate innovations for parameter estimates and for estimates of the latent volatility series. We approximate the density of the log of exchange rate innovations by a mixture of normals. The major findings of the paper are that: (1) explicitly incorporating fat-tailed innovations increases the estimates of the persistence of volatility dynamics; (ii) estimates of the latent volatility series depend strongly on the estimation technique; (iii) the estimation error of the volatility time series is so large that finance applications to option pricing should be interpreted with care. We reach these conclusions using three different estimation techniques: quasi maximum likelihood, simulated EM, and a Bayesian procedure based on the Gibbs sampler.

Suggested Citation

  • Ronald Mahieu & Peter Schotman, 1994. "Stochastic volatility and the distribution of exchange rate news," Discussion Paper / Institute for Empirical Macroeconomics 96, Federal Reserve Bank of Minneapolis.
  • Handle: RePEc:fip:fedmem:96
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    References listed on IDEAS

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    1. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
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    3. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    4. repec:cep:stiecm:/1993/268 is not listed on IDEAS
    5. Mahieu, Ronald & Schotman, Peter, 1994. "Neglected common factors in exchange rate volatility," Journal of Empirical Finance, Elsevier, vol. 1(3-4), pages 279-311, July.
    6. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    7. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
    8. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. repec:bla:restud:v:65:y:1998:i:3:p:361-93 is not listed on IDEAS
    11. Danielsson, J & Richard, J-F, 1993. "Accelerated Gaussian Importance Sampler with Application to Dynamic Latent Variable Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 153-173, Suppl. De.
    12. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    13. Schotman, Peter C., 1994. "Priors For The Ar(1) Model: Parameterization Issues and Time Series Considerations," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 579-595, August.
    14. Andrew C Harvey & N.G. Shephard, 1993. "Estimation and Testing of Stochastic Variance Models," STICERD - Econometrics Paper Series 268, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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    Citations

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    Cited by:

    1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November.
    3. Danielsson, Jon, 1998. "Multivariate stochastic volatility models: Estimation and a comparison with VGARCH models," Journal of Empirical Finance, Elsevier, vol. 5(2), pages 155-173, June.
    4. Eric Jacquier & Nicholas G. Polson & Peter Rossi, "undated". "Stochastic Volatility: Univariate and Multivariate Extensions," Rodney L. White Center for Financial Research Working Papers 19-95, Wharton School Rodney L. White Center for Financial Research.
    5. Per Bjarte Solibakke, 2003. "Validity of discrete-time stochastic volatility models in non-synchronous equity markets," The European Journal of Finance, Taylor & Francis Journals, vol. 9(5), pages 420-448.
    6. George J. Jiang & Pieter J. van der Sluis, 1998. "Pricing Stock Options under Stochastic Volatility and Stochastic Interest Rates with Efficient Method of Moments Estimation," Tinbergen Institute Discussion Papers 98-067/4, Tinbergen Institute.
    7. Sangjoon Kim, Neil Shephard & Siddhartha Chib, "undated". "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
    8. Éric Jacquier & Nicholas G. Polson & Peter E. Rossi, 1995. "Models and Priors for Multivariate Stochastic Volatility," CIRANO Working Papers 95s-18, CIRANO.
    9. Kondo, Koji, 1997. "Statistical analysis of foreign exchange rates: application of cointegration model and regime-switching stochastic volatility model," ISU General Staff Papers 1997010108000012997, Iowa State University, Department of Economics.
    10. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.

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    Keywords

    Foreign exchange rates;

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