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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.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Minneapolis in its series Discussion Paper / Institute for Empirical Macroeconomics with number 96.

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Date of creation: 1994
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Handle: RePEc:fip:fedmem:96

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Keywords: Foreign exchange rates;

References

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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, American Statistical Association, vol. 20(1), pages 69-87, January.
  2. Baillie, Richard T & Bollerslev, Tim, 1989. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 7(3), pages 297-305, July.
  3. Andrew C Harvey & N.G. Shephard, 1993. "Estimation and Testing of Stochastic Variance Models," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /1993/268, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  4. Ronald Mahieu & Peter Schotman, 1994. "Neglected Common Factors in Exchange Rate Volatility," CEPR Financial Markets Paper, European Science Foundation Network in Financial Markets, c/o C.E.P.R, 77 Bastwick Street, London EC1V 3PZ 0041, European Science Foundation Network in Financial Markets, c/o C.E.P.R, 77 Bastwick Street, London EC1V 3PZ.
  5. 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., John Wiley & Sons, Ltd., vol. 8(S), pages S153-73, Suppl. De.
  6. Schotman, Peter C., 1994. "Priors For The Ar(1) Model: Parameterization Issues and Time Series Considerations," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(3-4), pages 579-595, August.
  7. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  8. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, Econometric Society, vol. 41(1), pages 135-55, January.
  9. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  10. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, Econometric Society, vol. 51(2), pages 485-505, March.
  11. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 239-265.
  12. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  13. Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 4(2), pages 183-204.
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Citations

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Cited by:
  1. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9613, Universite de Montreal, Departement de sciences economiques.
  2. Danielsson, Jon, 1998. "Multivariate stochastic volatility models: Estimation and a comparison with VGARCH models," Journal of Empirical Finance, Elsevier, Elsevier, vol. 5(2), pages 155-173, June.
  3. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  4. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, Elsevier, vol. 3(1), pages 15-102, May.
  5. repec:dgr:uvatin:2098067 is not listed on IDEAS
  6. Eric Jacquier & Nicholas G. Polson & Peter Rossi, . "Stochastic Volatility: Univariate and Multivariate Extensions," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 19-95, Wharton School Rodney L. White Center for Financial Research.
  7. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1995. "Estimation of Stochastic Volatility Models with Diagnostics," Working Papers, Duke University, Department of Economics 95-36, Duke University, Department of Economics.
  8. Per Bjarte Solibakke, 2003. "Validity of discrete-time stochastic volatility models in non-synchronous equity markets," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 9(5), pages 420-448.
  9. van der Sluis Pieter J., 1997. "EmmPack 1.01: C/C++ Code for Use with Ox for Estimation of Univariate Stochastic Volatility Models with the Efficient Method of Moments," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(3), pages 1-20, October.
  10. 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.
  11. Éric Jacquier & Nicholas G. Polson & Peter E. Rossi, 1995. "Models and Priors for Multivariate Stochastic Volatility," CIRANO Working Papers, CIRANO 95s-18, CIRANO.
  12. 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.

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