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Range-Based Estimation of Stochastic Volatility Models or Exchange Rate Dynamics are More Interesting Than You Think

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Author Info
Sassan Alizadeh
Michael W. Brandt
Francis X. Diebold

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Abstract

We propose using the price range, a recently-neglected volatility proxy with a long history in finance, in the estimation of stochastic volatility models. We show both theoretically and empirically that the log range is approximately Gaussian, in sharp contrast to popular volatility proxies, such as log absolute or squared returns. Hence Gaussian quasi-maximum likelihood estimation based on the range is not only simple, but also highly efficient. We illustrate and enrich our theoretical results with a Monte Carlo study and a substantive empirical application to daily exchange rate volatility. Our empirical work produces sharp conclusions. In particular, the evidence points strongly to the inadequacy of one-factor volatility models, favoring instead two-factor models with one highly persistent factor and one quickly mean reverting factor.

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Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 00-28.

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Date of creation: Dec 1999
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Handle: RePEc:wop:pennin:00-28

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  8. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
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  16. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
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  21. Andersen, Torben G. & Sorensen, Bent E., 1997. "GMM and QML asymptotic standard deviations in stochastic volatility models: Comments on Ruiz (1994)," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 397-403. [Downloadable!] (restricted)
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  25. 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. [Downloadable!] (restricted)
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  27. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 247-64, April. [Downloadable!] (restricted)
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