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A no-arbitrage approach to range-based estimation of return covariances and correlations

Author

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  • Brandt, Michael W.
  • Diebold, Francis X.

Abstract

We extend the important idea of range-based volatility estimation to the multivariate case. In particular, we propose a range-based covariance estimator that is motivated by financial economic considerations (the absence of arbitrage), in addition to statistical considerations. We show that, unlike other univariate and multivariate volatility estimators, the range-based estimator is highly efficient yet robust to market microstructure noise arising from bid-ask bounce and asynchronous trading. Finally, we provide an empirical example illustrating the value of the high-frequency sample path information contained in the range-based estimates in a multivariate GARCH framework.

Suggested Citation

  • Brandt, Michael W. & Diebold, Francis X., 2004. "A no-arbitrage approach to range-based estimation of return covariances and correlations," CFS Working Paper Series 2004/07, Center for Financial Studies (CFS).
  • Handle: RePEc:zbw:cfswop:200407
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    References listed on IDEAS

    as
    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
    2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," Center for Financial Institutions Working Papers 02-27, Wharton School Center for Financial Institutions, University of Pennsylvania.
    3. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    4. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    5. Beckers, Stan, 1983. "Variances of Security Price Returns Based on High, Low, and Closing Prices," The Journal of Business, University of Chicago Press, vol. 56(1), pages 97-112, January.
    6. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    7. Ball, Clifford A & Torous, Walter N, 1984. "The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing," The Journal of Business, University of Chicago Press, vol. 57(1), pages 97-112, January.
    8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    9. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-491, July.
    10. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    11. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1047-1091, June.
    12. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," The Journal of Business, University of Chicago Press, vol. 65(2), pages 295-302, April.
    13. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    14. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    More about this item

    Keywords

    range-based estimation; volatility; covariance; correlation; absence of arbitrage; exchange rates; stock returns; bond returns; bid-ask bounce; asynchronous trading;

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets

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