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A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations

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  • Michael W. Brandt

    ()
    (The Fuqua School of Business, Duke University)

  • Francis X. Diebold

    ()
    (Department of Economics, University of Pennsylvania)

Abstract

We extend range-based volatility estimation to the multivariate case. In particular, we propose a range-based covariance estimator motivated by a key financial economic consideration, the absence of arbitrage, in addition to statistical considerations. We show that this estimator is highly efficient yet robust to market microstructure noise arising from bid-ask bounce and asynchronous trading.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 03-013.

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Length: 22 pages
Date of creation: 01 Sep 2001
Date of revision: 01 Apr 2003
Handle: RePEc:pen:papers:03-013

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

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  1. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers, Duke University, Department of Economics 02-12, Duke University, Department of Economics.
  2. Sassan Alizadeh & Michael W. Brandt & Francis X. Diebold, 2002. "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, American Finance Association, American Finance Association, vol. 57(3), pages 1047-1091, 06.
  3. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  4. 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, American Statistical Association, vol. 96, pages 42-55, March.
  5. Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
  6. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, American Finance Association, vol. 42(2), pages 281-300, June.
  7. Beckers, Stan, 1983. "Variances of Security Price Returns Based on High, Low, and Closing Prices," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 56(1), pages 97-112, January.
  8. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 53(1), pages 61-65, January.
  9. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 02-27, Wharton School Center for Financial Institutions, University of Pennsylvania.
  10. 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, University of Chicago Press, vol. 73(3), pages 477-91, July.
  11. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 61(1), pages 43-76, July.
  12. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 65(2), pages 295-302, April.
  13. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, Elsevier, vol. 19(1), pages 3-29, September.
  14. 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, University of Chicago Press, vol. 57(1), pages 97-112, January.
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