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

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Author Info
Michael W. Brandt () (Department of Finance, University of Pennsylvania, and NBER)
Francis X. Diebold () (Departments of Economics, Finance and Statistics, University of Pennsylvania, and NBER)

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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.

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Publisher Info
Paper provided by Center for Financial Studies in its series CFS Working Paper Series with number 2004/07.

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Length: 37 pages
Date of creation: 07 Jan 2004
Date of revision:
Handle: RePEc:cfs:cfswop:wp200407

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Related research
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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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. [Downloadable!] (restricted)
  2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," NBER Technical Working Papers 0279, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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, 06. [Downloadable!] (restricted)
  8. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics. [Downloadable!]
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  9. Kunitomo, Naoto, 1992. "Improving the Parkinson Method of Estimating Security Price Volatilities," Journal of Business, University of Chicago Press, vol. 65(2), pages 295-302, April. [Downloadable!] (restricted)
  10. 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.
  11. Joel Hasbrouck, 1999. "The Dynamics of Discrete Bid and Ask Quotes," Journal of Finance, American Finance Association, vol. 54(6), pages 2109-2142, December. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Vanessa Mattiussi & Giulia Iori, 2006. "Currency Futures Volatility during the 1997 East Asian Crisis: An Application of Fourier Analysis," City University Economics Discussion Papers 06/09, Department of Economics, City University, London. [Downloadable!]
  2. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago. [Downloadable!]
  3. Bo-Young Chang & Peter Christoffersen & Kris Jacobs & Gregory Vainberg, 2009. "Option-Implied Measures of Equity Risk," CIRANO Working Papers 2009s-33, CIRANO. [Downloadable!]
  4. S. Sanfelici & M. E. Mancino, 2008. "Covariance estimation via Fourier method in the presence of asynchronous trading and microstructure noise," Economics Department Working Papers 2008-ME01, Department of Economics, Parma University (Italy). [Downloadable!]
  5. Silja Kinnebrock & Mark Podolskij, 2008. "An Econometric Analysis of Modulated Realised Covariance, Regression and Correlation in Noisy Diffusion Models," CREATES Research Papers 2008-23, School of Economics and Management, University of Aarhus. [Downloadable!]
    Other versions:
  6. Marwan Izzeldin & Ana-Maria Fuertes & Elena Kalotychou, 2008. "On forecasting daily stock volatility: the role of intraday information and market conditions," Working Papers 005439, Lancaster University Management School, Economics Department. [Downloadable!]
    Other versions:
  7. Lin Peng & Turan G. Bali, 2006. "Is there a risk-return trade-off? Evidence from high-frequency data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1169-1198. [Downloadable!]
  8. Martin Becker & Ralph Friedmann & Stefan Klößner & Walter Sanddorf-Köhle, 2007. "A Hausman test for Brownian motion," AStA Advances in Statistical Analysis, Springer, vol. 91(1), pages 3-21, March. [Downloadable!] (restricted)
  9. Theodoros Diasakos, 2008. "Comparative Statics of General Equilibrium Asset Prices," Carlo Alberto Notebooks 72, Collegio Carlo Alberto. [Downloadable!]
  10. Olli Castrén & Stefano Mazzotta, 2005. "Foreign exchange option and returns based correlation forecasts - evaluation and two applications," Working Paper Series 447, European Central Bank. [Downloadable!]
  11. 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. [Downloadable!]
    Other versions:
  12. Peter Christoffersen & Kris Jacobs & Gregory Vainberg, 2007. "Forward-Looking Betas," CREATES Research Papers 2007-39, School of Economics and Management, University of Aarhus. [Downloadable!]
  13. Yan-Leung Cheung & Yin-Wong Cheung & Alan T. K. Wan, 2009. "A High-Low Model of Daily Stock Price Ranges," Working Papers 032009, Hong Kong Institute for Monetary Research. [Downloadable!]
    Other versions:
  14. L. C. G. Rogers & Fanyin Zhou, 2008. "Estimating correlation from high, low, opening and closing prices," Quantitative Finance Papers 0804.0162, arXiv.org. [Downloadable!]
  15. Kim Christensen & Mark Podolskij & Mathias Vetter, 2009. "Bias-correcting the realized range-based variance in the presence of market microstructure noise," Finance and Stochastics, Springer, vol. 13(2), pages 239-268, April. [Downloadable!] (restricted)
  16. Turan Bali & Kamil Yilmaz, 2009. "The Intertemporal Relation between Expected Return and Risk on Currency," TÜSİAD-Koç University Economic Research Forum Working Papers 0909, TUSIAD-Koc University Economic Research Forum. [Downloadable!]
  17. Yin-Wong Cheung, 2007. "An empirical model of daily highs and lows," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(1), pages 1-20. [Downloadable!]
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  18. Denis Pelletier, 2004. "Regime Switching for Dynamic Correlations," Econometric Society 2004 North American Summer Meetings 230, Econometric Society. [Downloadable!]
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