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

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Michael W. Brandt
Francis X. Diebold
April

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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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Paper provided by Wharton School Center for Financial Institutions, University of Pennsylvania in its series Center for Financial Institutions Working Papers with number 03-15.

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Handle: RePEc:wop:pennin:03-15

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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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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. 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)
  2. L. C. G. Rogers & Fanyin Zhou, 2008. "Estimating correlation from high, low, opening and closing prices," Quantitative Finance Papers 0804.0162, arXiv.org. [Downloadable!]
  3. 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)
  4. 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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  5. 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!]
  6. Theodoros Diasakos, 2008. "Comparative Statics of General Equilibrium Asset Prices," Carlo Alberto Notebooks 72, Collegio Carlo Alberto. [Downloadable!]
  7. 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!]
  8. 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!]
  9. 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!]
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  10. 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:
  11. Peter Christoffersen & Kris Jacobs & Gregory Vainberg, 2007. "Forward-Looking Betas," CREATES Research Papers 2007-39, School of Economics and Management, University of Aarhus. [Downloadable!]
  12. 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!]
  13. Denis Pelletier, 2004. "Regime Switching for Dynamic Correlations," Econometric Society 2004 North American Summer Meetings 230, Econometric Society. [Downloadable!]
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  14. Bo-Young Chang & Peter Christoffersen & Kris Jacobs & Gregory Vainberg, 2009. "Option-Implied Measures of Equity Risk," CIRANO Working Papers 2009s-33, CIRANO. [Downloadable!]
  15. 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!]
  16. 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!]
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  17. 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!]
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  18. Torben G. Andersen & Luca Benzoni, 2008. "Realized volatility," Working Paper Series WP-08-14, Federal Reserve Bank of Chicago. [Downloadable!]
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