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A No Arbitrage Fractional Cointegration Analysis Of The Range Based Volatility

  • Eduardo Rossi

    ()

    (Dipartimento di economia politica e metodi quantitativi, University of Pavia, Italy.)

  • Paolo Santucci de Magistris

    (Dipartimento di economia politica e metodi quantitativi, University of Pavia, Italy)

The no arbitrage relation between futures and spot prices implies an analogous relation between futures and spot volatilities as measured by daily range. Long memory features of the range-based volatility estimators of the two series are analyzed, and their joint dynamics are modeled via a fractional vector error correction model (FVECM), in order to explicitly consider the no arbitrage constraints. We introduce a two-step estimation procedure for the FVECM parameters and we show the properties by a Monte Carlo simulation. The out-of-sample forecasting superiority of FVECM, with respect to competing models, is documented. The results highlight the importance of giving fully account of long-run equilibria in volatilities in order to obtain better forecasts.

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Paper provided by Department of Economics and Business Economics, Aarhus University in its series CREATES Research Papers with number 2009-31.

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Length: 34
Date of creation: 15 Jul 2009
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Handle: RePEc:aah:create:2009-31
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. 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.
  2. Katarzyna Lasak, 2008. "Maximum likelihood estimation of fractionally cointegrated systems," CREATES Research Papers 2008-53, Department of Economics and Business Economics, Aarhus University.
  3. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  4. Michael W. Brandt & Francis X. Diebold, 2003. "A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," NBER Working Papers 9664, National Bureau of Economic Research, Inc.
  5. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
  6. John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
  7. Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a nonstationary fractional autoregressive model," Working Papers 1172, Queen's University, Department of Economics.
  8. Jinghong Shu & Jin E. Zhang, 2006. "Testing range estimators of historical volatility," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(3), pages 297-313, 03.
  9. Haldrup, Niels & Nielsen, Frank S. & Nielsen, Morten Ørregaard, 2010. "A vector autoregressive model for electricity prices subject to long memory and regime switching," Energy Economics, Elsevier, vol. 32(5), pages 1044-1058, September.
  10. Michael A. Pizzi & Andrew J. Economopoulos & Heather M. O'Neill, 1998. "An examination of the relationship between stock index cash and futures markets: A cointegration approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 18(3), pages 297-305, 05.
  11. Søren Johansen & Morten Ørregaard Nielsen, 2010. "Likelihood inference for a fractionally cointegrated vector autoregressive model," CREATES Research Papers 2010-24, Department of Economics and Business Economics, Aarhus University.
  12. Pierre Perron & Zhongjun Qu, 2008. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-004, Boston University - Department of Economics.
  13. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
  14. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
  15. Dwyer, Gerald P, Jr & Locke, Peter R & Yu, Wei, 1996. "Index Arbitrage and Nonlinear Dynamics between the S&P 500 Futures and Cash," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 301-32.
  16. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  17. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
  18. Andrew Patton, 2006. "Volatility Forecast Comparison using Imperfect Volatility Proxies," Research Paper Series 175, Quantitative Finance Research Centre, University of Technology, Sydney.
  19. Granger, Clive W J, 1986. "Developments in the Study of Cointegrated Economic Variables," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 48(3), pages 213-28, August.
  20. James B. Wiggins, 1992. "Estimating the volatility of S&P 500 futures prices using the extreme‐value method," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 12(3), pages 265-273, 06.
  21. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
  22. Cox, Charles C, 1976. "Futures Trading and Market Information," Journal of Political Economy, University of Chicago Press, vol. 84(6), pages 1215-37, December.
  23. Giuseppe Cavaliere & Anders Rahbek & A.M.Robert Taylor, 2009. "Co-integration Rank Testing under Conditional Heteroskedasticity," CREATES Research Papers 2009-22, Department of Economics and Business Economics, Aarhus University.
  24. Johansen, SØren, 2008. "A Representation Theory For A Class Of Vector Autoregressive Models For Fractional Processes," Econometric Theory, Cambridge University Press, vol. 24(03), pages 651-676, June.
  25. Davidson, James, 2002. "A model of fractional cointegration, and tests for cointegration using the bootstrap," Journal of Econometrics, Elsevier, vol. 110(2), pages 187-212, October.
  26. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
  27. Corbae, Dean & Ouliaris, Sam, 1988. "Cointegration and Tests of Purchasing Power Parity," The Review of Economics and Statistics, MIT Press, vol. 70(3), pages 508-11, August.
  28. Hualde, J. & Robinson, P.M., 2010. "Semiparametric inference in multivariate fractionally cointegrated systems," Journal of Econometrics, Elsevier, vol. 157(2), pages 492-511, August.
  29. Katsumi Shimotsu & Morten Ørregaard Nielsen, 2006. "Determining the Cointegrating Rank in Nonstationary Fractional Systems by the Exact Local Whittle Approach," Working Papers 1029, Queen's University, Department of Economics.
  30. Sowell, Fallaw, 1992. "Maximum likelihood estimation of stationary univariate fractionally integrated time series models," Journal of Econometrics, Elsevier, vol. 53(1-3), pages 165-188.
  31. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  32. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
  33. Joshy Jacob & Vipul, 2008. "Estimation and forecasting of stock volatility with range‐based estimators," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(6), pages 561-581, 06.
  34. 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.
  35. Michael Dueker & Richard Startz, 1998. "Maximum-Likelihood Estimation Of Fractional Cointegration With An Application To U.S. And Canadian Bond Rates," The Review of Economics and Statistics, MIT Press, vol. 80(3), pages 420-426, August.
  36. Bent Jesper Christensen & Paolo Santucci de Magistris, 2010. "Level Shifts in Volatility and the Implied-Realized Volatility Relation," CREATES Research Papers 2010-60, Department of Economics and Business Economics, Aarhus University.
  37. Brenner, Robin J. & Kroner, Kenneth F., 1995. "Arbitrage, Cointegration, and Testing the Unbiasedness Hypothesis in Financial Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(01), pages 23-42, March.
  38. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
  39. 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.
  40. 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.
  41. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  42. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
  43. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
  44. Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
  45. Chow, Ying-Foon & McAleer, Michael & Sequeira, John M, 2000. " Pricing of Forward and Futures Contracts," Journal of Economic Surveys, Wiley Blackwell, vol. 14(2), pages 215-53, April.
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