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Modeling and Forecasting Realized Volatility

Listed author(s):
  • Torben G. Andersen
  • Tim Bollerslev
  • Francis X. Diebold
  • Paul Labys

This paper provides a general framework for integration of high-frequency intraday data into the measurement, modeling and forecasting of daily and lower frequency volatility and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on restrictive and complicated parametric multivariate ARCH or stochastic volatility models, which often perform poorly at intraday frequencies. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time series procedures for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we formally develop the links between the conditional covariance matrix and the concept of realized volatility. Next, using continuously recorded observations for the Deutschemark/Dollar and Yen /Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatitilies perform admirably compared to popular daily ARCH and related models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, gives rise to well-calibrated density forecasts of future returns, and correspondingly accurate quintile estimates. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.

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File URL: http://fic.wharton.upenn.edu/fic/papers/01/0101.pdf
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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 01-01.

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Date of creation: Jan 2001
Handle: RePEc:wop:pennin:01-01
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  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. Jacob A. Mincer & Victor Zarnowitz, 1969. "The Evaluation of Economic Forecasts," NBER Chapters, in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 3-46 National Bureau of Economic Research, Inc.
  3. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  4. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
  5. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
  6. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
  7. 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.
  8. Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, vol. 40(1), pages 87-96, January.
  9. Andersen, Torben G & Bollerslev, Tim, 1997. " Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns," Journal of Finance, American Finance Association, vol. 52(3), pages 975-1005, July.
  10. Nelson, Daniel B. & Foster, Dean P., 1995. "Filtering and forecasting with misspecified ARCH models II : Making the right forecast with the wrong model," Journal of Econometrics, Elsevier, vol. 67(2), pages 303-335, June.
  11. repec:cup:etheor:v:13:y:1997:i:6:p:808-17 is not listed on IDEAS
  12. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
  13. Yock Y. Chong & David F. Hendry, 1986. "Econometric Evaluation of Linear Macro-Economic Models," Review of Economic Studies, Oxford University Press, vol. 53(4), pages 671-690.
  14. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(06), pages 808-817, December.
  15. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
  16. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
  17. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
  18. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  19. 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.
  20. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
  21. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
  22. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
  23. Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January.
  24. 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.
  25. Bollerslev, Tim & Wright, Jonathan H., 2000. "Semiparametric estimation of long-memory volatility dependencies: The role of high-frequency data," Journal of Econometrics, Elsevier, vol. 98(1), pages 81-106, September.
  26. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2000. "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," Multinational Finance Journal, Multinational Finance Journal, vol. 4(3-4), pages 159-179, September.
  27. Bollerslev, Tim & Ole Mikkelsen, Hans, 1999. "Long-term equity anticipation securities and stock market volatility dynamics," Journal of Econometrics, Elsevier, vol. 92(1), pages 75-99, September.
  28. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
  29. Beltratti, Andrea & Morana, Claudio, 1999. "Computing value at risk with high frequency data," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 431-455, December.
  30. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237.
  31. Basak, Suleyman & Shapiro, Alexander, 2001. "Value-at-Risk-Based Risk Management: Optimal Policies and Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 371-405.
  32. 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.
  33. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  34. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  35. Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-844.
  36. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford.
  37. 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.
  38. Sheedy, Elizabeth, 1998. "Correlation in currency markets a risk-adjusted perspective," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 8(1), pages 59-82, January.
  39. Andersen, Torben G. & Bollerslev, Tim & Lange, Steve, 1999. "Forecasting financial market volatility: Sample frequency vis-a-vis forecast horizon," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 457-477, December.
  40. Hsieh, David A, 1991. " Chaos and Nonlinear Dynamics: Application to Financial Markets," Journal of Finance, American Finance Association, vol. 46(5), pages 1839-1877, December.
  41. 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.
  42. Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February.
  43. Hsieh, David A, 1989. "Modeling Heteroscedasticity in Daily Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 307-317, July.
  44. Taylor, Stephen J. & Xu, Xinzhong, 1997. "The incremental volatility information in one million foreign exchange quotations," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 317-340, December.
  45. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  46. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
  47. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
  48. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
  49. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
  50. S. Baranzoni & P. Bianchi & L. Lambertini, 2000. "Multiproduct Firms, Product Differentiation, and Market Structure," Working Papers 368, Dipartimento Scienze Economiche, Universita' di Bologna.
  51. King, Mervyn & Sentana, Enrique & Wadhwani, Sushil, 1994. "Volatility and Links between National Stock Markets," Econometrica, Econometric Society, vol. 62(4), pages 901-933, July.
  52. 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.
  53. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
  54. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November.
  55. 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.
  56. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
  57. Busse, Jeffrey A, 1999. "Volatility Timing in Mutual Funds: Evidence from Daily Returns," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1009-1041.
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