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Analytic Evaluation of Volatility Forecasts

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  • Torben G. Andersen
  • Tim Bollerslev
  • Nour Meddahi

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Abstract

The development of estimation and forecasting procedures using empirically realistic continuous-time stochastic volatility models is severely hampered by the lack of closed-form expressions for the transition densities of the observed returns. In response to this, Andersen, Bollerslev, Diebold and Labys (2002) have recently advocated modeling and forecasting the (latent) integrated volatility of primary import from a pricing perspective based on simple reduced form time series models for the observable realized volatilities, constructed from the summation of high-frequency squared returns. Building on the eigenfunction stochastic volatility class of models introduced by Meddahi (2001), we present analytical expressions for the loss in forecast efficiency associated with this easy-to-implement procedure as a function of the sampling frequency of the returns underlying the realized volatility measures. On numerically quantifying this efficiency loss for such popular continuous-time models as GARCH, multi-factor affine, and log-normal diffusions, we find that the realized volatility reduced form procedures perform remarkably well in comparison to the optimal (non-feasible) forecasts conditional on the full sample path realization of the latent instantaneous volatility process. Le développement de procédures d'estimation et de prévision utilisant des modèles réalistes, en temps continu et à volatilité stochastique est sévèrement bloqué par la non disponibilité de la densité de transition des rendements. En réponse à ce problème, Andersen, Bollerslev, Diebold et Labys (2002) ont récemment proposé de modéliser et de prévoir la volatilité intégrée (et inobservable), qui est importante pour la valorisation des produits dérivés, à partir de formes réduites simples de la volatilité réalisée, calculée en sommant des carrés des rendements à haute fréquence. En utilisant la classe de modèles à volatilité stochastique basée sur des fonctions propres introduites dans Meddahi (2001), nous présentons les expressions analytiques des fonctions de pertes de ces prévisions simples en fonction du pas de temps des rendements à haute fréquence. En quantifiant ces fonctions de pertes pour les modèles en temps continu usuels comme les modèles de diffusion GARCH, affine à plusieurs facteurs, et log-normal, nous trouvons que les procédures à base de formes réduites se comportent très bien par rapport aux procédures optimales (et infaisables) qui utilisent toute la trajectoire de la volatilité instantanée et inobservable.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2002s-90.

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Date of creation: 01 Dec 2002
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Handle: RePEc:cir:cirwor:2002s-90

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Keywords: Continuous-time models; eigenfunction stochastic volatility models; integrated volatility; realized volatility; high-frequency data; time series forecasting; Mincer-Zarnowitz regressions; modèles à temps continu; modèles à volatilité stochastique basée sur des fonctions propres; volatilité intégrée; volatilité réalisée; données à haute fréquence; prévision de séries chronologiques; régressions de Mincer-Zarnowitz;

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  1. Xiaohong Chen & Lars Peter Hansen & Jos´e A. Scheinkman, 2005. "Principal Components and the Long Run," Levine's Bibliography 122247000000000997, UCLA Department of Economics.
  2. Neil Shephard & Ole E. Barndorff-Nielsen, 2002. "Estimating quadratic variation using realised variance," Economics Series Working Papers 2001-W20, University of Oxford, Department of Economics.
  3. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  4. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. Nour Meddahi, 2001. "An Eigenfunction Approach for Volatility Modeling," CIRANO Working Papers 2001s-70, CIRANO.
  6. 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.
  7. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper 1992-40, Tilburg University, Center for Economic Research.
  8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  9. 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.
  10. G. William Schwert, 1990. "Stock Volatility and the Crash of '87," NBER Working Papers 2954, National Bureau of Economic Research, Inc.
  11. Gallant, A. Ronald & Tauchen, George, 2002. "Simulated Score Methods and Indirect Inference for Continuous-time Models," Working Papers 02-09, Duke University, Department of Economics.
  12. Peter F. Christoffersen & Francis X. Diebold, 1998. "How Relevant is Volatility Forecasting for Financial Risk Management?," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-080, New York University, Leonard N. Stern School of Business-.
  13. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
  14. Fabienne Comte & Eric Renault, 1998. "Long memory in continuous-time stochastic volatility models," Mathematical Finance, Wiley Blackwell, vol. 8(4), pages 291-323.
  15. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
  16. 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.
  17. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
  18. 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.
  19. Elena Andreou & Eric Ghysels, 2000. "Rolling-Sample Volatility Estimators: Some New Theoretical, Simulation and Empirical Results," CIRANO Working Papers 2000s-19, CIRANO.
  20. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
  21. 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.
  22. Chong, Yock Y & Hendry, David F, 1986. "Econometric Evaluation of Linear Macro-Economic Models," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 671-90, August.
  23. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  24. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2001. "An Empirical Investigation of Continuous-Time Equity Return Models," NBER Working Papers 8510, National Bureau of Economic Research, Inc.
  25. G. William Schwert, 1990. "Why Does Stock Market Volatility Change Over Time?," NBER Working Papers 2798, National Bureau of Economic Research, Inc.
  26. Tim Bollerslev & Hao Zhou, 2001. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Finance and Economics Discussion Series 2001-49, Board of Governors of the Federal Reserve System (U.S.).
  27. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  28. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  29. 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.
  30. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," Center for Financial Institutions Working Papers 99-08, Wharton School Center for Financial Institutions, University of Pennsylvania.
  31. Gallant, A. Ronald & Hsu, Chien-Te & Tauchen, George, 2000. "Using Daily Range Data to Calibrate Volatility Diffusions and Extract the Forward Integrated Variance," Working Papers 00-04, Duke University, Department of Economics.
  32. 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.
  33. Nour Meddahi, 2002. "ARMA Representation of Two-Factor Models," CIRANO Working Papers 2002s-92, CIRANO.
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