IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons

  • Subbotin, Alexandre

    (HSE, Moscow)

Registered author(s):

    We overview main approaches to modeling stock prices and exchange rates volatility in connection with empirical properties of the corresponding time series. Special attention is due to properties of volatility at multiple time hori-zons and to characteristics of econometric models associated with time aggregation

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://pe.cemi.rssi.ru/pe_2009_3_94-138.pdf
    File Function: Full text
    Download Restriction: no

    Article provided by Publishing House "SINERGIA PRESS" in its journal Applied Econometrics.

    Volume (Year): 15 (2009)
    Issue (Month): 3 ()
    Pages: 94-138

    as
    in new window

    Handle: RePEc:ris:apltrx:0113
    Contact details of provider: Web page: http://appliedeconometrics.cemi.rssi.ru/

    References listed on IDEAS
    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.:

    as in new window
    1. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    2. M. Pasquini & M. Serva, 2000. "Clustering of volatility as a multiscale phenomenon," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 16(1), pages 195-201, July.
    3. Drost, F.C. & Nijman, T.E., 1990. "Temporal Aggregation Of Garch Processes," Papers 9066, Tilburg - Center for Economic Research.
    4. Xue-Zhong (Tony) He & Carl Chiarella, 2001. "Asset Price and Wealth Dynamics under Heterogeneous Expectations," CeNDEF Workshop Papers, January 2001 5A.2, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    5. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Estimating quadratic variation using realized variance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 457-477.
    6. Valentina Corradi & Walter Distaso, 2006. "Semi-Parametric Comparison of Stochastic Volatility Models using Realized Measures," Review of Economic Studies, Oxford University Press, vol. 73(3), pages 635-667.
    7. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    8. 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..
    9. Giovanni Barone-Adesi & Robert F. Engle & Loriano Mancini, 2008. "A GARCH Option Pricing Model with Filtered Historical Simulation," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1223-1258, May.
    10. Laurent-Emmanuel Calvet & Adlai J. Fisher, 2001. "Forecasting multifractal volatility," Post-Print hal-00477952, HAL.
    11. Peter Reinhard Hansen & Asger Lunde, 2005. "A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(4), pages 525-554.
    12. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    13. Paul Lynch & Gilles Zumbach, 2003. "Market heterogeneities and the causal structure of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 320-331.
    14. David M. Cutler & James M. Poterba & Lawrence H. Summers, 1988. "What Moves Stock Prices?," NBER Working Papers 2538, National Bureau of Economic Research, Inc.
    15. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
    16. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-84, March.
    17. Kimio Morimune, 2007. "Volatility Models," The Japanese Economic Review, Japanese Economic Association, vol. 58(1), pages 1-23.
    18. Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2003. "Multiple time scales in volatility and leverage correlation: A stochastic volatility model," Science & Finance (CFM) working paper archive 50001, Science & Finance, Capital Fund Management.
    19. Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
    20. Liu, Ming, 2000. "Modeling long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 99(1), pages 139-171, November.
    21. Jun Liu, 2007. "Portfolio Selection in Stochastic Environments," Review of Financial Studies, Society for Financial Studies, vol. 20(1), pages 1-39, January.
    22. Conrad, Jennifer & Gultekin, Mustafa N & Kaul, Gautam, 1997. "Profitability of Short-Term Contrarian Strategies: Implications for Market Efficiency," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(3), pages 379-86, July.
    23. B. LeBaron, 2001. "Stochastic volatility as a simple generator of apparent financial power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 621-631.
    24. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    25. Martens, Martin & van Dijk, Dick, 2007. "Measuring volatility with the realized range," Journal of Econometrics, Elsevier, vol. 138(1), pages 181-207, May.
    26. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    27. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
    28. 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.
    29. Alexander Subbotin, 2008. "A multi-horizon scale for volatility," Documents de travail du Centre d'Economie de la Sorbonne bla08020, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    30. 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.
    31. Eric Ghysels & Pedro Santa-Clara & Rossen Valkanov, 2004. "Predicting Volatility: Getting the Most out of Return Data Sampled at Different Frequencies," CIRANO Working Papers 2004s-19, CIRANO.
    32. Biais, Bruno & Glosten, Larry & Spatt, Chester, 2005. "Market microstructure: A survey of microfoundations, empirical results, and policy implications," Journal of Financial Markets, Elsevier, vol. 8(2), pages 217-264, May.
    33. Jaume Masoliver & Josep Perello, 2005. "Multiple time scales and the exponential Ornstein-Uhlenbeck stochastic volatility model," Papers cond-mat/0501639, arXiv.org.
    34. 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 542-47, August.
    35. Renner, Ch. & Peinke, J. & Friedrich, R., 2001. "Evidence of Markov properties of high frequency exchange rate data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 499-520.
    36. F. M. Bandi & J. R. Russell, 2008. "Microstructure Noise, Realized Variance, and Optimal Sampling," Review of Economic Studies, Oxford University Press, vol. 75(2), pages 339-369.
    37. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
    38. Benoit Pochart & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 303-314.
    39. 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.
    40. Michael McAleer & Marcelo Cunha Medeiros, 2006. "Realized volatility: a review," Textos para discussão 531 Publication status: F, Department of Economics PUC-Rio (Brazil).
    41. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    42. 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.
    43. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
    44. Peter F. Christoffersen & Francis X. Diebold, 1997. "How Relevant is Volatility Forecasting for Financial Risk Management?," Center for Financial Institutions Working Papers 97-45, Wharton School Center for Financial Institutions, University of Pennsylvania.
    45. Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
    46. Markku Lanne & Pentti Saikkonen, 2005. "Non-linear GARCH models for highly persistent volatility," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 251-276, 07.
    47. 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.
    48. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
    49. Wolfgang Breymann & Shoaleh Ghashghaie & Peter Talkner, 2000. "A Stochastic Cascade Model for FX Dynamics," Papers cond-mat/0004179, arXiv.org.
    50. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-27, October.
    51. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    52. Asger Lunde & Peter R. Hansen, 2005. "A forecast comparison of volatility models: does anything beat a GARCH(1,1)?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
    53. Gordon R. Richards, 2004. "A fractal forecasting model for financial time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(8), pages 586-601.
    54. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    55. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
    56. William A. Brock & Cars H. Hommes, 1997. "A Rational Route to Randomness," Econometrica, Econometric Society, vol. 65(5), pages 1059-1096, September.
    57. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    58. Sentana,E., 1995. "Quadratic Arch Models," Papers 9517, Centro de Estudios Monetarios Y Financieros-.
    59. Benoit Pochard & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Science & Finance (CFM) working paper archive 0204047, Science & Finance, Capital Fund Management.
    60. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    61. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
    62. 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.
    63. Soosung Hwang & Steve E. Satchell & Pedro L. Valls Pereira, 2007. "How Persistent is Stock Return Volatility? An Answer with Markov Regime Switching Stochastic Volatility Models," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 34(5-6), pages 1002-1024.
    64. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-34, October.
    65. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    66. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
    67. Chan, Wing H & Maheu, John M, 2002. "Conditional Jump Dynamics in Stock Market Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 377-89, July.
    68. 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.
    69. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    70. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    71. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    72. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
    73. Peter Ritchken & Rob Trevor, 1999. "Pricing Options under Generalized GARCH and Stochastic Volatility Processes," Journal of Finance, American Finance Association, vol. 54(1), pages 377-402, 02.
    74. Christensen, Kim & Podolskij, Mark, 2007. "Realized range-based estimation of integrated variance," Journal of Econometrics, Elsevier, vol. 141(2), pages 323-349, December.
    75. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    76. J-F. Muzy & D. Sornette & J. delour & A. Arneodo, 2001. "Multifractal returns and hierarchical portfolio theory," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 131-148.
    77. 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.
    78. Mandelbrot, Benoit B, 1971. "When Can Price Be Arbitraged Efficiently? A Limit to the Validity of the Random Walk and Martingale Models," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 225-36, August.
    79. 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.
    80. LeBaron, Blake, 2001. "Evolution And Time Horizons In An Agent-Based Stock Market," Macroeconomic Dynamics, Cambridge University Press, vol. 5(02), pages 225-254, April.
    81. 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.
    82. Bertrand Maillet & Thierry Michel, 2003. "An index of market shocks based on multiscale analysis," Quantitative Finance, Taylor & Francis Journals, vol. 3(2), pages 88-97.
    83. Lars Forsberg & Eric Ghysels, 2007. "Why Do Absolute Returns Predict Volatility So Well?," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(1), pages 31-67.
    84. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-58, February.
    85. Bai, Xuezheng & Russell, Jeffrey R. & Tiao, George C., 2003. "Kurtosis of GARCH and stochastic volatility models with non-normal innovations," Journal of Econometrics, Elsevier, vol. 114(2), pages 349-360, June.
    86. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
    87. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    88. Drost, F.C. & Werker, B.J.M., 1996. "Closing the GARCH gap : Continuous time GARCH modeling," Other publications TiSEM c3d29817-403a-4ad1-9295-8, Tilburg University, School of Economics and Management.
    89. Gita Persand & Chris Brooks, 2003. "Volatility forecasting for risk management," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(1), pages 1-22.
    90. 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.
    91. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
    92. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
    93. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    94. Alexander Subbotin, 2008. "A multi-horizon scale for volatility," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00261514, HAL.
    95. A. A.G. Cortines & R. Riera & C. Anteneodo, 2007. "From short to fat tails in financial markets: a unified description," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(3), pages 385-389, December.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:ris:apltrx:0113. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Anatoly Peresetsky)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.