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A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility


  • Jeff Fleming
  • Chris Kirby


We show that, for three common SARV models, fitting a minimum mean square linear filter is equivalent to fitting a GARCH model. This suggests that GARCH models may be useful for filtering, forecasting, and parameter estimation in stochastic volatility settings. To investigate, we use simulations to evaluate how the three SARV models and their associated GARCH filters perform under controlled conditions and then we use daily currency and equity index returns to evaluate how the models perform in a risk management application. Although the GARCH models produce less precise forecasts than the SARV models in the simulations, it is not clear that the performance differences are large enough to be economically meaningful. Consistent with this view, we find that the GARCH and SARV models perform comparably in tests of conditional value-at-risk estimates using the actual data. , .

Suggested Citation

  • Jeff Fleming & Chris Kirby, 2003. "A Closer Look at the Relation between GARCH and Stochastic Autoregressive Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 365-419.
  • Handle: RePEc:oup:jfinec:v:1:y:2003:i:3:p:365-419

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    1. Norris I. Bruce, 2008. "Pooling and Dynamic Forgetting Effects in Multitheme Advertising: Tracking the Advertising Sales Relationship with Particle Filters," Marketing Science, INFORMS, vol. 27(4), pages 659-673, 07-08.
    2. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    3. Caldeira, João F. & Moura, Guilherme V. & Santos, André A.P., 2016. "Bond portfolio optimization using dynamic factor models," Journal of Empirical Finance, Elsevier, vol. 37(C), pages 128-158.
    4. Stentoft, Lars, 2011. "American option pricing with discrete and continuous time models: An empirical comparison," Journal of Empirical Finance, Elsevier, vol. 18(5), pages 880-902.
    5. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    6. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers 2012-50, Department of Economics and Business Economics, Aarhus University.
    7. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, Elsevier.
    8. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2009. "Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options," CIRANO Working Papers 2009s-34, CIRANO.
    9. repec:mes:emfitr:v:52:y:2016:i:1:p:52-65 is not listed on IDEAS
    10. Fung, Ka Wai Terence & Lau, Chi Keung Marco & Chan, Kwok Ho, 2013. "The Conditional CAPM, Cross-Section Returns and Stochastic Volatility," MPRA Paper 52469, University Library of Munich, Germany.
    11. Kirby, Chris, 2006. "Linear filtering for asymmetric stochastic volatility models," Economics Letters, Elsevier, vol. 92(2), pages 284-292, August.
    12. John M Maheu & Thomas H McCurdy, 2007. "Modeling foreign exchange rates with jumps," Working Papers tecipa-279, University of Toronto, Department of Economics.
    13. Ren-Her Wang & John Aston & Cheng-Der Fuh, 2010. "The Role of Additional Information in Option Pricing: Estimation Issues for the State Space Model," Computational Economics, Springer;Society for Computational Economics, vol. 36(4), pages 283-307, December.
    14. Tsiakas, Ilias, 2008. "Overnight information and stochastic volatility: A study of European and US stock exchanges," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 251-268, February.
    15. Chih-Wei Lee & Cheng-Kun Kuo, 2015. "Combining hazard rates with the CreditGrades model: A hybrid method to value CDS contracts," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-14, December.
    16. Fung, Ka Wai Terence & Lau, Chi Keung Marco & Chan, Kwok Ho, 2014. "The conditional equity premium, cross-sectional returns and stochastic volatility," Economic Modelling, Elsevier, vol. 38(C), pages 316-327.
    17. Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 1(2), pages 179-202, November.
    18. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
    19. Ender Demir & Ka Wai Terence Fung & Zhou Lu, 2016. "Capital Asset Pricing Model and Stochastic Volatility: A Case Study of India," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 52(1), pages 52-65, January.
    20. Fulvio Corsi & Francesco Audrino, 2012. "Realized Covariance Tick-by-Tick in Presence of Rounded Time Stamps and General Microstructure Effects," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 10(4), pages 591-616, September.
    21. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    22. Franses, Ph.H.B.F. & van der Leij, M.J. & Paap, R., 2005. "A simple test for GARCH against a stochastic volatility," Econometric Institute Research Papers EI 2005-41, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    23. Jeff Fleming & Chris Kirby & Barbara Ostdiek, 2006. "Stochastic Volatility, Trading Volume, and the Daily Flow of Information," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1551-1590, May.
    24. Ilias Tsiakas, 2004. "Analysis of the predictive ability of information accumulated over nights, weekends and holidays," Econometric Society 2004 Australasian Meetings 208, Econometric Society.
    25. Prateek Sharma & Vipul _, 2015. "Forecasting stock index volatility with GARCH models: international evidence," Studies in Economics and Finance, Emerald Group Publishing, vol. 32(4), pages 445-463, October.

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