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

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  • Jeff Fleming
  • Chris Kirby

Abstract

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. , .

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Bibliographic Info

Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 1 (2003)
Issue (Month): 3 ()
Pages: 365-419

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Handle: RePEc:oup:jfinec:v:1:y:2003:i:3:p:365-419

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Cited by:
  1. Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, CEJEME, CEJEME, vol. 1(2), pages 179-202, November.
  2. 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, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute EI 2005-41, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  3. Lars Stentoft, 2011. "American Option Pricing with Discrete and Continuous Time Models: An Empirical Comparison," CREATES Research Papers, School of Economics and Management, University of Aarhus 2011-34, School of Economics and Management, University of Aarhus.
  4. Mark J. Jensen & John M. Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Paper, Federal Reserve Bank of Atlanta 2008-15, Federal Reserve Bank of Atlanta.
  5. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2012. "GARCH Option Valuation: Theory and Evidence," CREATES Research Papers, School of Economics and Management, University of Aarhus 2012-50, School of Economics and Management, University of Aarhus.
  6. Fung, Ka Wai Terence & Demir, Ender & Zhou, Lu, 2014. "Capital Asset Pricing Model and Stochastic Volatility: A Case study of India," MPRA Paper 56180, University Library of Munich, Germany.
  7. Peter Christoffersen & Kris Jacobs & Chayawat Ornthanalai, 2009. "Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options," CIRANO Working Papers, CIRANO 2009s-34, CIRANO.
  8. 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.
  9. Tsiakas, Ilias, 2008. "Overnight information and stochastic volatility: A study of European and US stock exchanges," Journal of Banking & Finance, Elsevier, Elsevier, vol. 32(2), pages 251-268, February.
  10. Ilias Tsiakas, 2004. "Analysis of the predictive ability of information accumulated over nights, weekends and holidays," Econometric Society 2004 Australasian Meetings, Econometric Society 208, Econometric Society.
  11. 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, Elsevier, vol. 38(C), pages 316-327.
  12. 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, Elsevier, vol. 106(3), pages 447-472.
  13. Kirby, Chris, 2006. "Linear filtering for asymmetric stochastic volatility models," Economics Letters, Elsevier, Elsevier, vol. 92(2), pages 284-292, August.
  14. John M Maheu & Thomas H McCurdy, 2007. "Modeling foreign exchange rates with jumps," Working Papers, University of Toronto, Department of Economics tecipa-279, University of Toronto, Department of Economics.
  15. 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, Society for Computational Economics, Society for Computational Economics, vol. 36(4), pages 283-307, December.
  16. 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, University of Chicago Press, vol. 79(3), pages 1551-1590, May.

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