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Estimation of objective and risk-neutral distributions based on moments of integrated volatility

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  • Garcia, René
  • Lewis, Marc-André
  • Pastorello, Sergio
  • Renault, Éric

Abstract

In this paper, we present an estimation procedure which uses both option prices and high-frequency spot price feeds to estimate jointly the objective and risk-neutral parameters of stochastic volatility models. The procedure is based on a method of moments that uses analytical expressions for the moments of the integrated volatility and series expansions of option prices and implied volatilities. This results in an easily implementable and rapid estimation technique. An extensive Monte Carlo study compares various procedures and shows the efficiency of our approach. Empirical applications to the Deutsche mark-US dollar exchange rate futures and the S&P 500 index provide evidence that the method delivers results that are in line with the ones obtained in previous studies where much more involved estimation procedures were used.

Suggested Citation

  • Garcia, René & Lewis, Marc-André & Pastorello, Sergio & Renault, Éric, 2011. "Estimation of objective and risk-neutral distributions based on moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 22-32, January.
    • Handle: RePEc:eee:econom:v:160:y:2011:i:1:p:22-32
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    4. Stanislav Khrapov, 2011. "Pricing Central Tendency in Volatility," Working Papers w0168, Center for Economic and Financial Research (CEFIR).
    5. Isao Ishida & Michael McAleer & Kosuke Oya, 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX," Documentos de Trabajo del ICAE 2011-17, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    6. Markellos, Raphael N. & Psychoyios, Dimitris, 2018. "Interest rate volatility and risk management: Evidence from CBOE Treasury options," The Quarterly Review of Economics and Finance, Elsevier, vol. 68(C), pages 190-202.
    7. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Modeling microstructure price dynamics with symmetric Hawkes and diffusion model using ultra-high-frequency stock data," Journal of Economic Dynamics and Control, Elsevier, vol. 79(C), pages 154-183.
    8. Bollerslev, Tim & Zhou, Hao, 2002. "Estimating stochastic volatility diffusion using conditional moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 109(1), pages 33-65, July.
    9. Frazier, David T. & Maneesoonthorn, Worapree & Martin, Gael M. & McCabe, Brendan P.M., 2019. "Approximate Bayesian forecasting," International Journal of Forecasting, Elsevier, vol. 35(2), pages 521-539.
    10. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S. & Grose, Simone D., 2012. "Probabilistic forecasts of volatility and its risk premia," Journal of Econometrics, Elsevier, vol. 171(2), pages 217-236.
    11. Andersen, Torben G. & Bollerslev, Tim & Meddahi, Nour, 2011. "Realized volatility forecasting and market microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 220-234, January.
    12. Corradi, Valentina & Distaso, Walter & Mele, Antonio, 2013. "Macroeconomic determinants of stock volatility and volatility premiums," Journal of Monetary Economics, Elsevier, vol. 60(2), pages 203-220.
    13. René Garcia & Eric Ghysels & Eric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
    14. Torben G. Andersen & Viktor Todorov, 2009. "Realized Volatility and Multipower Variation," CREATES Research Papers 2009-49, Department of Economics and Business Economics, Aarhus University.
    15. Lee Kyungsub, 2016. "Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(1), pages 19-36, February.
    16. Ishida, I. & McAleer, M.J. & Oya, K., 2011. "Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 VIX," Econometric Institute Research Papers EI 2011-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Calvet, Laurent E. & Fearnley, Marcus & Fisher, Adlai J. & Leippold, Markus, 2015. "What is beneath the surface? Option pricing with multifrequency latent states," Journal of Econometrics, Elsevier, vol. 187(2), pages 498-511.
    18. Zhenyu Cui & Anne MacKay & Marie-Claude Vachon, 2022. "Analysis of VIX-linked fee incentives in variable annuities via continuous-time Markov chain approximation," Papers 2207.14793, arXiv.org.
    19. Bregantini, Daniele, 2013. "Moment-based estimation of stochastic volatility," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4755-4764.
    20. Xinyu WU & Hailin ZHOU, 2016. "GARCH DIFFUSION MODEL, iVIX, AND VOLATILITY RISK PREMIUM," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(1), pages 327-342.
    21. Massimo Guidolin & Erwin Hansen & Gabriel Cabrera, 2023. "Time-Varying Risk Aversion and International Stock Returns," BAFFI CAREFIN Working Papers 23203, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    22. Caldana, Ruggero & Fusai, Gianluca & Roncoroni, Andrea, 2017. "Electricity forward curves with thin granularity: Theory and empirical evidence in the hourly EPEXspot market," European Journal of Operational Research, Elsevier, vol. 261(2), pages 715-734.
    23. Kyungsub Lee, 2013. "Probabilistic and statistical properties of moment variations and their use in inference and estimation based on high frequency return data," Papers 1311.5036, arXiv.org, revised Jul 2015.

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