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Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX

Author

Listed:
  • Isao Ishida

    (Center for the Study of Finance and Insurance Osaka University, Japan)

  • Michael McAleer

    (Econometrisch Instituut (Econometric Institute), Faculteit der Economische Wetenschappen (Erasmus School of Economics), Erasmus Universiteit, Tinbergen Instituut (Tinbergen Institute).)

  • Kosuke Oya

    (Graduate School of Economics and Center for the Study of Finance and Insurance Osaka University, Japan)

Abstract

This paper proposes a new method for estimating continuous-time stochastic volatility (SV) models for the S&P 500 stock index process using intraday high-frequency observations of both the S&P 500 index and the Chicago Board of Exchange (CBOE) implied (or expected) volatility index (VIX). Intraday high-frequency observations data have become readily available for an increasing number of financial assets and their derivatives in recent years, but it is well known that attempts to directly apply popular continuous-time models to short intraday time intervals, and estimate the parameters using such data, can lead to nonsensical estimates due to severe intraday seasonality. A primary purpose of the paper is to provide a framework for using intraday high frequency data of both the index estimate, in particular, for improving the estimation accuracy of the leverage parameter, p, that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively. As a special case, we focus on Heston’s (1993) square-root SV model, and propose the realized leverage estimator for p, noting that, under this model without measurement errors, the “realized leverage,” or the realized covariation of the price and VIX processes divided by the product of the realized volatilities of the two processes, is in-fill consistent for p. Finite sample simulation results show that the proposed estimator delivers more accurate estimates of the leverage parameter than do existing methods.

Suggested Citation

  • 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.
  • Handle: RePEc:ucm:doicae:1117
    Note: The authors are most grateful to two referees for helpful comments and suggestions. The first author wishes to thank Yusho Kaguraoka, Toshiaki Watanabe, and participants at the 2010 Annual Meeting of the Nippon Finance Association, the CSFI Nakanoshima Workshop 2009, and the Hiroshima University of Economics Financial Econometrics Workshop 2010 for valuable comments, and the Japan Society for the Promotion of Science (Grants-in-Aid for Scientific Research No. 20530265) for financial support. The second author is most grateful for the financial support of the Australian Research Council, National Science Council, Taiwan, and the Japan Society for the Promotion of Science. The third author is thankful for Grants-in-Aid for Scientific Research No. 22243021 from the Japan Society for the Promotion of Science.
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    References listed on IDEAS

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    Cited by:

    1. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Amaral, Teodosio Perez, 2013. "The rise and fall of S&P500 variance futures," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 151-167.
    2. David E. Allen & Michael McAleer & Robert Powell & Abhay K. Singh, 2013. "A Non-Parametric and Entropy Based Analysis of the Relationship between the VIX and S&P 500," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 6(1), pages 1-25, October.
    3. Gonzalez-Perez, Maria T., 2015. "Model-free volatility indexes in the financial literature: A review," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 141-159.
    4. Bregantini, Daniele, 2013. "Moment-based estimation of stochastic volatility," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4755-4764.

    More about this item

    Keywords

    Continuous time; high frequency data; stochastic volatility; S&P 500; implied volatility; VIX.;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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