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

Isao Ishida, Michael McAleer and Kosuke Oya
Additional contact information
Kosuke Oya: Graduate School of Economics and Center for the Study of Finance and Insurance Osaka University, Japan

No 2011-17, Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico

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.

Keywords: Continuous time; high frequency data; stochastic volatility; S&P 500; implied volatility; VIX. (search for similar items in EconPapers)
JEL-codes: G13 G17 G32 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2011
New Economics Papers: this item is included in nep-ets, nep-mst, nep-ore and nep-rmg
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.
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://eprints.ucm.es/id/eprint/12807/1/1117.pdf revised May 2011 (application/pdf)

Related works:
Working Paper: Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX (2011)
Working Paper: Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX (2011)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ucm:doicae:1117

Ordering information: This working paper can be ordered from
Facultad de Ciencias Económicas y Empresariales. Pabellón prefabricado, 1ª Planta, ala norte. Campus de Somosaguas, 28223 - POZUELO DE ALARCÓN (MADRID)
https://www.ucm.es/f ... -de-trabajo-del-icae

Access Statistics for this paper

More papers in Documentos de Trabajo del ICAE from Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico Contact information at EDIRC.
Bibliographic data for series maintained by Águeda González Abad ().