Ishida , Isao and McAleer, Michael and Oya, Kosuke (2011) Estimating the Leverage Parameter of Continuous-time Stochastic Volatility Models Using High Frequency S&P 500 and VIX. [Working Paper or Technical Report] (Unpublished)
Available under License Creative Commons Attribution Non-commercial.
Official URL: http://eprints.ucm.es/12807/
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 estimate the parameters of popular continuous-time models can lead to nonsensical estimates due to severe intraday seasonality. A primary purpose of the paper is to estimate the leverage parameter, rho, that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively. We show that, under the special case of Heston’s (1993) square-root SV 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, converges to rho in probability as the time intervals between observations shrink to zero, even if the length of the whole sample period is fixed. Finite sample simulation results show that the proposed estimator delivers accurate estimates of the leverage parameter, unlike existing methods.
|Item Type:||Working Paper or Technical Report|
|Additional Information:||JEL Classifications: G13, G17, G32. 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.|
|Uncontrolled Keywords:||Continuous time, High frequency data, Stochastic volatility, S&P 500, Implied volatility, VIX.|
|Subjects:||Social sciences > Economics > Econometrics|
Social sciences > Economics > Economic indicators
|Series Name:||Documentos de Trabajo del Instituto Complutense de Análisis Económico|
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|Deposited On:||01 Jun 2011 09:25|
|Last Modified:||15 Nov 2013 11:49|
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