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

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  • Isao Ishida
  • Michael McAleer

    ()
    (University of Canterbury)

  • Kosuke Oya

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 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, ρ, 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 ρ 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.

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File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/1111.pdf
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Bibliographic Info

Paper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 11/11.

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Length: 31 pages
Date of creation: 01 Feb 2011
Date of revision:
Handle: RePEc:cbt:econwp:11/11

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

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Cited by:
  1. 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 6-30, October.
  2. 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.
  3. Bregantini, Daniele, 2013. "Moment-based estimation of stochastic volatility," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4755-4764.

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