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Modeling and predicting the CBOE market volatility index

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Author Info
Marcelo Fernandes () (Queen Mary, University of London)
Marcelo Cunha Medeiros () (Department of Economics, PUC-Rio)
MArcelo Scharth ()

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Abstract

This paper performs a thorough statistical examination of the time-series properties of the market volatility index (VIX) from the Chicago Board Options Exchange (CBOE). The motivation lies on the widespread consensus that the VIX is a barometer to the overall market sentiment as to what concerns risk appetite. To assess the statistical behavior of the time series, we run a series of preliminary analyses whose results suggest there is some long-range dependence in the VIX index. This is consistent with the strong empirical evidence in the literature supporting long memory in both options-implied and realized volatilities. We thus resort to linear and nonlinear heterogeneous autoregressive (HAR) processes, including smooth transition and threshold HAR-type models, as well as to smooth transition autoregressive trees (START) for modeling and forecasting purposes. The in-sample results for the HAR-type indicate that they cope with the long-range dependence in the VIX time series as well as the more popular ARFIMA model. In addition, the highly nonlinear START specification also does a god job in controlling for the long memory. The out-of-sample analysis evince that the linear ARMA and ARFIMA models perform very well in the short run and very poorly in the long-run, whereas the START model entails by far the best results for the longer horizon despite of failing at shorter horizons. In contrast, the HAR-type models entail reasonable relative performances in most horizons. Finally, we also show how a simple forecast combination brings about great improvements in terms of predictive ability for most horizons.

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Publisher Info
Paper provided by Department of Economics PUC-Rio (Brazil) in its series Textos para discussão with number 548.

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Length: 35p
Date of creation: Aug 2007
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Handle: RePEc:rio:texdis:548

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Related research
Keywords: heterogeneous autoregression implied volatility smooth transition VIX.

Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy

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References listed on IDEAS
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  1. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June. [Downloadable!] (restricted)
  2. U. A. Muller & M. M. Dacorogna & R. D. Dave & O. V. Pictet & R. B. Olsen & J.R. Ward, . "Fractals and Intrinsic Time - a Challenge to Econometricians," Working Papers 1993-08-16, Olsen and Associates. [Downloadable!]
  3. Van Dijk, D. & Franses, P.H., 1997. "Modelling Multiple Regimes in the Business Cycle," Papers 9734/a, Erasmus University of Rotterdam - Econometric Institute.
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