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VIX Dynamics with Stochastic Volatility of Volatility

Andreas Kaeck and Carol Alexander ()
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Andreas Kaeck: ICMA Centre, Henley Business School, University of Reading

ICMA Centre Discussion Papers in Finance from Henley Business School, University of Reading

Abstract: This paper examines the ability of several different continuous-time one and two-factor jump-diffusion models to capture the dynamics of the VIX volatility index for the period between 1990 and 2010. For the one-factor models we study affine and non-affine specifications, possibly augmented with jumps. Jumps in one-factor models occur frequently, but add surprisingly little to the ability of the models to explain the dynamic of the VIX. We present a stochastic volatility of volatility model that can explain all the time-series characteristics of the VIX studied in this paper. Extensions demonstrate that sudden jumps in the VIX are more likely during tranquil periods and the days when jumps occur coincide with major political or economic events. Using several statistical and operational metrics we find that non-affine one-factor models outperform their affine counterparts and modeling the log of the index is superior to modeling the VIX level directly.

Keywords: VIX; Volatility Indices; Jumps; Stochastic volatility of-volatility (search for similar items in EconPapers)
JEL-codes: C15 C32 G13 G15 (search for similar items in EconPapers)
Date: 2010-09
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