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Continuous-time VIX dynamics: on the role of stochastic volatility of volatility

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posted on 2023-06-08, 15:06 authored by Andreas KaeckAndreas Kaeck, Carol AlexanderCarol Alexander
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.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

International Review of Financial Analysis

ISSN

10575219

Publisher

Elsevier

Volume

28

Page range

46-56

Department affiliated with

  • Business and Management Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2013-06-02

First Open Access (FOA) Date

2013-06-02

First Compliant Deposit (FCD) Date

2013-06-02

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