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How Does the Volatility of Volatility Depend on Volatility?

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  • Sigurd Emil Rømer

    (Department of Mathematical Sciences, University of Copenhagen, 2100 København Ø, Denmark)

  • Rolf Poulsen

    (Department of Mathematical Sciences, University of Copenhagen, 2100 København Ø, Denmark)

Abstract

We investigate the state dependence of the variance of the instantaneous variance of the S&P 500 index empirically. Time-series analysis of realized variance over a 20-year period shows strong evidence of an elasticity of variance of the variance parameter close to that of a log-normal model, albeit with an empirical autocorrelation function that one-factor diffusion models fail to capture at horizons above a few weeks. When studying option market behavior (in-sample pricing as well as out-of-sample pricing and hedging over the period 2004–2019), messages are mixed, but systematic, model-wise. The log-normal but drift-free SABR (stochastic-alpha-beta-rho) model performs best for short-term options (times-to-expiry of three months and below), the Heston model—in which variance is stationary but not log-normal—is superior for long-term options, and a mixture of the two models does not lead to improvements.

Suggested Citation

  • Sigurd Emil Rømer & Rolf Poulsen, 2020. "How Does the Volatility of Volatility Depend on Volatility?," Risks, MDPI, vol. 8(2), pages 1-18, June.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:2:p:59-:d:366678
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    References listed on IDEAS

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