How Does the Volatility of Volatility Depend on Volatility?

Sigurd Emil Rømer and Rolf Poulsen
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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

Risks, 2020, vol. 8, issue 2, 1-18

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.

Keywords: stochastic volatility; elasticity of variance of variance; Heston; SABR (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
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