How Does the Volatility of Volatility Depend on Volatility?

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ID: 115177
2020
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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.
Reference Key
rømer2020riskshow Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Sigurd Emil Rømer;Rolf Poulsen;Rømer, Sigurd Emil;Poulsen, Rolf;
Journal risks
Year 2020
DOI
10.3390/risks8020059
URL
https://www.mdpi.com/2227-9091/8/2/59
Keywords
stochastic volatility elasticity of variance of variance heston sabr

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