Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258012 
Year of Publication: 
2020
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 2 [Article No.:] 59 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-18
Publisher: 
MDPI, Basel
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.
Subjects: 
stochastic volatility
elasticity of variance of variance
Heston
SABR
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
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