How does the volatility of volatility depend on volatility?

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Risks ; ISSN: 2227-9091 ; Volume: 8 ; Year: 2020 ; Issue: 2 ; Pages: 1-18 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft
• Subject: stochastic volatility ; elasticity of variance of variance ; Heston ; SABR

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Rømer, Sigurd Emil ; Poulsen, Rolf
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2020

Further information

• DOI: doi:10.3390/risks8020059
• Handle: http://hdl.handle.net/10419/258012
• Last update: 10.03.2025, 11:42 AM CET