Short-time at-the-money skew and rough fractional volatility
By Masaaki Fukasawa. 2015
107 citations recorded by the source corpus.
The Black–Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time to maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian motion with Hurst parameter less than half. The fractional Brownian motion is correlated with a Brownian motion which drives the asset price process. We derive an asymptotic expansion of the implied volatility as the time to maturity tends to zero. For this purpose, we introduce a new approach to validate such an expansion, which enables us to treat more general models than in the literature. The local-stochastic volatility model is treated as well under an essentially minimal regularity condition in order to show such a standard model cannot be dynamically consistent to the power law.
Subfields: Finance
View Paper: https://www.semanticscholar.org/paper/f0973d140517466f1a77c4190c282413e39cff93
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In Finance
- Eduardo Abi Jaber
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Citations in the corpus
- Lifting the Heston model (2018, methodology): “5−H , see also Fukasawa (2017). We discuss the simulation procedure and the statistical estimation of H of our lifted model in the next subsection.”
- A regularity structure for rough volatility (2017, background): “[2] and Fukasawa [24, 25]) that in the previously considered simple rough volatility models, now writing σ(.”
- Rough volatility: Evidence from option prices (2017, background): “In particular, the exploding term structure when maturity goes to zero of the at-the-money skew (the derivative of the implied volatility with respect to strike) is readily obtained, see [1, 11].”
- Decoupling the Short- and Long-Term Behavior of Stochastic Volatility (2016, background): “This is due to both theoretical developments in implied volatility modeling (Alòs et al., 2007; Fukasawa, 2017) as well as empirical evidence based on realized volatility (Gatheral et al., 2014; Bennedsen, 2016).”