The fractional volatility model and rough volatility
The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus for fractional processes, an option pricing equation and its solution are obtained.
Code (0)
등록된 구현이 없습니다.
Tasks
modelSimilar Papers 제목 키워드 기반
Rough volatility: fact or artefact?
We investigate the statistical evidence for the use of `rough' fractional processes with Hurst exponent $H< 0.5$ for the modeling of volatility of financial assets, using a model-free approach. We introduce a non-paramet…
Time Series AnalysisRough volatility: evidence from range volatility estimators
In Gatheral et al. 2018, first posted in 2014, volatility is characterized by fractional behavior with a Hurst exponent $H < 0.5$, challenging traditional views of volatility dynamics. Gatheral et al. demonstrated this u…
Short-time asymptotics for non self-similar stochastic volatility models
We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumption…
MathCorrection to Black-Scholes formula due to fractional stochastic volatility
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model…
Crypto Inverse-Power Options and Fractional Stochastic Volatility
Recent empirical evidence has highlighted the crucial role of jumps in both price and volatility within the cryptocurrency market. In this paper, we integrate price--volatility co-jumps and volatility short-term dependen…
Computational Efficiency