On the skew-curvature power law relationship in a stochastic volatility model with infinite variation L\'evy jumps

\`Oscar Bur\'es and Josep Vives

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Abstract: The short-term blow up behaviour of the ATM-IV skew is commonly modelled by either a rough volatility process with small Hurst index or an infinite variation L\'evy process in the log-price dynamics. In this paper, we examine which is the effect of mixed dynamics (i.e. rough volatility and infinite variation L\'evy processes) on the ATM-IV skew and curvature. The results of the paper show that the analysis of the leading terms of the short-time expansion of both ATM-IV skew and curvature allow us to determine, from a mixed dynamics model, which mechanism originates the power-law behaviour on the skew and on the curvature. Apart from showing that the mixed model also originates a power law, it has also key implications in model design and calibration. Numerical evidences for the rough Heston model with CGMY L\'evy jumps are provided.

Date: 2026-10
New Economics Papers: this item is included in nep-rmg
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