On the skew-curvature power law relationship in a stochastic volatility model with infinite variation Lévy jumps

By Òscar Burés, Josep Vives

Rating

1788
Battle Count: 51

Relevance

8/10
Highly relevant for sophisticated options trading and risk management desks that calibrate stochastic volatility models. Understanding the interplay between skew and curvature helps in selecting appropriate models (rough vs. jump) and avoiding mis-calibration due to identifiability issues.

Implementation Complexity

9/10
The theoretical framework involves advanced stochastic analysis (Malliavin calculus, Volterra processes, Lévy processes). Implementing the numerical validation requires solving fractional Riccati equations and performing Fourier inversions for complex characteristic functions.

Reproducibility

3/5
The paper provides full mathematical derivations, specific parameter sets for numerical experiments, and references to standard numerical methods (fractional Euler scheme, Fourier inversion). However, no public code repository is explicitly linked in the text provided.

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 Lévy 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 Lévy 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 Lévy jumps are provided.

Links

arXiv:2610.23488 · Paper rankings

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