Paper: arXiv 2610.23488

Authors: Òscar Burés, Josep Vives

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a highly mathematical and theoretical analysis of implied volatility skew and curvature in complex stochastic models. While it offers novel insights into mixed dynamics, the empirical validation is limited to numerical examples rather than extensive backtesting on real market data. The heavy reliance on Malliavin calculus makes it challenging for a broader audience.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze ATM-IV Skew & Curvature in Mixed Dynamics] --> B{Methodology: Short-time Expansion of Skew/Curvature};
    B --> C[Inputs: Rough Volatility Model + Infinite Variation Lévy Process];
    C --> D{Computational Process: Leading Term Analysis & Numerical Evidence};
    D --> E[Outcome 1: Mixed Model Produces Power-Law Behavior for Skew/Curvature];
    D --> F[Outcome 2: Identify Mechanism Originating Power-Law in Mixed Dynamics];
    D --> G[Outcome 3: Implications for Model Design & Calibration];

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and 9 more
  1. The variance gamma process and option pricing (1998)
  2. The fine structure of asset returns: An empirical investigation (2002)
  3. Short-time at-the-money skew and rough fractional volatility (2017)
  4. Rough volatility and CGMY jumps with a finite history and the Rough Heston model – small-time asymptotics in the kt regime (2021) — link
  5. Short-Time Behavior of the At-the-Money Implied Volatility for the Jump-Diffusion Stochastic Volatility Bachelier Model — → 2503.22282
  6. A Hull and White formula for a stochastic volatility L 'e vy model with infinite activity (2013)
  7. A BDG Inequality for Stochastic Volterra Integrals (2025) — link
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1 of 17 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.