Paper: arXiv 2611.15391

Authors: Elisa Alòs, Òscar Burés, Vladimir Lucic

Abstract

In this paper we give general sufficient conditions for a stochastic volatility model to be a counterexample for Gatheral’s conjecture. The conditions, achieved by asymptotic properties of integrated variance derivatives and Wiener chaos expansions, show that a general class of rough volatility models are generally counterexamples to Gatheral’s conjecture. For stochastic volatility models with Markovian variance, the conjecture fails under a relationship on the coefficients of the SDE defining the variance process. Particular examples are provided.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is highly theoretical, focusing on mathematical conditions for refuting Gatheral’s conjecture using advanced stochastic calculus. While it provides specific examples, there is no empirical backtesting or data validation presented. The novelty lies in extending previous counterexamples to a general class of rough volatility models.

Research Flowchart

  flowchart TD
    A[Research Goal: Refute Gatheral's Conjecture for SV Models] --> B{Methodology: Asymptotic Properties & Wiener Chaos};
    B --> C[Inputs: Integrated Variance Derivatives, Volatility Derivatives];
    C --> D[Computational Processes: Analyze asymptotic behavior, Wiener Chaos Expansions];
    D --> E{Findings: General sufficient conditions for refutation};
    E --> F[Outcome 1: Rough Volatility Models are counterexamples];
    E --> G[Outcome 2: Markovian Variance models fail under specific SDE coefficient relations];

Cited References (13)

  1. On smile properties of volatility derivatives: Understanding the VIX skew (2022)
  2. On the skew-curvature power law relationship in a stochastic volatility model with infinite variation L 'e vy jumps — → 2610.23488
  3. Gatheral’s Conjecture Revisited — → 2609.05047
  4. Spatial ergodicity for SPDEs via Poincar 'e -type inequalities (2021)
  5. On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility (2007)
  6. New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients (2014)
  7. The boundedness of solutions of linear differential equations $y’’+A(t)y=0$ (1957)
  8. Discrete non-linear inequalities and applications to boundary value problems (2006)
and 5 more
  1. Valuation of volatility derivatives (2005)
  2. Volatility swaps made simple (2000)
  3. Is the minimum value of an option on variance generated by local volatility? (2011)
  4. Mimicking an I t ^o process by a solution of a stochastic differential equation (2013)
  5. Nonnegativity preserving convolution kernels. Application to Stochastic Volterra Equations in closed convex domains and their approximation — → 2302.07758

3 of 13 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2570 linked papers.