Power law in Sandwiched Volterra Volatility model

Paper: arXiv 2311.01228

Authors: Giulia Di Nunno, Anton Yurchenko-Tytarenko

Abstract

In this paper, we present analytical proof demonstrating that the Sandwiched Volterra Volatility (SVV) model is able to reproduce the power-law behavior of the at-the-money implied volatility skew, provided the correct choice of the Volterra kernel. To obtain this result, we assess the second-order Malliavin differentiability of the volatility process and investigate the conditions that lead to explosive behavior in the Malliavin derivative. As a supplementary result, we also prove a general Malliavin product rule.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents high theoretical sophistication through Malliavin calculus and Volterra kernels to prove power-law behaviors in ATM implied volatility skew. However, it lacks empirical validation, calibration, or backtesting on real market option data.

Research Flowchart

  flowchart TD
    A["Research Goal: Prove SVV model reproduces ATM implied volatility skew power-law"] --> B["Input: Sandwiched Volterra Volatility SVV model & Volterra Kernel"]
    B --> C["Assess 2nd-order Malliavin differentiability of volatility process"]
    C --> D["Analyze conditions for explosive behavior in Malliavin derivative"]
    D --> E["Derive general Malliavin product rule"]
    E --> F["Main Outcome: Analytical proof of power-law skew for appropriate Volterra kernel"]