Weak error approximation for rough and Gaussian mean-reverting stochastic volatility models

Paper: arXiv 2602.18234

Authors: Aurélien Alfonsi, Ahmed Kebaier

Abstract

For a class of stochastic models with Gaussian and rough mean-reverting volatility that embeds the genuine rough Stein-Stein model, we study the weak approximation rate when using a Euler type scheme with integrated kernels. Our first result is a weak convergence rate for the discretised rough Ornstein-Uhlenbeck process, that is essentially in $\min(3α-1,1)$, where $\frac{t^{α-1}}{Γ(α)} $ is the fractional convolution kernel with $α\in (1/2,1)$. Then, our main result is to obtain the same convergence rate for the corresponding stochastic rough volatility model with polynomial test functions.

Complexity vs Empirical Score

• Math Complexity: 9.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a rigorous theoretical probability analysis of weak convergence rates for discretization schemes of rough stochastic volatility models using Malliavin calculus. While highly sophisticated analytically, it is purely theoretical math with no empirical data, backtesting, or code provided.

Research Flowchart

  flowchart TD
    A["Research Goal: Analyze weak approximation rate for rough & Gaussian mean-reverting volatility models"] --> B["Inputs: Rough Stein-Stein model, Fractional kernel t<sup>α-1</sup>/Γ(α) (α ∈ (1/2, 1))"]
    B --> C["Methodology: Euler-type scheme with integrated kernels & polynomial test functions"]
    C --> D["Process 1: Discretize rough Ornstein-Uhlenbeck process & evaluate weak error"]
    D --> E["Process 2: Extend error analysis to full stochastic rough volatility model"]
    E --> F["Outcomes: Weak convergence rate established as min(3α-1, 1) for both OU process and full model"]