Strong Solutions and Quantization-Based Numerical Schemes for a Class of Non-Markovian Volatility Models

Martino Grasselli and Gilles Pag\`es

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Abstract: We investigate a class of non-Markovian processes that hold particular relevance in the realm of mathematical finance. This family encompasses path-dependent volatility models, including those pioneered by [Platen and Rendek, 2018] and, more recently, by [Guyon and Lekeufack, 2023]. Our study unfolds in two principal phases. In the first phase, we introduce a functional quantization scheme based on an extended version of the Lamperti transformation that we propose to handle the presence of a memory term incorporated into the diffusion coefficient. In the second phase, we study the problem of existence and uniqueness of a strong solution for the SDEs related to the examples that motivate our study, in order to provide a theoretical basis to correctly apply the proposed numerical schemes.

Date: 2025-02, Revised 2026-01
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