A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration
Abstract
Calibration to a surface of option prices requires specifying a suitably flexible martingale model for the discounted asset price under a risk-neutral measure. Assuming Brownian noise and mean-square integrability, we construct an over-parameterized model based on the martingale representation theorem. In particular, we approximate the terminal value of the martingale via a truncated Wiener--chaos expansion and recover the intermediate dynamics by computing the corresponding conditional expectations. Using the Hermite-polynomial formulation of the Wiener chaos, we obtain easily implementable expressions that enable fast calibration to a target implied-volatility surface. We illustrate the flexibility and expressive power of the resulting model through numerical experiments on both simulated and real market data.
Keywords
Cite
@article{arxiv.2602.16232,
title = {A Wiener Chaos Approach to Martingale Modelling and Implied Volatility Calibration},
author = {Pere Diaz-Lozano and Thomas K. Kloster},
journal= {arXiv preprint arXiv:2602.16232},
year = {2026}
}