Martingale expansion for stochastic volatility
Probability
2026-02-06 v2 Mathematical Finance
Abstract
The martingale expansion provides a refined approximation to the marginal distributions of martingales beyond the normal approximation implied by the martingale central limit theorem. We develop a martingale expansion framework specifically suited to continuous stochastic volatility models. Our approach accommodates both small volatility-of-volatility and fast mean-reversion models, yielding first-order perturbation expansions under essentially minimal conditions.
Cite
@article{arxiv.2601.09324,
title = {Martingale expansion for stochastic volatility},
author = {Masaaki Fukasawa},
journal= {arXiv preprint arXiv:2601.09324},
year = {2026}
}