Martingale Expansions for Stochastic Volatility Distributions

Summary

This work develops a martingale expansion to approximate marginal distributions more accurately than the normal approximation associated with the martingale central limit theorem. It adapts the framework to continuous stochastic volatility models and derives first-order perturbation expansions.

The approach covers settings with small volatility-of-volatility as well as models with fast mean reversion, under essentially minimal conditions. The document describes a theoretical approximation framework, but provides no empirical evaluation, numerical results, or detailed conditions in the supplied summary. Its stated scope is therefore distributional approximation in continuous stochastic volatility models.

Key ideas

• Martingale expansions refine marginal distribution approximations beyond the normal central limit approximation.
• The framework is tailored to continuous stochastic volatility models.
• First-order perturbation expansions are derived for small volatility-of-volatility settings.
• The method also accommodates fast mean-reversion models under minimal conditions.

Tags

# Martingale expansion for stochastic volatility


# Martingale expansion for stochastic volatility









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.