Asymptotic analysis for stochastic volatility: Edgeworth expansion

TL;DR

This paper proves the validity of an approximation formula for European option prices under stochastic volatility models using Edgeworth expansion, validating existing perturbation methods for fast mean reverting models.

Contribution

It provides a rigorous proof of the approximation's validity via Edgeworth expansion, enhancing the theoretical foundation of option pricing under stochastic volatility.

Findings

The approximation formula is valid uniformly for bounded payoffs.

The Edgeworth expansion accurately describes the distribution of ergodic diffusions.

Validation of perturbation expansion for fast mean reverting models.

Abstract

The validity of an approximation formula for European option prices under a general stochastic volatility model is proved in the light of the Edgeworth expansion for ergodic diffusions. The asymptotic expansion is around the Black-Scholes price and is uniform in bounded payoff func- tions. The result provides a validation of an existing singular perturbation expansion formula for the fast mean reverting stochastic volatility model.