Edgeworth expansions for volatility models

TL;DR

This paper develops Edgeworth expansions in Kolmogorov and Wasserstein metrics for various discrete-time volatility models, aiding in more accurate approximation of their distributions for option pricing.

Contribution

It introduces Edgeworth expansions for a broad class of volatility models, including GARCH, iterated random functions, and Volterra processes, extending existing methods.

Findings

Edgeworth expansions derived for multiple volatility models

Applicable in both Kolmogorov and Wasserstein metrics

Enhances approximation accuracy for derivative pricing

Abstract

Motivated from option and derivative pricing, this note develops Edgeworth expansions both in the Kolmogorov and Wasserstein metric for many different types of discrete time volatility models and their possible transformations. This includes, among others, H\"{o}lder-type functions of (augmented) Garch processes of any order, iterated random functions or Volterra-processes.