Option Pricing from Wavelet-Filtered Financial Series

TL;DR

This paper demonstrates that wavelet filtering of high-frequency financial data, specifically using Haar basis, retains essential non-Gaussian features for option pricing while significantly reducing data complexity.

Contribution

It introduces a wavelet-based method to simplify financial time series for option valuation without losing critical statistical properties.

Findings

Small scale wavelet components can be neglected for option pricing.

Low-pass wavelet filtering preserves non-Gaussian features over longer expiration times.

Wavelet decomposition effectively compresses financial data while maintaining relevant information.

Abstract

We perform wavelet decomposition of high frequency financial time series into large and small time scale components. Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out that the small scale component defined by most ($\simeq$ 99.6%) of the wavelet coefficients can be neglected for the purpose of option premium evaluation. The relevance of the hugely compressed information provided by low-pass wavelet-filtering is related to the fact that the non-gaussian statistical structure of the original financial time series is essentially preserved for expiration times which are larger than just one trading day.