Variance-Gamma (VG) model: Fractional Fourier Transform (FRFT)

TL;DR

This paper explores the use of Fractional Fourier Transform to estimate the Variance-Gamma model, demonstrating its effectiveness in fitting asset return data better than traditional models.

Contribution

It introduces a novel application of FRFT for estimating the VG model and compares its performance to classical models using real ETF data.

Findings

VG model fits data better than CLM based on KS test

FRFT provides accurate estimation of the VG distribution

VG model estimated via FRFT captures asset return distribution effectively

Abstract

The paper examines the Fractional Fourier Transform (FRFT) based technique as a tool for obtaining the probability density function and its derivatives, and mainly for fitting stochastic model with the fundamental probabilistic relationships of infinite divisibility. The probability density functions are computed, and the distributional proprieties are reviewed for Variance-Gamma (VG) model. The VG model has been increasingly used as an alternative to the Classical Lognormal Model (CLM) in modelling asset prices. The VG model was estimated by the FRFT. The data comes from the SPY ETF historical data. The Kolmogorov-Smirnov (KS) goodness-of-fit shows that the VG model fits the cumulative distribution of the sample data better than the CLM. The best VG model comes from the FRFT estimation.