Constrained Mixture Models for Asset Returns Modelling

TL;DR

This paper introduces a constrained mixture model combining Gamma and Gaussian distributions to accurately model asset return distributions, capturing positive, negative, or ranging trends with heavy tails and kurtosis.

Contribution

It proposes a novel constrained mixture modeling approach for asset returns, integrating Gamma and Gaussian components within an EM framework with model order estimation.

Findings

Effective modeling of asset return distributions with heavy tails.

Accurate identification of price trend regimes.

Robust parameter estimation under model constraints.

Abstract

The estimation of asset return distributions is crucial for determining optimal trading strategies. In this paper we describe the constrained mixture model, based on a mixture of Gamma and Gaussian distributions, to provide an accurate description of price trends as being clearly positive, negative or ranging while accounting for heavy tails and high kurtosis. The model is estimated in the Expectation Maximisation framework and model order estimation also respects the model's constraints.