Mining Financial Data using Mixtures of Mirrored Weibull Distributions

TL;DR

This paper introduces a mixture of mirrored Weibull distributions for modeling stock returns, offering a flexible alternative to normal-based models and demonstrating improved risk estimation in financial markets.

Contribution

The paper proposes a novel mixture of mirrored Weibull distributions that better captures non-normal features in financial data and improves risk measure estimation.

Findings

MMW model outperforms Gaussian and t-mixture models in VaR estimation.

The model has a simple density expression and allows fast parameter estimation.

Demonstrated effectiveness on S&P500 stocks.

Abstract

Risk management is an important part of financial practice, essential for protecting assets and investments in modern-day volatile markets. This paper proposes a mixture of mirrored Weibull (MMW) distribution for modelling stock returns and estimating risk measures. Unlike common practices which are typically based on the normal distribution, the MMW model can flexibly accommodate non-normal features frequently exhibited in financial data. It also enjoys appealing properties such as having a simple density expression and fast parameter estimation. We demonstrate the effectiveness of our model by assessing its performance in Value-at-Risk (VaR) estimation of three S&P500 stocks. The MMW model compares favourably to Gaussian mixture model and t-mixture model, with significant improvements in VaR estimation and prediction.