Bayesian Analysis of Stochastic Volatility Model using Finite Gaussian Mixtures with Unknown Number of Components

TL;DR

This paper presents a Bayesian semi-parametric stochastic volatility model using finite Gaussian mixtures with an unknown number of components, employing a Birth-Death process for model flexibility, demonstrated on stock return data.

Contribution

Introduces a novel Bayesian algorithm with Birth-Death process for finite Gaussian mixture models with unknown components in volatility modeling.

Findings

Effective modeling of stock returns with mixture distributions.

Successful application of Gibbs sampling for posterior inference.

Model adapts the number of mixture components to data complexity.

Abstract

Financial studies require volatility based models which provides useful insights on risks related to investments. Stochastic volatility models are one of the most popular approaches to model volatility in such studies. The asset returns under study may come in multiple clusters which are not captured well assuming standard distributions. Mixture distributions are more appropriate in such situations. In this work, an algorithm is demonstrated which is capable of studying finite mixtures but with unknown number of components. This algorithm uses a Birth-Death process to adjust the number of components in the mixture distribution and the weights are assigned accordingly. This mixture distribution specification is then used for asset returns and a semi-parametric stochastic volatility model is fitted in a Bayesian framework. A specific case of Gaussian mixtures is studied. Using appropriate prior specification, Gibbs sampling method is used to generate posterior chains and assess model convergence. A case study of stock return data for State Bank of India is used to illustrate the methodology.