Non-Gaussian Stochastic Volatility Model with Jumps via Gibbs Sampler

TL;DR

This paper introduces a non-Gaussian stochastic volatility model with jumps, utilizing a Gibbs sampler for exact Bayesian inference, improving volatility estimation in financial time series by capturing jumps and avoiding Metropolis algorithms.

Contribution

It presents a novel model that allows automatic volatility estimation with known full conditional distributions, enabling exact sampling via Gibbs sampler, unlike previous MCMC-based methods.

Findings

Model accurately captures jumps in returns.

Gibbs sampler provides exact posterior samples.

Performance validated on synthetic and real data.

Abstract

In this work, we propose a model for estimating volatility from financial time series, extending the non-Gaussian family of space-state models with exact marginal likelihood proposed by Gamerman, Santos and Franco (2013). On the literature there are models focused on estimating financial assets risk, however, most of them rely on MCMC methods based on Metropolis algorithms, since full conditional posterior distributions are not known. We present an alternative model capable of estimating the volatility, in an automatic way, since all full conditional posterior distributions are known, and it is possible to obtain an exact sample of parameters via Gibbs Sampler. The incorporation of jumps in returns allows the model to capture speculative movements of the data, so that their influence does not propagate to volatility. We evaluate the performance of the algorithm using synthetic and real data time series. Keywords: Financial time series, Stochastic volatility, Gibbs Sampler, Dynamic linear models.