Riemann Manifold Langevin Methods on Stochastic Volatility Estimation

TL;DR

This paper introduces Riemann manifold Langevin methods for Bayesian estimation of stochastic volatility models with heavy tails, demonstrating their effectiveness through simulations and real financial data analysis.

Contribution

It provides analytical expressions for Riemann manifold Langevin methods and evaluates their performance in stochastic volatility estimation.

Findings

Methods outperform traditional approaches in simulated data

Effective in modeling heavy-tailed financial data

Demonstrated on real financial time series datasets

Abstract

In this paper we perform Bayesian estimation of stochastic volatility models with heavy tail distributions using Metropolis adjusted Langevin (MALA) and Riemman manifold Langevin (MMALA) methods. We provide analytical expressions for the application of these methods, assess the performance of these methodologies in simulated data and illustrate their use on two financial time series data sets.