Volatility estimation using Stein particle filter

Abstract

We focus on the critical task of accurately estimating volatility in financial markets, which is essential for risk management and portfolio optimization. Since volatility cannot be directly observed, we typically rely on theoretical models such as GARCH and Stochastic Volatility (SV) models. However, SV models are known for their nonlinearity and high dimensionality, which require computationally intensive methods like MCMC or particle filters. These methods, however, often face challenges related to computational efficiency and convergence. In this study, we propose a new approach to volatility estimation using a SV model with a Stein Particle Filter (SPF). By leveraging interactions between particles, we address the limitations of traditional particle filters based on importance sampling. Specifically, we adopt a gradient-based update rule using a Radial Basis Function kernel, enabling particles to efficiently converge to the true posterior distribution. Through numerical experiments with a regime-switching SV model, we demonstrate that SPF outperforms conventional SIR filters in both accuracy and convergence speed.