Sequential Monte Carlo for fractional Stochastic Volatility Models

TL;DR

This paper introduces a sequential Monte Carlo approach for estimating volatility and parameters in fractional stochastic volatility models, capturing long-range dependence and antipersistent behaviors with proven asymptotic properties.

Contribution

It develops a novel Monte Carlo methodology applicable to both long memory and antipersistent processes in stochastic volatility modeling.

Findings

Proven central limit theorem for filters

Asymptotic consistency and normality of estimates

Successful application to S&P 500 data

Abstract

In this paper we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behavior. We propose a dynamic sequential Monte Carlo methodology that is applicable to both long memory and antipersistent processes in order to estimate the volatility as well as the unknown parameters of the model. We establish a central limit theorem for the state and parameter filters and we study asymptotic properties (consistency and asymptotic normality) for the filter. We illustrate our results with a simulation study and we apply our method to estimating the volatility and the parameters of a long-range dependent model for S&P 500 data.