A Harris process to model stochastic volatility

TL;DR

This paper introduces a flexible, tractable stochastic volatility model based on Harris processes, extending Harris chains to continuous time, with demonstrated practical applications and competitive performance.

Contribution

It develops a new continuous-time Harris process for stochastic volatility modeling, offering high flexibility and tailored invariant distributions, with methods for construction, inference, and empirical validation.

Findings

Model shows strong performance in simulations.

Flexible invariant distribution fitting various scenarios.

Competitiveness with existing short-range stochastic volatility models.

Abstract

We present a tractable non-independent increment process which provides a high modeling flexibility. The process lies on an extension of the so-called Harris chains to continuous time being stationary and Feller. We exhibit constructions, properties, and inference methods for the process. Afterwards, we use the process to propose a stochastic volatility model with an arbitrary but fixed invariant distribution, which can be tailored to fit different applied scenarios. We study the model performance through simulation while illustrating its use in practice with empirical work. The model proves to be an interesting competitor to a number of short-range stochastic volatility models.