Weighted least squares estimation for the subcritical Heston process

TL;DR

This paper introduces a weighted least squares estimator for the subcritical Heston process, allowing for more flexible modeling of stochastic volatility and demonstrating strong theoretical properties and good numerical performance.

Contribution

It proposes a novel weighted least squares estimation method for the subcritical Heston process that does not restrict volatility to stay positive, with proven consistency and asymptotic normality.

Findings

Estimator shows strong consistency and asymptotic normality.

Numerical simulations confirm good estimation performance.

Method handles cases where volatility reaches zero.

Abstract

We simultaneously estimate the four parameters of a subcritical Heston process. We do not restrict ourself to the case where the stochastic volatility process never reaches zero. In order to avoid the use of unmanageable stopping times and natural but intractable estimator, we propose to make use of a weighted least squares estimator. We establish strong consistency and asymptotic normality for this estimator. Numerical simulations are also provided, illustrating the good performances of our estimation procedure.