Asymptotic properties and drift parameter estimations of the ergodic double Heston model based on continuous-time observations

TL;DR

This paper investigates the statistical properties and parameter estimation methods for the ergodic double Heston model, a key tool in financial modeling, focusing on stationarity, ergodicity, and asymptotic behavior of estimators based on continuous data.

Contribution

It provides new theoretical results on the stationarity and ergodicity of the double Heston model and analyzes the asymptotic properties of maximum likelihood and least squares estimators.

Findings

Proves stationarity and ergodicity of the double Heston process.

Derives asymptotic properties of estimators in the ergodic case.

Analyzes maximum likelihood and conditional least squares estimators.

Abstract

The double Heston model is one of the most popular option pricing models in financial theory. It is applied to several issues such that risk management and volatility surface calibration. This paper deals with the problem of global parameter estimations in this model. Our main stochastic results are about the stationarity and the ergodicity of the double Heston process. The statistical part of this paper is about the maximum likelihood and the conditional least squares estimations based on continuous-time observations; then for each estimation method, we study the asymptotic properties of the resulted estimators in the ergodic case.