Asymptotic behavior of maximum likelihood estimators for a jump-type Heston model

TL;DR

This paper investigates the asymptotic properties of maximum likelihood estimators for a jump-type Heston model with non-Gaussian Lévy jumps, establishing consistency and normality results under broad conditions.

Contribution

It provides the first comprehensive analysis of MLE asymptotics for jump-type Heston models with general Lévy processes, including cases with unbounded variation.

Findings

Proves strong consistency and asymptotic normality for most parameters.

Identifies an exceptional parameter case with only weak consistency and mixed normal behavior.

Numerical simulations support theoretical results.

Abstract

We study asymptotic properties of maximum likelihood estimators of drift parameters for a jump-type Heston model based on continuous time observations, where the jump process can be any purely non-Gaussian L\'evy process of not necessarily bounded variation with a L\'evy measure concentrated on $(-1,\infty)$. We prove strong consistency and asymptotic normality for all admissible parameter values except one, where we show only weak consistency and mixed normal (but non-normal) asymptotic behavior. It turns out that the volatility of the price process is a measurable function of the price process. We also present some numerical illustrations to confirm our results.