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

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.
Document type :
Journal articles
Domain :

https://hal-normandie-univ.archives-ouvertes.fr/hal-02332410
Contributor : Mohamed Ben Alaya <>
Submitted on : Thursday, October 24, 2019 - 5:35:03 PM
Last modification on : Tuesday, October 20, 2020 - 3:56:27 PM

### Identifiers

• HAL Id : hal-02332410, version 1
• ARXIV : 1509.08869

### Citation

Matyas Barczy, Mohamed Ben Alaya, Ahmed Kebaier, Gyula Pap. Asymptotic behavior of maximum likelihood estimators for a jump-type Heston model. Journal of Statistical Planning and Inference, Elsevier, 2019. ⟨hal-02332410⟩

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