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

Matyas Barczy
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Gyula Pap
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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.
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hal-02185354 , version 1 (13-02-2024)

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Matyas Barczy, Mohamed Ben Alaya, Ahmed Kebaier, Gyula Pap. Asymptotic behavior of maximum likelihood estimators for a jump-type Heston model. 2024. ⟨hal-02185354⟩
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