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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.
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Contributor : Mohamed Ben Alaya Connect in order to contact the contributor
Submitted on : Thursday, October 24, 2019 - 5:35:03 PM
Last modification on : Thursday, November 4, 2021 - 5:14:09 PM

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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. Journal of Statistical Planning and Inference, Elsevier, 2019, 198, pp.139-164. ⟨10.1016/j.jspi.2018.02.002⟩. ⟨hal-02332410⟩

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