Asymptotic properties of maximum-likelihood estimators for Heston models based on continuous time observations

Abstract

We study asymptotic properties of maximum-likelihood estimators for Heston models based on continuous time observations of the log-price process. We distinguish three cases: subcritical (also called ergodic), critical and supercritical. In the subcritical case, asymptotic normality is proved for all the parameters, while in the critical and supercritical cases, non-standard asymptotic behaviour is described.

Keywords:

• Heston model
• maximum-likelihood estimator

Mathematics Subject Classifications:

• 60H10
• 91G70
• 60F05
• 62F12

Acknowledgement

We would like to thank the referees for their comments that helped us to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of M. Barczy and G. Pap was realized in the frames of TÁMOP 4.2.4.A/2-11-1-2012-0001 ‘National Excellence Program – Elaborating and operating an inland student and researcher personal support system’. The project was subsidized by the European Union and co-financed by the European Social Fund.