Estimation statistique des paramètres pour les processus de Cox-Ingersoll-Ross et de Heston

Abstract : The Cox-Ingersoll-Ross process and the Heston process are widely used in financial mathematics for pricing and hedging or to model interest rates. In this thesis, we focus on estimating their parameters using continuous-time observations. Firstly, we restrict ourselves to the most tractable situation where the CIR processis geometrically ergodic and does not vanish. We establish a large deviations principle for the maximum likelihood estimator of the couple of dimensionnal and drift parameters of a CIR process. Then we establish a moderate deviations principle for the maximum likelihood estimator of the four parameters of an Heston process, as well as for the maximum likelihood estimator of the couple of parameters of a CIR process. In contrast to the previous literature, parameters are estimated simultaneously. Secondly, we do not restrict ourselves anymore to the case where the CIR process never reaches zero and we introduce a new weighted least squares estimator for the quadruplet of parameters of an Heston process. We establish its strong consitency and asymptotic normality, and we illustrate numerically its good performances.
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Marie Du Roy de Chaumaray. Estimation statistique des paramètres pour les processus de Cox-Ingersoll-Ross et de Heston. Mathématiques générales [math.GM]. Université de Bordeaux, 2016. Français. ⟨NNT : 2016BORD0299⟩. ⟨tel-01416623⟩

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