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| HAL: hal-00579644, version 1 |
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| Parameter Estimation for the Square-root Diffusions : Ergodic and Nonergodic Cases |
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Mohamed Ben Alaya 1Ahmed Kebaier 1 |
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| For the Mohamed Ben Alaya collaboration(s) |
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| (2010-04-09) |
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| This paper deals with the problem of parameter estimation in the Cox-Ingersoll-Ross (CIR) model $(X_t)_{t\geq 0}$. This model is frequently used in finance for example as a model for computing the zero-coupon bound price or as a dynamic of the volatility in the Heston model. When the diffusion parameter is known, the maximum likelihood estimator (MLE) of the drift parameters involves the quantities : $\int_{0}^{t}X_sds$ and $\int_{0}^{t}\frac{ds}{X_s}$. At first, we study the asymptotic behavior of these processes. This allows us to obtain various and original limit theorems on our estimators, with different rates and different types of limit distributions. Our results are obtained for both cases : ergodic and nonergodic diffusion. Numerical simulations were processed using an exact simulation algorithm. |
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| 1: | Laboratoire Analyse, Géométrie et Application (LAGA) |
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CNRS : UMR7539 – Université Paris XIII - Paris Nord – Université Paris VIII - Vincennes Saint-Denis |
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| Subject | : | Mathematics/Probability Mathematics/Statistics Statistics/Statistics Theory |
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| Cox-Ingersoll-Ross processes – Nonergodic diffusion – Laplace transform – Limit theorems – Parameter inference – Simulation efficiency : Exact methods. |
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| hal-00579644, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00579644 | |
| oai:hal.archives-ouvertes.fr:hal-00579644 | |
| From: Ahmed Kebaier | |
| Submitted on: Thursday, 24 March 2011 14:52:24 | |
| Updated on: Thursday, 10 November 2011 15:39:21 | |
