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This paper deals with the problem of global parameter estimation of affinediffusions in $\mathbb{R}_+ \times \mathbb{R}^n$ denoted by $AD(1, n)$ where$n$ is a positive integer which is a subclass of affine diffusions introducedby Duffie et al in [14]. The $AD(1, n)$ model can be applied to the pricing ofbond and stock options, which is illustrated for the Vasicek,Cox-Ingersoll-Ross and Heston models. Our first result is about theclassification of $AD(1, n)$ processes according to the subcritical, criticaland supercritical cases. Then, we give the stationarity and the ergodicitytheorems of this model and we establish asymptotic properties for the maximumlikelihood estimator in both subcritical and a special supercritical cases.

Asymptotic properties of AD(1, n) model and its maximum likelihood estimator