Méthode d'inférence utilisant la vraisemblance empirique basée sur l'entropie pour les modèles de diffusion avec sauts
|Abstract:||With the advent of increasingly sophisticated models for modeling stock market returns, the classical maximum likelihood method for inferring parameters is generally no longer applicable since, for example, the density function has no closed form or very difficult to calculate numerically. In the literature, inference by the method of moments (MM) is therefore generally suggested. In this master’s thesis, a more efficient inference method, the maximum empirical entropy likelihood (MEEL), is proposed for two particular cases of the Lévy process, namely the Merton and Tsay models. First, a review of some models developed in the past is done. The flaws of the geometric Brownian motion are presented to justify the use of more sophisticated models. Then, the two models, Merton and Tsay, and their properties are presented in more detail. Subsequently, there is a comparative analysis between the effectiveness of the MEEL and the MM; an example with real data is also presented. Finally, two approaches to pricing derivatives are presented.|
|Document Type:||Mémoire de maîtrise|
|Open Access Date:||5 March 2019|
|Collection:||Thèses et mémoires|
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