Analytical approximations for financial derivatives
نویسندگان
چکیده
We propose a new approach to the analytical approximation of transition densities typically arising in finance. This allows to obtain an expansion of the price of financial derivatives using as starting point the classical Black&Scholes formula. Explicit error estimates for the expansion truncated at any order are available. A numerical test is presented and possible applications to Monte Carlo methods are discussed. Résumé Approximations analytiques pour l’évaluation de produits financiers dérivés. Nous proposons ici une nouvelle approche à l’approximation analytique de certaines densités de transitions qui se présentent typiquement en finance mathématique. Ceci nous permet d’obtenir une expansion des prix des instruments financiers dérivés en partant de la formule classique de Black&Scholes. Il est possible d’obtenir des estimations explicites de l’erreur pour des expansions tronquées à tout ordre. Nous présentons aussi un test numérique et discutons des applications possibles aux méthodes Monte Carlo.
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