Processus de Lévy en finance : problèmes inverses et modélisation de dépendance

摘要: This thesis deals with the modelling of stock prices by exponentials Levy processes. In first part we develop a non-parametric method allowing to calibrate exponential models, that is, reconstruct such models from market-quoted options. We study stability and convergence properties this calibration method, describe its numerical implementation give examples use. Our approach is reformulate problem as finding risk-neutral model reproduces option best possible precision has smallest relative entropy respect given prior process, then solve via regularization methodology, used in theory ill-posed inverse problems. Applying empirical data sets index options allows us some measures, implied market prices. The second proposes characterize dependence structures among components multidimensional process construct models. done introducing notion copula, which can be seen an analog for processes statistics between real-valued random variables. parametric families copulas simulating copula.