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The aims of this lecture is to introduce Lévy processes in modeling of financial assets. The features of this type of stochastic process is to present jumps, thus modeling sudden changes in assets. Unlike the Black and Scholes option pricing which leads to solving parabolic second order PDE, in the jump model option pricing problem leads to solving integro-differential equations (IDE). The last part of the lecture will be devoted to the implementation of these IDE solving techniques.Contact Raphaël ROSSIGNOL, Georges-Henri COTTET, Emmanuel MAITRE
I Lévy Processes
II integro-differential equations for option prices
III Numerical Methods
PDE for finance lecture
Session 1 : written, with lectures notes. Duration : 2H
Session 2 : written, with lectures notes. Durations : 2H
Equations intégro-différentielles d'évolution: méthodes numériques et appliquations en finance. Ekaterina Voltchkova, Ecole Polytechnique X, 2005.
Financial modelling with jump processes, Rama Cont et Peter Tankov, Chapman et Hall 2004.