Simulation of Lévy processes and option pricing
Résumé
We use Monte-Carlo methods to valuate exotic options in the exponential Lévy model when the Lévy process has an infinite activity. We first approximate the Lévy process by either truncating its small jumps or replacing them by a Brownian motion with the same variance. Then we use an original method to simulate the big jumps to avoid rejection sampling. The errors resulting from the small jump approximations are also derived for some exotic options (barrier, lookback, American and Asian). Further we propose a simple method to valuate Asian options.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)