Error bounds for small jumps of Lévy processes and financial applications
Résumé
The pricing of exotic options in exponential Lévy models amounts to the computation of expectations of functionals of the whole path of a Lévy process. In many situations, Monte-Carlo methods are used. However, the simulation of a Lévy process with infinite Lévy measure generally requires either to truncate small jumps or to replace them by a Brownian motion with the same variance. We derive bounds for the errors generated by these two types of approximation. These bounds can be applied to a number of exotic options (barriers, lookback, American, Asian).
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