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Jump-adapted discretization schemes for Lévy-driven SDEs. (English) Zbl 1202.60113

Summary: We present new algorithms for weak approximation of stochastic differential equations driven by pure jump Lévy processes. The method uses adaptive non-uniform discretization based on the times of large jumps of the driving process. To approximate the solution between these times we replace the small jumps with a Brownian motion. Our technique avoids the simulation of the increments of the Lévy process, and in many cases achieves better convergence rates than the traditional Euler scheme with equal time steps. To illustrate the method, we discuss an application to option pricing in the Libor market model with jumps.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
65C05 Monte Carlo methods
60G51 Processes with independent increments; Lévy processes
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