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We provide a method for the generation of paths of Lévy processes which has many of the benefits that the Brownian bridge construction has for Brownian motion. We show how, using our method, one can apply stratified sampling and quasi-Monte Carlo methods to obtain better numerical schemes analog to the Brownian case. As a numerical example we consider the problem of pricing an asian option in the so-called hyperbolic market model.doi:10.1515/156939606778705155 fatcat:otpclcm2abfl3amsjifpenfvy4