Gunther Leobacher: A Brownian bridge construction for non-Gaussian processes

The classical Brownian bridge construction depends heavily on the fact that two normals are independent if and only if they are uncorrelated, which makes it hard to generalize to more general Lévy processes. We demonstrate how one can find a construction of paths of a Lévy process which has all the advantages of a Brownian bridge construction. We give numerical results from applications in finance.


Ernst Eberlein and U. Keller.
Hyperbolic distributions in finance.
Bernoulli, 1:281-299, 1995.

Gerhard Larcher, Martin Predota, and Robert F. Tichy.
Arithmetic average options in the hyperbolic model.
Monte Carlo Methods Appl., 9(3):227-239, 2003.

William J. Morokoff.
Generating quasi-random paths for stochastic processes.
SIAM Rev., 40(4):765-788 (electronic), 1998.

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