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SYFT: Fat-Tail Distributions - Applications from Physics to Finance

SYFT 3: Fat-Tail Distributions - Applications from Physics to Finance

SYFT 3.1: Poster

Montag, 8. März 2004, 16:00–18:00, Poster D

Extreme value distributions for processes with Gaussian, Lévy and truncated Lévy distributed increments: A computer simulation study — •Thomas Schwiertz and Wolfgang Paul — Institut für Physik, Johannes Gutenberg-Universität, 55099 Mainz

For many applications it is not so much of interest what the average behavior of a stochastic process is but what its extremal excursions in a time interval are. Examples are material failure, portfolio risk and the pricing of barrier options. For sequences of identically distributed random numbers there exists an exact classification of limiting distributions for their extremal values. For sum variables (the time-dependent stock price for instance) no general solution is known. Specifically it is of interest to contrast Gaussian distributed increments to Lévy distributed ones and to analyze the crossover between the two for truncated Lévy distributed increments known to describe stock price fluctuations on the time scale of a few minutes.