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

SYFT 1: Fat-Tail Distributions - Applications from Physics to Finance

SYFT 1.3: Hauptvortrag

Donnerstag, 11. März 2004, 10:30–11:00, H1

Non-Gaussian option pricing — •Hagen Kleinert — Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195 Berlin

A new option pricing formula is derived which takes into account the risk of rare dramatic price changes by using non-Gaussian distributions with heavy tails. The derivation is based on a solvable path integral corresponding to a Gaussian process in which the width fluctuates with Gaussian noise. The resulting returns fit the Dow Jones data over many times scales.

[1] H. Kleinert, Physica A 311, 536 (2002) (cond-mat/0203157)

[2] H. Kleinert, Physica A 312, 217 (2002) (cond-mat/0202311)

[3] See Chapter 20 in the textbook Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, World Scientific, Singapore, 2003.