The physics of finance: Collective dynamics in a complex world

Abstract

Exploring the dynamics of financial time-series is an exciting and interesting challenge because of the many truly complex interactions that underly the price formation process. In this contribution we describe some of the anomalous statistical features of such time-series and review models of the price dynamics both across time and across the universe of stocks. In particular we discuss a non-Gaussian statistical feedback process of stock returns which we have developed over the past years with the particular application of option pricing. We then discuss a cooperative model for the correlations of stock dynamics which has its roots in the field of synergetics. In all cases numerical simulations and comparisons with real data are presented.