Stochastic price processes with epsilon-correlated returns

Kremer, Torsten , Richter, Matthias , Hans-Jörg Starkloff and Ralf Wunderlich

Preprint 2001-17, TU Chemnitz, Faculty of Mathematics

Abstract :

Empirical autocorrelation functions of returns of stochastic price processes show phenomena of correlation on small intervals of time, which decay to zero after a short time. The paper deals with the concept of weakly correlated random processes to describe a mathematical model which takes into account this behaviour of statistical data. Weakly correlated functions have been applied to model numerous problems of physics and engineering. The main idea is, that the values of the functions at two points are uncorrelated if the distance between the points exceeds a certain quantity epsilon>0. In contrast to the white noise model, for distances smaller than epsilon a correlation between the values is permitted. A property of the introduced price model is, that the corresponding stochastic processes possess absolutely continuous sample paths. Therefore the used concept implies, that the so called condition of ''No Free Lunch with Vanishing Risk'' is not fulfilled.

Keywords :
Arbitrage; Bounded Variation Processes; Financial Analysis; Weakly Correlated Processes