Power Laws as Tail Distributions of Returns in Markets with Trading Specialists: Simulation Results

Abstract

This paper presents preliminary simulation results on tail distributions of returns in a market which trades one kind of stocks, regarded as stocks of a holding company, mediated by a trading specialist who buys and sells the stocks at prices he posts.

When the market excess demands exceed the limits he sets, then he adjust prices in proportion to the excess demands. In the market, two types of participants are on the opposite sides of the market. A jump Markov process formulation is used to model stationary distributions of the number of participants of both types. Under appropriate conditions, they are independent Poisson distributions with related means. We show that the distribution of returns of this artificial model exhibits fat-tail behavior of Lévy distribution, and satisfactorily minic the observed distributions of returns in real markets.