Mathematics and Financial Economics

, Volume 3, Issue 2, pp 89–114 | Cite as

Microfoundations for diffusion price processes

Article

Abstract

We study microeconomic foundations of diffusion processes as models of stock price dynamics. To this end, we develop a microscopic model of a stock market with finitely many heterogeneous economic agents, who trade in continuous time, giving rise to an endogeneous pure-jump process describing the evolution of stock prices over time. When the number of agents in the market is large, we show that the price process can be approximated by a diffusion, with price-dependent drift and volatility coefficients that are determined by small excess demands and trading volume in the microscopic model. We extend the microscopic model further by allowing for non-market interactions between agents, to model herd behavior in the market. In this case, price dynamics can be approximated by a process with stochastic volatility. Finally, we demonstrate how heavy-tailed stock returns emerge when agents have a strong tendency towards herd behavior.

Keywords

Stock prices Microfoundations Diffusion processes Stochastic volatility Heavy tails 

Mathematics Subject Classification (2000)

91B26 60F17 60J75 

JEL Classification

C65 D53 G12 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsingin yliopistoFinland

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