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.
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Pakkanen, M.S. Microfoundations for diffusion price processes. Math Finan Econ 3, 89–114 (2010). https://doi.org/10.1007/s11579-010-0029-7
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DOI: https://doi.org/10.1007/s11579-010-0029-7