Microfoundations for diffusion price processes
- 129 Downloads
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.
KeywordsStock prices Microfoundations Diffusion processes Stochastic volatility Heavy tails
Mathematics Subject Classification (2000)91B26 60F17 60J75
JEL ClassificationC65 D53 G12
Unable to display preview. Download preview PDF.
- 2.Bayraktar, E., Horst, U., Sircar, R.: Queueing theoretic approaches to financial price fluctuations. In: Birge, J.R., Linetsky, V. (eds.) Financial Engineering, Handbooks in Operations Research and Management Science, vol. 15, pp. 637–680. Elsevier, Amsterdam (2007)Google Scholar
- 14.Hoffmann-Jørgensen, J.: Probability in Banach space. In: École d’Été de Probabilités de Saint-Flour, VI-1976. Lecture Notes in Math., vol. 598, pp. 1–186. Springer, Berlin (1977)Google Scholar
- 22.R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. URL: http://www.R-project.org (2008)