Microfoundations for diffusion price processes
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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
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- 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)