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Queueing Theoretic Approaches to Financial Price Fluctuations

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  • Erhan Bayraktar
  • Ulrich Horst
  • Ronnie Sircar

Abstract

One approach to the analysis of stochastic fluctuations in market prices is to model characteristics of investor behaviour and the complex interactions between market participants, with the aim of extracting consequences in the aggregate. This agent-based viewpoint in finance goes back at least to the work of Garman (1976) and shares the philosophy of statistical mechanics in the physical sciences. We discuss recent developments in market microstructure models. They are capable, often through numerical simulations, to explain many stylized facts like the emergence of herding behavior, volatility clustering and fat tailed returns distributions. They are typically queueing-type models, that is, models of order flows, in contrast to classical economic equilibrium theories of utility-maximizing, rational, ``representative'' investors. Mathematically, they are analyzed using tools of functional central limit theorems, strong approximations and weak convergence. Our main examples focus on investor inertia, a trait that is well-documented, among other behavioral qualities, and modelled using semi-Markov switching processes. In particular, we show how inertia may lead to the phenomenon of long-range dependence in stock prices.

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Paper provided by arXiv.org in its series Papers with number math/0703832.

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Date of creation: Mar 2007
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Handle: RePEc:arx:papers:math/0703832

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Cited by:
  1. Christian Bayer & Ulrich Horst & Jinniao Qiu, 2014. "A Functional Limit Theorem for Limit Order Books," Papers 1405.5230, arXiv.org.
  2. Yipeng Yang & Allanus Tsoi, 2013. "Prospect Agents and the Feedback Effect on Price Fluctuations," Papers 1308.6759, arXiv.org, revised Jan 2014.

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