An analysis of the effect of noise in a heterogeneous agent financial market model

Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the s...

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Bibliographic Details
Published in:Journal of economic dynamics & control 2011, Vol.35 (1), p.148-162
Main Authors: Chiarella, Carl, He, Xue-Zhong, Zheng, Min
Format: Article
Language:English
Subjects:
Agency theory
Asset pricing
Chartists
Derivatives
Dynamical systems
Economic models
Financial engineering
Financial models
Financial speculation
Heterogeneous agents
Heterogeneous agents Speculative behaviour Stochastic bifurcations Stationary measures Chartists
Mathematical finance
Option pricing
Prices
Speculative behaviour
Stationary measures
Stochastic bifurcations
Stochastic models
Studies
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Summary:Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, it is well known that this indirect approach may not properly characterise the nature of the stochastic model. This paper aims to tackle this issue by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging and stochastic bifurcation theory, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of price trends used by the chartists is far away from zero. However, when this lag approaches zero, such consistency breaks down.
ISSN:0165-1889
1879-1743
DOI:10.1016/j.jedc.2010.09.006