We introduce a microscopic model for the dynamics of the order book to study how the lack of liquidity influences price fluctuations. We use the average density of the stored orders (granularity g) ...as a proxy for liquidity. This leads to a Price Impact Surface which depends on both volume ω and g. The dependence on the volume (averaged over the granularity) of the Price Impact Surface is found to be a concave power law function 〈φ(ω,g)〉
g
∼ω
δ
with δ≈0.59. Instead the dependence on the granularity is φ(ω,g|ω)∼g
α
with α≈-1, showing a divergence of price fluctuations in the limit g→0. Moreover, even in intermediate situations of finite liquidity, this effect can be very large and it is a natural candidate for understanding the origin of large price fluctuations.
Minimal agent based model for financial markets I Alfi, V.; Cristelli, M.; Pietronero, L. ...
The European physical journal. B, Condensed matter physics,
2/2009, Letnik:
67, Številka:
3
Journal Article
Recenzirano
We introduce a minimal agent based model for financial markets to understand the nature and self-organization of the stylized facts. The model is minimal in the sense that we try to identify the ...essential ingredients to reproduce the most important deviations of price time series from a random walk behavior. We focus on four essential ingredients: fundamentalist agents which tend to stabilize the market; chartist agents which induce destabilization; analysis of price behavior for the two strategies; herding behavior which governs the possibility of changing strategy. Bubbles and crashes correspond to situations dominated by chartists, while fundamentalists provide a long time stability (on average). The stylized facts are shown to correspond to an intermittent behavior which occurs only for a finite value of the number of agents N. Therefore they correspond to finite size effects which, however, can occur at different time scales. We propose a new mechanism for the self-organization of this state which is linked to the existence of a threshold for the agents to be active or not active. The feedback between price fluctuations and number of active agents represents a crucial element for this state of self-organized intermittency. The model can be easily generalized to consider more realistic variants.
Minimal agent based model for financial markets II Alfi, V.; Cristelli, M.; Pietronero, L. ...
The European physical journal. B, Condensed matter physics,
2/2009, Letnik:
67, Številka:
3
Journal Article
Recenzirano
We present a detailed study of the statistical properties of the Agent Based Model introduced in paper I Eur. Phys. J. B, DOI: 10.1140/epjb/e2009-00028-4 and of its generalization to the ...multiplicative dynamics. The aim of the model is to consider the minimal elements for the understanding of the origin of the stylized facts and their self-organization. The key elements are fundamentalist agents, chartist agents, herding dynamics and price behavior. The first two elements correspond to the competition between stability and instability tendencies in the market. The herding behavior governs the possibility of the agents to change strategy and it is a crucial element of this class of models. We consider a linear approximation for the price dynamics which permits a simple interpretation of the model dynamics and, for many properties, it is possible to derive analytical results. The generalized non linear dynamics results to be extremely more sensible to the parameter space and much more difficult to analyze and control. The main results for the nature and self-organization of the stylized facts are, however, very similar in the two cases. The main peculiarity of the non linear dynamics is an enhancement of the fluctuations and a more marked evidence of the stylized facts. We will also discuss some modifications of the model to introduce more realistic elements with respect to the real markets.
Price dynamics is analyzed in terms of a model which includes the possibility of effective forces due to trend followers or trend adverse strategies. The method is tested on the data of a ...minority–majority model and indeed it is capable of reconstructing the prevailing traders’ strategies in a given time interval. Then we also analyze real (NYSE) stock-prices dynamics and it is possible to derive an indication for the “sentiment” of the market for time intervals of at least one day.
PDF
