Ebook Stochastic Behavioral Asset Pricing Models and the Stylized Facts
The finance literature hast a somewhat ambiguous approach towards the salient empirical features that characterize financial markets. While they are identified as `stylized facts' in recent surveys (de Vries, 1994; Pagan, 1996), they have more often been christened as `anomalies' in the past (cf. Frankfurter and McGoun, 2001, who argue that the increasing (mis)use of the term `anomaly' in the finance literature is evidence of a propagandistic "effort to imply that ... the reigning paradigm is irreplaceable..." (from their abstract)). The difference in language is perplexing: while the former notion implies an identification of robust features of the data that call for a scientific explanation, the later rather appears to denounce the same features as a minor nuisance for the established theoretical framework. One certainly does not do injustice to a large body of theoretical research in finance by stating that it had almost entirely ignored some of the most pervasive characteristics of financial markets for quite some time. While this does not hold for all of the stylized facts, it is certainly undisputable for two important regularities that have motivated a large part of the empirical finance literature: the fat tails of asset returns and the characteristic time-variation of their fluctuations. To be honest, a few attempts at explaining these features on the base of standard modeling frameworks do exist in recent literature (cf. Vanden, 2005), but at least there has been no systematic theoretical approach towards their explanation within `mainstream' models.
However, it also needs to be emphasized that mainstream finance had not been careless about empirical results altogether: on the contrary, one of the most important empirical findings, the martingale character of prices, is at the heart of its main paradigmatic approach, the efficient market hypothesis. It appears, however, that focusing on the explanation of this single feature, other equally universal findings have been deliberately neglected and marginalized as anomalies. The point that will be made in this chapter is that, from a different perspective, what has been found to be strange and unexpected behavior of markets, might appear as revealing charac-teristics that could guide the scientist towards a candidate explanation of price dynamics in financial markets. The surprising insight here is that when presented in an appropriate format - the stylized facts so well known to econometricians and market practitioners would immediately be identified as scaling laws by natural scientists. Viewed from this perspective, a picture emerges that differs enormously from that of traditional finance: scaling laws in natural science are viewed as imprints of complex systems composed of many interacting subunits that have to be explained as a result of their microscopic interaction.
This motivates an approach towards modeling of financial markets that focusing on the interaction of many actors rather than intertemporal optimization of representative investors. Models with such an emphasis have been proposed from the early nineties both by economists dissatisfied with the representative agent methodology as well as by physicists in the evolving `econophysics' movement. To some extent, the promise of the scaling approach seems to have materialized: models with interacting agents of a certain type appear to be quite robust generators of the formerly mysterious anomalies of fat tails and clustered volatility. This explanatory power for some of the previously unexplained characteristics of financial markets might lend some credibility to this new approach.
The remainder of this chapter starts with an outline of the empirical stylized facts that have been of such utmost importance for the development of stochastic agent-based models. In section 2 we discuss in turn: the martingale property, fat tails and clustering of volatility and have a cursory look at other reported regularities. Section 3 highlights the interpretation of these stylized facts as `scaling laws' and the connotations of this view for theoretical modeling. Section 4 goes into details about some representative models in the area: we start with a short exposition of sources of inspiration for these models in 4.1 in the older literature on interaction of different groups of speculators (e.g. fundamentalists vs. chartists) and then move on to models that are very explicitly based on microscopic interactions: Kirman's (1993) `ant' model and its financial interpretations is dealt with in 4.2 and the models of interacting speculators proposed by Lux and Marchesi are featured in sec 4.3. More complicated models with a lattice-based topological structure are considered in sec. 4.4. Section 5 concludes and tries to provide an assessment of the state of this new approach vis-à-vis other approaches in the field of behavioral finance.
Contents
1 Introduction
2 The Stylized Facts of Financial Data
2.1 Martingales, Lack of Predictability and Informational Efficiency
2.2 Fat Tails of Asset Returns
2.3 Volatility Clustering and Dependency in Higher Moments
2.4 Other Stylized Facts
3 The Stylized Facts as `Scaling Laws'
4 Behavioral Asset Pricing Models with Interacting Agents
4.1 Interaction of Chartists and Fundamentalists in Complex Nonlinear Dynamics
4.2 Kirman's Model of Opinion Formation and Speculation
4.3 Beyond Local Interactions: Socio-Economic Group Dynamics in Financial Markets
- 4.3.1 Social Interactions: A General Framework
4.3.2 An Asset Pricing Model with Social Interactions
4.3.3 Realistic Dynamics and the `Stylized Facts'
4.4 Lattice Topologies of Agents' Connections
5 Conclusions
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