Lehrstuhl für Geld, Währung und Internationale Finanzmärkte

VW-Project: Financial Markets as Complex Networks (completed)

Project discription

Proposal for the VolkswagenStiftung Grant

"Complex Networks as a Phenomenon Across Disciplines"


Prices and returns in financial markets exhibit robust statistical regularities across space and time. We argue that the network structure among financial market participants (investors, traders, analysts, service providers, institutional platforms, etc.) is of crucial importance for the generation of these regularities, but has been neglected to a large extent until now. As a starting point, we illustrate how a simple model with hierarchical “superstructures” in complex networks could explain these statistical regularities. Our project focuses (i) on an inverse identification of relevant network structures, given the statistical regularities of financial returns; (ii) on the calibration of behavioral parameters in these complex hierarchical networks; and (iii) on economically motivated processes that are capable of generating such complex hierarchical networks.

Research Team

Jun.-Prof. Dr. Simone Alfarano
Economics Dept., University of Kiel
Olshausenstr. 40, D-24118 Kiel
+49 431 880 5136
Prof. Dr. Albrecht Irle
Mathematics Dept., University of Kiel
Ludewig-Meyn-Str. 4, D-24098 Kiel
+49 431 880 4650
Dipl.-Math. Jonas Kauschke
Mathematics Dept., University of Kiel
Ludewig-Meyn-Str. 4, D-24118 Kiel
Prof. Dr. Thomas Lux (Project Coordinator)
Economics Dept., University of Kiel
Olshausenstr. 40, D-24118 Kiel
+49 431 880 3661

 Mishael Milakovic, PhD
Economics Dept., University of Kiel
Olshausenstr. 40, D-24118 Kiel
+49 431 880 3369
Prof. Dr. Friedrich Wagner (em.)
Physics Dept., University of Kiel
Leibnizstr. 15, D-24098 Kiel
+49 431 880 4111

Working papers

"Should Network Structure Matter in Agent-Based Finance?"

by S. Alfarano and M. Milaković


We derive microscopic foundations for a well-known probabilistic herding model in the agent-based finance literature. Lo and behold, the model is quite robust with respect to behavioral heterogeneity, yet structural heterogeneity, in the sense of an underlying network structure that describes the very feasibility of agent interaction, has a crucial and non-trivial impact on the macroscopic properties of the model.


"Network Hierarchy in Kirman's Ant Model: Fund Investments Can Create Risks"


by S. Alfarano, M. Milaković and M. Raddant


Kirman's "ant model" has been used to characterize the expectation formation of financial investors who are prone to herding. In Kirman's original version, however, the model suffers from the problem of Ndependence: the model's ability to replicate the statistical features of financial returns vanishes once the system size N is increased, and the network structure that describes the feasibility of agent interaction in a generalized version of the ant model determines whether or not the model suffers from N-dependence. We investigate a class of hierarchical networks and find that they do overcome the problem of N-dependence, but at the same time they also increase system-wide volatility, and therefore embody an additional source of volatility besides the behavioral heterogeneity of interacting agents. Interpreting these findings in the context of fund investment, the desire of investors to "play it safe" might increase systemic risk if core-periphery networks indeed describe the organizational structure of fund investment.


 "A Hierarchical Network Model as Birth and Death Process in Random Environment"

 by A. Irle and J. Kauschke


In this paper we look at a hierarchical network model for a herding mechanism. We introduce a new class of agents in the network. These agents are not necessary trading on the market, but are con- nected to all other agents in the network and influence the opinions about the future of the market. In mathematical terms, we replace the birth and death processes in the herding mechanism by birth and death processes in random environment. In this article we show that these birth and death processes in random environment converge to a switching diffusion process if the number of agents on the market grows to infinity.


"Diffusion Approximation of Birth and Death Processes with Applications in Financial Market Herding Models"


 by A. Irle and J. Kauschke


We take a mathematical look on the herding mechanism in the herding model for financial markets as described in [4]. The main aspect of this article is the convergence of the birth and death process of optimistic agents to a diffusion process. Apart from this we look on some aspects of the limiting diffusion process with concentration on the boundary point behaviour.



"Switching Rates and the Asymptotic Behaviour of Herding Models"


by A. Irle and J. Kauschke


Continuous-time Markov chains are a popular tool for stochastic modelling in a great variety of fields, ranging from population genetics to communication networks. The mathematical theory of such processes is well understood and provides powerful results for the handling of applied problems. Recently such processes have entered economical theory as agent-based models which are able to explain some of the stylized facts of financial markets. Starting with the work [9] of Kirman, herding model are used to describe the behaviour of agents in financial markets, see [1], [2], [3], [4], [7], [10]. In this note, we shall review some of the relevant mathematical facts and show how they apply to agent-based models and provide insights into the asymptotic behaviour.