Complexity Theory and the Financial Crisis: A Critical Review
Rodrigo M Zeidan and Kurt Richardson
We present a critical review of the impact of complexity theory on the analysis of
financial markets, concentrating on the differences between Econophysics and
Econobiology. Both approaches show that there are limitations in our current
understanding of the banking system, which can lead to regulatory problems, and in
turn may have contributed to the inability of most academics and economic agents
(including the FED) in predicting the crisis.
The effects of the Financial Crisis are still being felt, and speculations on the
predictability of the crisis and what measures should be taken to prevent another one
are hot topics in financial circles. The purpose of this article is to analyze the financial
crisis through the lens of complexity theory and to ponder which explanations can be
given and which path should be open if one considers the world through the complexity
The main advantage of using a complexity-based approach is that it meets head-on a
common discontent of many researchers after the crisis: that current financial models
IBMEC/RJ and ISCE, respectively. Contact information: firstname.lastname@example.org and
were incapable of signaling the crisis. But there are no easy answers, because one of
the main characteristics of complexity theory is incompressibility (for more, see
Richardson (2008) and Ciliers (2005)), which puts a limit on the information that can be
extracted from complex systems, and which also necessarily leads to theoretical
pluralism. If we take the reasonable assumption that financial systems are complex in
nature, there is no single theory that could explain every feature of each system, which
makes a simple, decisive explanation for the crisis impossible. However, that does not
mean that we cannot extract predictions, lessons, policies, or insights from thinking
complexly about financial systems. In fact, it is just the opposite; thinking deeply on the
impacts of complexity into financial system can lead to different kind of analyses that
should bring testable implications for financial research. Here we focus on one possible
explanation for the crisis, that the true nature of systemic risk is ignored by the Central
Bank, due to an incomplete understanding of the true nature of financial markets and
thus its available actions will be inherently curbed until it properly models the banking
1. Complexity in Financial Markets: A Primer
Richardson (2008) divides the approaches of how complexity thinking can impact
management studies into three broad schools: the neo-reductionist school, the
metaphorical school, and the critical pluralist school. Although the impact of complexity
research on management studies is still in its infancy, the complexity school in financial
market is much more developed. There is no question that complexity matters in
financial markets, and the literature is developing in such a way that even investor
strategies are now being designed based on complexity concepts (for instance,
Brunnermeier and Oehmke (2009) point out three different ways in which boundedly
rational investors can deal with complexity).
In fact, there are two main general approaches to complexity in economics and finance,
that of Econophysics and Econobiology. Both are bottom-up, population-based
approaches (Rickles, 2010), but differ sharply in their methods to deal with complexity.
Econophysics is a term coined by Stanley et al (1996) and is preoccupied with the
application of the physics of complex system into financial and economics markets [see,
for instance, Mantegna and Stanley (1999) and Rickle (2010)], while Econobiology
takes its lessons from biological complexity models (e.g. Arthur, 1995)). Because both
approaches have its origins clearly defined, the implications for complexity studies in
finance are finely traceable.
First a caveat: while in the realm of Finance complexity models are much more common
than in management studies, the confusion that Richardson (2008) observed between
complexity and complicatedeness still persists, as can be seen in the examples of
Caballero and Simsek (2009) and Bushman et al (2004), both of which use complexity
in the common usage of the word. There is nothing wrong with either works, but here
we analyze complexity in its technical form.
Using Richardson’s classification, we can easily put the majority of Econophysics in the
neo-reductionist school and much of Econobiology in the metaphorical school. This
classification is so straightforward that it is uninteresting at first sight. However, when
applied to a broader perspective of financial systems, this classification allows for some
interesting insights, as will be shown later.
Rickle (2010) summarizes the Econophysics literature and the relationship with
complexity, arguing that: ”according to the econophysicist’s conception of financial
markets the prices (of assets) are viewed as fluctuating macroscopic variables that are
determined by the interactions of vast numbers of agents”, and presents some
important findings regarding asset returns that can be explained by econophysics, but
not necessarily by regular financial models, such as fat tails, volatility clustering, and
volatility persistence as examples. The methods of Econophysics are based on the tools
of dynamical physics, like statistical mechanics and chaos theory, for instance. Since
those tools are numerous, there are a multitude of different Econophysics models that
try to deal with particular questions in financial markets, but all share the same
epistemology – i.e. are based on data analysis first and hypothesis formulation second.
The idea of a paradigm shift brought by Econophysics to financial and economic
modelling is strong: “Econophysics is viewed (by most of its practitioners) as a
revolutionary reaction to standard economic theory that threatens to enforce a paradigm
shift in thinking about economic systems and phenomena” (Rickles, 2010, p.13).
Some Econophysics models are by now mainstream in the financial literature,
especially those dealing with volatility clustering and persistence, and with fat tails in
asset returns – in this area statistical mechanics modelling thrives, due to the inherent
characteristics of probabilistic function in asset pricing and returns.
However, important critiques of econophysics have surfaced, even when the discipline
was in its infancy. One particular relevant critique comes from Mirowski (1989), where
the author argues that much of Econophysics is problematic due to epistemological
considerations (specifically, that there is no theory behind the transposition of physics
models to economics), even though it can be argued that financial systems are much
more akin to physical systems than most economics models. Econophysics then helps
in a better understanding of the statistical properties of financial systems. Econobiology,
on the other hand, has a different approach to the complexity of financial systems.
Arthur (1995) offers a paradigmatic view of Econobiology processes. In Econobiology
models, the complex systems develop bottom-up through agent-based interactions, as
in Econophysics models, but the difference is that while in the former the locus of
analysis is agent interactions and the processes of emergence, in the latter the goal is
to determine the statistical properties of the results of the agents’ interactions. The
difference is not only on the mechanics of both approaches, but also in their
epistemology – Arthur (1995, p.20) expresses the view that one should look into
economics and financial markets in “psychological terms: as a collection of beliefs,
anticipations, expectations, and interpretations; with decision-making and strategizing
and action-taking predicated upon these beliefs and expectations”.
The bottom-up approach of Econobiology models is preoccupied with emergent
properties from agent interactions. It is very useful to analyze innovation activity, for
instance, because this kind of activity fits nicely as an emergent property of agents
searching for innovation (since Nelson and Winter’s (1982) seminal work, evolutionary
economics modelling of innovative activity has become mainstream in the industrial
organization literature). For financial models, Arthur et al (1995) show how a simple
model of stock valuation can be radically transformed by changing a simple assumption
on the behavior of rational investors, now assuming that investors are heterogeneous in
their expectations. The result is that (p.24) “Under heterogeneity, deductive logic leads
not just to indeterminate expectations but also to unstable ones. (…) Given differences
in agent expectations, deductive expectation formation becomes indeterminate, and so
even perfectly rational investors cannot form expectations in a determinate way”.
The main avenue of research of Econobiology models in finance is then the inductive
approach through the use of simulation. The idea is to populate the simulator with
heterogeneous agents and identify the properties of the emergent features of the
interactions. Arthur et al (1996) studied asset pricing under inductive reasoning using a
simulation with 100 artificial investors each with 60 expectational models. The main
results are that, if agents believe in the standard model of finance, their beliefs and the
standard model is evolutionary stable and thus upheld; and that the market possesses a
psychology, with evolving strategies and different periods of volatility in the
price series (sometimes consistent with GARCH processes). The advantage of this kind
of models is that regular stylized facts of financial models (such as stocks crosscorrelations)
can be generated instead of being simply observed. More recent models
have stretched the use of simulation (Ponzi and Aizawa, 2000) and evolutionary models
to refine the analyses of emergent properties in financial markets, with the use of neural
networks (Azzini and Tettamanzi, 2006), biological algorithms (Brabazon and O’Neil,
2006), and grammatical evolution (Adamu and Phelps, 2009). The main problems with
evolutionary finance models are that there is still a reliance on simulations, with many
results still exploratory; and that the models offer a different way to look at financial
markets but are too scant in terms of definite predictions.
Here we concentrate on network topology and other models to analyze some of the
possible dynamics of financial systems. Which is the best approach to analyze this
important feature of the crisis? In the next section we review some works in each
approach to complexity in finance, and try to extract some insights to help explain the
building of the crisis.
2. Complexity Models, Risk Creation and the Financial Crisis.
There are many proposed explanations for the crisis: lack of regulation; cheap money;
irrational exuberance; “creative” exotic financial instruments; and excessive risk-taking.
Here we want to concentrate on the fact that the problem of banking regulation is more
fundamental than simply choosing the level of regulation – we may not understand
important features of the banking system dynamics.
Take risk, for instance. Regular financial micro models divide risk in idiosyncratic and
systemic components. For regulation purposes the focus is usually on systemic risk, the
component that can affect the whole financial system. The proponents of financial
deregulation usually claim that markets are efficient – i.e. that it operates on the basis of
a “Law of Conservation of Risk”, in which banks are efficient in allocating risk throughout
the system, and risk is neither created nor destroyed, merely shuffled around efficiently.
Risk, instead of being a static feature of financial systems, is part of a dynamic process
where it is destroyed and created in the course of trading activity. Shifting risk may allow
for more efficiency in terms of costs to market agents, but what may be lacking in
regular economic models is the notion that systemic risk is more than the sum of its
parts. Recent models are specifically looking into general equilibrium banking models,
because as Acharya (2009, p.2) observes: “The standard theoretical approach to the
design of bank regulation considers a “representative” bank and its response to
particular regulatory mechanisms such as taxes, closure policy, capital requirements,
etc.” Such partial equilibrium approach has a serious shortcoming from the standpoint of
understanding sources of, and addressing, inefficient systemic risk. In particular, it
ignores that in general equilibrium, each bank’s investment choice has an externality on
the payoffs of other banks and thus on their investment choices”.
Acharya’s model shows that “optimal regulation should be “collective” in nature and
should involve the joint failure risk of banks as well as their individual failure risk”. For
that, he simply defines systemic risk as “the joint failure risk arising from the correlation
of returns on asset-side of bank balance-sheets”. Both definition and conclusion are the
jumpstart for our complexity-based analysis of financial markets. The idea that systemic
risk is based on a joint-failure is simple enough, as is the idea that regulation should be
collective. Another interesting network banking model is that of Caballero and Simsek
(2009), where the authors propose a model of a financial crisis based on the costs of
gathering information on the soundness of their trading activity. Financial crises happen
when, after an emergence of acute financial distress in a part of the system, the cost of
information gathering becomes too unmanageable for banks, and they have no option
but to withdraw from loan commitments and illiquid positions. All these models would be
considerably enhanced by looking into the world through a complexity lens.
2.1. Econophysics Modelling of the Banking System
There is no single econophysics model of the banking system, but recent work can
enlighten some of the important features of financial markets.
The main avenue of research considers the banking system as a network of payment
flows, and studies its topology, with the underlying risk determining the stability of the
network. One simple illustration of this is presented in graph 1, with an example of the
the topology of the Danish network payment system, from Rørdam and Bech (2009).
Graph 1 – The Network Topology of the Danish Payment System (Rørdam and Bech,
(Rørdam and Bech, 2009)
In the figure the white nodes are the biggest banks. This topology highlights one of the
most discussed aspects of the banking crisis,- that some banks are too big to fail. This
is measured through the systemic impact of each node on the network stability – a
network is more stable if nodes can disappear without loss of payment flows.
Inaoka et al (2004) develop a network banking model based which measures the
network stability and is based on power laws and cumulative distributions. The result is
that the banking network shows a power-law degree distribution. Also, the main
characteristic of the network, in this case, is that it is much more efficient than stable –
i.e. there is a trade-off between banks searching for efficiency and the whole stability of
the network. Becher et al (2008) don’t observe this trade-off in their analysis of the
topology of the UK payment system, concluding that “liquidity is able to flow efficiently
around the network and that the network is quite resilient to shocks (p.1)” – even taking
a node off the network doesn’t undermine the ability of banks to have payments flow
freely. Pröper et al (2008), in another topological analysis, this time on the Dutch
payment system, find some indication of a lack of efficiency – the network is small,
compact and sparse, using a mere 12% of possible connections in the long run, and
also of stability, stating that the network is subject to possible serious instability.
Another issue of network topology is the network connectivity, which is related to the
problem of collective bankruptcy. Aleksiejuk et al (2001) present a model of a banking
network, with the goal of relating collective bankruptcies to self-organized criticality. In
their model the main parameter is the mean number of interbank connections, q. Two
competing processes increase (A) or decrease (B) q (p.5):
A. Due to the random character of the stochastic variable i(t) and the random selection
of a financial partners from the nearest neighbors.
B. Due to collective bankruptcies, because new banks that replace bankrupts are not
involved in the interbank market at the beginning of their activity.
The authors conclude that (p.6) “if the value of q is below the percolation threshold then
the mean size of contagion cluster is small and the process A overcomes the process B.
It follows that in the course of time the number of interbank connections q is growing up
driving the system to the critical state. If the value of q exceeds a critical value (the
percolation threshold) then a large contagion cluster spreading all over the system can
There are other works concerning banking system network topology, but the ones
presented here show the relevance of this kind of analysis to the stability analysis of
banking systems. There are, of course, still many unresolved issues regarding which
features are relevant to regulatory policy, and, more importantly, what should be done
once different network characteristics are identified.
Network topology is hardly the only way to analyze financial markets with Econophysics
models. For instance, the analysis of entropy in financial markets yields important
information on risk creation (Michael and Johnson, 2004), while Bartolozzi and Thomas
(2004) analyze a stochastic cellular automata model and conclude that crashes or
bubbles are triggered by a phase transition in the state of the bigger clusters present in
the network system.
2.2 Econobiology Modelling of the Banking System
Econobiology research in our present context begins with agent-based modelling of the
banking system. The main advantage is that the models treat banks as agents in a
biological population and analyze their process of evolution – in this sense, risk is one of
the determinants of a bank “evolution”. Because in a population agents are always
entering and leaving, the models have a clear parallel with financial markets. The main
problem is that it is difficult to get out of the metaphorical level towards a working agentbased
banking model, even though modelling risk is increasingly promising as an
avenue of research. However, some frontier research is now breaching the
metaphorical level into workable models. Here we present three classes of models
which are surprisingly effective in determining banking failures through the lens of
The first kind of models use neural networks [beginning with Tam (1991) and Tam and
Kyiang (1992), and surveyed by Atiya (2001)]. “An artificial neural network (NN) is a
computational structure modelled loosely on biological processes. NNs explore many
competing hypotheses simultaneously using a massively parallel network composed of
non-linear relatively computational elements interconnected by links with variable
weights. It is this interconnected set of weights that contains the knowledge generated
by the NN” (Adya and Collopy, 1996, p. 481). The linkage to financial markets is direct,
because it is easy to think of banks being interconnected and generating information in
the process of transactions between them. Again, as in Econophysics modelling, we
arrive at networks as basis of the analysis, but the method of analysis is quite different.
The evolution of the neural network yield information on banking failures through
decaying processes due to loss of information.
Support vector machines (SVM) can also be used to model risk in financial markets
[e.g. Tay and Cao (2001) and Chen and Shih (2006)]. SVM is a type of learning
machine based on statistical learning theory. Instead of considering the network
structure as in neural networks models, it uses optimization procedures based on
learning processes, another important feature of biological processes.
The last class of banking models based on evolutionary biology briefly described here is
that of genetic algorithms (GA). A genetic algorithm is an optimization procedure based
the idea that evolution happens through changes in genes, hence concepts like
inheritance, mutation, and selection. If we think of banks as agents searching for
survival, a selection processes based on evolutionary biology can describe what
happens on financial markets. Min et al (2006) presents a model that uses GA to
improve on their model of SVM to analyze the probability of banking failures. In their
model, the authors were able to measure relative performance and conclude that it
outperforms regular financial models in detecting the probability of banking failures. In
this sense, their model would be complementary on Value-at-Risk internal models.
Table 1 summarizes the main implications and disadvantages of the Econophysics and
Econobiology approaches to financial markets. The table below is far from exhaustive,
its goal being merely to illustrate some of the research agenda of complexity theory in
Table 1 – Econophysics; Econobiology and Financial Markets.
Methods Financial Markets Disadvantages
Volatility Clustering and
Persistence; Fat Tails;
Hard to model.
3. Final Comments
The purpose of the paper was to present important contributions of complexity theory to
the analysis of financial markets, focusing on the distinction between Econophysics and
Econobiology and their possible contribution to the better understanding of financial
markets dynamics. It was our intention to bring new issues into the fold, instead of
answering decisively questions like why the major crisis of 2007-8 happened.
We followed the reasoning of authors like Mainzer (2009, p.1): “the world-wide crisis of
financial markets and economies is a challenge of complexity research. Misleading
concepts of linear thinking and mild randomness (e.g. Gaussian distributions of
Brownian motion) must be overcome by new approaches of nonlinear mathematics
(e.g., non-Gaussian distribution), modelling the wild randomness of turbulence at the
stock markets. Systemic crises need systemic answers”. Bouchaud (2008) goes
beyond it, calling for a scientific revolution for economics based on complexity theory.
Here we don’t take a strong position against regular financial and economic models,
and we don’t advocate that complexity theory will answer everything, because there is
no simple explanation or easy answers to be given.
However, the models and results here can bring to light some important questions
regarding the shaping of financial markets – if the banking system presents
characteristics like self-criticality, power law distributions, risk emergence, bounded
rationality, and other non-deterministic features, the problem of the regulator is much
more difficult than regular economic models allow for. It is just not a question of how
stringent to regulate the system or not, but a more fundamental question of what is
Further research on the complexity approach should greatly enhance our understanding
of financial markets, and a specific line of research could concentrate on developing an
encompassing theory to tie all the different approaches together to arrive, at some point,
at a complexity-based standard model of finance.
Acharya, V.V. (2009). A theory of systemic risk and design of prudential bank
regulation, Journal of Financial Stability, 5: 224-255.
Adya, M., and F. Collopy (1998). How effective are neural vided fine research
assistance. Journal of Forecasting 17, 481–495.
Adamu, K. and S. Phelps (2009). Modelling Financial Time Series using Grammatical
Evolution. Working Paper, (http://web.mac.com/davidrh/AMLCF09/papers/5.pdf).
Aleksiejuk, A., A.J. Holyst, and G. Kossinets (2001). Self-organized Criticality in a
model of collective bank bankruptcies, cond-mat/0111586
Arthur, B. (1995). Complexity in Economic and Financial Markets, Complexity, 1(1): 20-
Arthur, W. B., J. Holland, B. LeBaron, R. Palmer and P. Taylor (1996). Asset Pricing
Under Endogenous Expectations in an Artificial Stock Market, in The Economy as An
Evolving Complex System II, edited by W. Brian Arthur, Stephen Durlauf and David A.
Lane, A Proceedings Volume, Santa Fe Studies in the Sciences of Complexity, 15-44.
Atiya, A. F. (2001). Bankruptcy prediction for credit risk using neural networks: A survey
and new results. IEEE Transactions on Neural Networks, 12:, 929–935.
Azzini A. and A. Tettamanzi (2006). A neural evolutionary approach to financial
modelling. In Proceedings of the Genetic and Evolutionary Computation Conference,
GECCO’06, vol. 2, pp. 1605-1612.
Bartolozzi, M. and A.W. Thomas (2004). Stochastic cellular automata model for stock
market dynamics, Phys. Rev. E 69, 046112.
Becher, C., S. Millard and K. Soramäki (2008).
The network topology of CHAPS
, Bank of England Working Paper No. 355.
Brabazon, A. and M. O’Neill (2006). Biologically Inspired Algorithms for Financial
Modelling. Springer, Berlin.
Brunnermeier, M.K. and M. Oehmke (2009). Complexity in Financial Markets, Princeton
University Working Paper.
Bushman, R., Q. Chen, E. Engle, A. Smith (2004). Financial accounting information,
organizational complexity and corporate governance systems. Journal of Accounting
and Economics 37: 167–201.
Caballero, R.J. and A. Simsek (2009). Complexity and Financial Panics, NBER Working
Chen, W. H. and J.Y Shih (2006). A study of Taiwan’s issuer credit rating systems using
support vector machines. Expert Systems with Applications, 30:427–435.
Cilliers, P. (2005). Knowing complex systems, in K. A. Richardson (ed.), Managing
Organizational Complexity: Philosophy, Theory, and Application, Boston: ISCE, 7-19.
Gordon, D. (1991). A review of More Heat Than Light: Economics as Social Physics,
Physics as Nature’s Economics. By Philip Mirowski. The Review of Austrian Economics,
Inaoka, H, T. Ninomiya, T. Shimizu, H. Takayasu, and K. Taniguchi (2004). Fractal
network derived from banking transaction – an analysis of network structures formed by
financial institutions, Bank of Japan Working Paper no. 04-E-04.
Michael, F. and M.D. Johnson, Financial market dynamics, Physica A 320, 525 (2003).
Min, S. H., J. Lee, and I. Han (2006). Hybrid genetic algorithms and support vector
machines for bankruptcy prediction. Expert Systems with Applications, 31, 652–660.
Mirowski, P. (1989). More Heat Than Light: Economics as Social Physics, Physics as
Nature’s Economics. Cambridge: Cambridge University Press.
Mantegna, R.N. and H.E. Stanley. (1999). An Introduction to Econophysics, Cambridge:
Cambridge University Press.
Nelson, R. and S. Winter (1982). An Evolutionary Theory of Economic Change. Belknap
Press of Harvard University Press: Cambridge, MA.
Ponzi, A. and Y. Aizawa (2000). Evolutionary financial market models, Physica A:
Statistical Mechanics and its Applications 287: 507-523.
Pröpper, Marc, I. Lelyveld and R. Heijmans (2008). Towards a Network Description of
Interbank Payment Flows, DNB Working Paper No. 177/May 2008, De Nederlandsche
Richardson, K. (2008). Managing Complex Organizations: Complexity Thinking and the
Science and Art of Management, Corporate Finance Review, 13: 23-30.
Rickles, D. (2010). Econophysics and the Complexity of Financial Markets, forthcoming
in J. Collier and C. Hooker (eds.): Handbook of the Philosophy of Science, Vol.10:
Philosophy of Complex Systems. North Holland: Elsevier.
Rørdam, K.B. and M.L. Bech (2009). The Topology of Danish Interbank Money Flows,
FRU Working Paper, University of Copenhagen, Working Paper No. 2009/01.
Tam, K.Y. (1991). Neural Network Models and the Prediction of Bank Bankruptcy,
Omega, The International Journal of Management Science, 19: 429-445.
Tam, K.Y. and M.Y. Kiang (1992). Managerial Applications of Neural Networks: The
Case of Bank Failure Predictions, Management Science, 1992, 38, 926-947.
Tay, F. E. H., and L. Cao (2001). Application of support vector machines in financial
time series forecasting. Omega, 29: 309–317.