Dear colleagues,
I find very interesting the efforts made by Didier Sornette and
collaborators, and Nicolas Vandwalle et al, to describe markets near crashes
in analogy with critical phenomena. Indeed we know in physics that a large
number of systems undergo phase transitions, and all can be described in
terms of a finite number of universality classes. If we consider a market
crash, we can be tempted to think of it in terms of a phase transition
between order and disorder where a large number of noisy traders start to
behave in a co-operative way. Indeed invoking a hierarchical structure of
the market place, the evolution near the critical point can be modelled as
an exponential divergence decorated by some log-periodic oscillations. This
behaviour, observed in many physical systems, seem to fit correctly pre and
post crashes market evolution. It is clear, in the spirit of this
explanation, that if there is a crash it can be preceded by a critical
evolution (indeed observed in all major crashes this century:
cond-mat/9903321) but being able to fit a critical evolution on a part of
the market curve do not necessarily mean that the system is going critical
(see e.g. cond-mat/9804111).
In such models, one try to determine critical exponents in order to specify
the universality class of financial crashes. If such a universality class
has to be found, a constant critical exponent for all the observed market
crashes should be observed (Vandewalle and al.). In the various works
published on this subject (Johansen and al. cont-mat/9903321, Feigenbaum and
al. ...) such critical exponents have values which fluctuate and doesn't
seem to be constant.
According to this theory, can we consider that these fluctuations are in a
reasonable range thus giving a confirmation of the applicability of the
theory or should we interpret these fluctuation more as an incapacity of the
theory to describe some more fundamental features (such as the interaction
between stock market and incoming exogenous information)? Or it is because
universality makes strict sense only for a closed system with a stationary
process which isn't the case of financial markets? Or maybe we are just
facing critical phenomena of an open system driven out of equilibrium and
showing critical exponents continuously varying with the problem's
parameters?
Any comment from different horizons (Economy, Physics, Finance, etc.) are
welcome.
Thanks
Gabriele Susinno & Marco Rigo
Dr Gabriele C. F. Susinno
Monis Software Ltd.
E-mail: [log in to unmask]
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http://www.monis.co.uk
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