Plenarvorträge - DPG-Tagungen

Symposium Fat-Tail Distributions - Applications from Physics to Finance Donnerstag
Fachsitzungen
– Haupt-, Fachvorträge und Posterbeiträge –
SYFT 1 Fat-Tail Distributions - Applications from Physics to Finance
Zeit: Donnerstag 09:30–11:00 Raum: H1
Hauptvortrag SYFT 1.1 Do 09:30 H1
Fat Tail Statistics and Beyond — •Joachim Peinke — Hydrodynamics
Group , Faculty of Physics, Carl v. Ossietzky University, D -
26111 Oldenburg
Many complex systems are characterized by non-Gaussian statistics,
which show pronounced fat tails. For risk analysis these fat tails play a
very important role. Analyzing different systems with respect to their fat
tail statistics, the question arises whether there are common or universal
features behind this stochastic phenomenon or not. In this talk data from
different systems are presented together with their fat tail statistics. In
particular we present results from environmental systems, from turbulent
flows and from the financial exchange market. Besides the comparison of
the statistics, we present a method to reconstruct from the data stochastic
processes which model the heavy tail statistics accurately. These reconstructed
stochastic systems are given as a specific Fokker-Planck equation,
which provides a statistically more complete characterization of the
system’s complexity. Even for similar fat tail statistics we find that different
underlying stochastic processes are present.
Hauptvortrag SYFT 1.2 Do 10:00 H1
Use and Abuse of Ito vs. non-Ito Stochastic Calculus — •Peter
Hänggi — Universität Augsburg, Institut für Physik
Brownian motion dynamics, discovered first in 1789 by Jan Ingen-
Housz on charcoal particles under his microscope and by Robert Brown
in 1828 in his observations of pollen, inspired many physicists to develop
guiding contributions to the theory of fluctuation phenomena and
statistical mechanics of irreversible processes per se. The list includes distinguished
names such as Langevin, Einstein, Smoluchowski, Ornstein,
Uhlenbeck, to name but a few. The use of stochastic differential equations
plays a key role in most phenomena involving noisy perturbations.
The paper by K. Ito (Proc. Imp. Acad. Tokyo, 20: 519 (1944)) gave the
corresponding stochastic integral a mathematical precise meaning while
Stratonovich in his works introduced a different notion that is appealing
for many from a physics point of view. In this talk I will survey the use –
and abuse – of actually infinite many differing stochastic integral definitions
for Gaussian white noise and, as well as, for white Poisson shot noise
[1]. With this talk I elaborate on various pitfalls and comment on the use
of colored noise (or correlated) driven flows. Moreover, I will clarify the
connection with a path integral representation of the stochastic dynamics
and clear up some confusion of Ito vs. Stratonovitch discretization rules.
Finally, I present results of multiplicative Langevin equations to describe
long time tail phenomena and anomalous diffusion.
[1] P. Hänggi and H. Thomas, Phys. Rep. 88: 207 (1982); sec. 2.4; P.
Hänggi, Helv. Phys. Acta 51: 183 (1978).
Hauptvortrag SYFT 1.3 Do 10:30 H1
Non-Gaussian option pricing — •Hagen Kleinert — Institut
für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, 14195
Berlin
A new option pricing formula is derived which takes into account the
risk of rare dramatic price changes by using non-Gaussian distributions
with heavy tails. The derivation is based on a solvable path integral corresponding
to a Gaussian process in which the width fluctuates with
Gaussian noise. The resulting returns fit the Dow Jones data over many
times scales.
[1] H. Kleinert, Physica A 311, 536 (2002) (cond-mat/0203157)
[2] H. Kleinert, Physica A 312, 217 (2002) (cond-mat/0202311)
[3] See Chapter 20 in the textbook Path Integrals in Quantum Mechanics,
Statistics, Polymer Physics, and Financial Markets, World Scientific,
Singapore, 2003.
SYFT 2 Fat-Tail Distributions - Applications from Physics to Finance
Zeit: Donnerstag 11:30–13:00 Raum: H1
Hauptvortrag SYFT 2.1 Do 11:30 H1
Credit Risk in Banking - Methods, Problems, Implications —
•Axel Müller-Groeling and Jan-Hendrik Schmidt — McKinsey
Company, Inc.
We give a short introduction into credit risk and its fundamental importance
for the banking sector. We compare the main methods currently
in use for measuring the loss distribution originating from loan portfolios
and highlight some of the practical and methodological problems
involved. The main observable used by banks, credit value-at-risk, depends
sensitively on the tails of the distribution. It plays an important
role in the overall steering model of banks, as it characterizes the economic
capital required to run the credit business safely. We conclude with
a discussion of value-based steering and the optimal capital allocation to
credit-risk taking business units.
Hauptvortrag SYFT 2.2 Do 12:00 H1
Understanding large fluctuations in stock market activity using
methods of statistical physics — •H. Eugene Stanley — Department
of Physics, Boston University, Boston, Massachusetts 02215, USA
After a very short introduction to some of the most recent results
obtained in the field of econophysics we consider the problem of “rare
events” of the stock market price dynamics. It is becoming widely appreciated
that even extremely large movements in stock market activity may
not be “outliers” but rather may conform to newly-uncovered empirical
laws, such as the (i) power law distribution of returns with exponent
3, outside the Levy-stable regime, (ii) power law distribution of trading
volume with exponent 1.5 [1]. We discuss these new empirical laws, and
also discuss how one interdisciplinary “economist/physicist” collaboration
is beginning to gain theoretical insight and understanding of these
new empirical laws using concepts drawn from both the economics and
physical sciences [2-6].
The research reported was done primarily in collaboration with X.
Gabaix MIT Economics Dept), P. Gopikrishnan (now at Goldman Sachs),
and V. Plerou (Boston University) and has been supported by NSF.
[1] R. N. Mantegna and H. E. Stanley, Introduction to Econophysics:
Correlations and Complexity in Finance (Cambridge University Press,
Cambridge, 2000).
[2] V. Plerou, P. Gopikrishnan, X. Gabaix, and H. E. Stanley, “Quantifying
Stock Price Response to Demand Fluctuations,” Phys. Rev. E
66, 027104-1 – 027104-4 (2002) cond-mat 0106657; B. Rosenow, “Fluctuations
and market friction in financial trading” Int J Mod Phys C 13,
419-425 (2002).
[3] V. Plerou, P. Gopikrishnan, and H. E. Stanley, “Two-Phase
Behaviour of Financial Markets” Nature 421, 130 (2003). condmat/0111349.
[4] X. Gabaix, P. Gopikrishnan, V. Plerou, and H. E. Stanley, “A Theory
of Power-Law Distributions in Financial Market Fluctuations,” Nature
423, 267–270 (2003).
[5] X. Gabaix, P. Gopikrishnan, V. Plerou, and H. E. Stanley, “A Simple
Theory of Asset Market Fluctuations, Motivated by the Cubic and
Half Cubic Laws of Trading Activity in the Stock Market” Quarterly
Journal of Economics (submitted).
[6] V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, T. Guhr,
and H. E. Stanley, “A Random Matrix approach to Financial Cross-
Correlations” Phys. Rev. E 65, 066126 (2002) cond-mat/0108023.