Download Quick Links - University of Leicester

Solanum mauritianum hairs
Universality on markets
Ryszard Kutner
Faculty of Physics, University of Warsaw, Poland
Econophysics Network – Inaugural Workshop
School of Business, University of Leicester
Leicester UK, 10th October 2016
[1] J. Ludescher and A. Bunde, Phys. Rev. E 90,
062809 (2014).
[2] J. Ludescher, C. Tsallis, A. Bunde, Eur. Phys.
Lett. 95, 68002 (2011).
[3] M. I. Bogachev and Bunde, Phys. Rev. E 80,
026131 (2009).
[4] M. I. Bogachev and A. Bunde, Phys. Rev. E 78,
036114 (2008).
[5] A. Corral, Physica A 340, 590 (2004).
[6] M. Denys, M. Jagielski, T. Gubiec, R. Kutner,
H.E. Stanley, Phys. Rev. E 94, 042305 (2016).
25-years of Rosario N. Mantegna
paper:
`Lévy walk and Enhanced Diffusion in Milan Stock
Exchange', Physica A 179, 232 (1991).
He empirically proved that the Central Limit Theorem is
broken on the Milan Stock Exchange. That is, the Bachelier
paradigm was broken. It inspired the avalanche of papers.
In fact, it was the beginning of modern econophysics (although
this name was introduced later).
Generic goal
Presentation of a novel (advanced) way of the
non-Gaussian time series classification
Schedule
Motivation
(1) Definiton of the problem and generic goal: inspiration from
geophysics.
(2) Extended the Gutenberg-Richter law (Earthquakes) for financial
markets.
(3)
Superstatistics of excessive losses: empirical data colapse.
(4)
Superscaling
(5) Concluding remarks: (i) excessive profits, (ii) risk estimation, and
(ii) weighted superstatistics for Earthquakes.
(1) Definition of the problem and a goal
Our goal is to describe a universal behaviour of empirical
statistics: (i) of interoccurrence (interevent) times between
excessive losses and separately (ii) the excessive profits,
as well as (iii) of interevent times between Earthquakes
having amplitude above some threshold (defined by the
Richter scale).
Three basic concepts in study of excessive losses,
ecessive profits, and Earthquakes:
- activity
- threshold
- universality
(1) Definition of the problem and a goal
Two concrete related problems caused by empirical
data of Ludescher, Bogachev, Tsallis, and Bunde
arise:
(i) Finding of probability of losses greater or equal than
some threshold value vs. threshold value Q (e.g., VaR
approach is a special case);
(ii) Finding of probability distribution of intervent times ΔQt
between successive excessive losses for various values of
the threshold (basic distribution of the Continuous-time
Random Walk).
(1) Definition of the problem and a goal
What is the statistics of excessive losses?
Market seismograph measures Marketquakes.
(Figures taken from [2])
(2) Extended the Gutenberg-Richter law for Earthquakes
Jan. 2000 – June 2010: USD/GBP, S&P 500, IBM, WTI (crude oil)
Subsequent inspiration from geophysics.
Econo(geo)physics:
main distribution
Mean conditional discrete time period
(3) Superstatistics vs. empirical data colapse
Parameters of the superstatistics (for the IBM)
Appendix: Particular cases
(4) Superscaling.
Final goal:
(5) Concluding remarks:
(i) Excessive profits
Functional (not literal) balance
between losses and profits.
(5) Concluding remarks:
(ii) Risk estimation: dynamical VaR.
Zipf law for long-time limit
(5) Concluding remarks:
(iii) Weighted superstatistics vs. Earthquakes
(5) Concluding remarks:
Criticality
Market activity, measured by the length of interevent time,
has multiscale character. This activity defines a
hierarchy of long interevent times as their distribution
constitutes (asymptotically) a power-law. This means
that slowly vanishing memory is present in the system.
Hence, the system as a whole participates in this
vanishing. Therefore, we can suppose that system is
controlled by large fluctuations and long-range
dependences. System is dominated by critical behaviour.
There is also dependence between interevent times.
Universality (data colapse) of this distribution is
observed.
The challenge.
M. Jagielski, R.Kutner, and D. Sornette
Which class of fractional stochastic dynamic
equation leads to our solution?
Which class of fractional kinetic equations
produces our solution?
Which class of agent-based models gives our
waiting-time distributions so good fitted to
empirical data?
The challenge.
(Figure taken from [1])
Thank you very much for your attention