A number of papers claim that a Log Periodic Power Law (LPPL) fitted to
financial market bubbles that precede large market falls or 'crashes', contain
parameters that are confined within certain ranges. The mechanism that has been
claimed as underlying the LPPL, is based on influence percolation and a
martingale condition. This paper examines these claims and the robustness of
the LPPL for capturing large falls in the Hang Seng stock market index, over a
30-year period, including the current global downturn. We identify 11 crashes
on the Hang Seng market over the period 1970 to 2008. The fitted LPPLs have
parameter values within the ranges specified post hoc by Johansen and Sornette
(2001) for only seven of these crashes. Interestingly, the LPPL fit could have
predicted the substantial fall in the Hang Seng index during the recent global
downturn. We also find that influence percolation combined with a martingale
condition holds for only half of the pre-crash bubbles previously reported.
Overall, the mechanism posited as underlying the LPPL does not do so, and the
data used to support the fit of the LPPL to bubbles does so only partially.
Paweł Sieczka, Didier Sornette, Janusz A. Hołyst
posted by Matúš Medo
(9 February 2010)
Inspired by the bankruptcy of Lehman Brothers and its consequences on the
global financial system, we develop a simple model in which the Lehman default
event is quantified as having an almost immediate effect in worsening the
credit worthiness of all financial institutions in the economic network. In our
stylized description, all properties of a given firm are captured by its
effective credit rating, which follows a simple dynamics of co-evolution with
the credit ratings of the other firms in our economic network. The existence of
a global phase transition explains the large susceptibility of the system to
negative shocks. We show that bailing out the first few defaulting firms does
not solve the problem, but does have the effect of alleviating considerably the
global shock, as measured by the fraction of firms that are not defaulting as a
consequence. This beneficial effect is the counterpart of the large
vulnerability of the system of coupled firms, which are both the direct
consequences of the collective self-organized endogenous behaviors of the
credit ratings of the firms in our economic network.
Fei Ren, Wei-Xing Zhou
posted by Matúš Medo
(9 February 2010)
We study the statistical properties of the recurrence intervals $\tau$
between successive trading volumes exceeding a certain threshold $q$. The
recurrence interval analysis is carried out for the 20 liquid Chinese stocks
covering a period from January 2000 to May 2009, and two Chinese indices from
January 2003 to April 2009. Similar to the recurrence interval distribution of
the price returns, the tail of the recurrence interval distribution of the
trading volumes follows a power-law scaling, and the results are verified by
the goodness-of-fit tests using the Kolmogorov-Smirnov (KS) statistic, the
weighted KS statistic and the Cram{\'{e}}r-von Mises criterion. The
measurements of the conditional probability distribution and the detrended
fluctuation function show that both short-term and long-term memory effects
exist in the recurrence intervals between trading volumes. We further study the
relationship between trading volumes and price returns based on the recurrence
interval analysis method. It is found that large trading volumes are more
likely to occur following large price returns, and the comovement between
trading volumes and price returns is more pronounced for large trading volumes.
T. Carletti, D. Fanelli, S. Righi
posted by Matúš Medo
(9 February 2010)
In this paper we show that the small world and weak ties phenomena can
spontaneously emerge in a social network of interacting agents. This dynamics
is simulated in the framework of a simplified model of opinion diffusion in an
evolving social network where agents are made to interact, possibly update
their beliefs and modify the social relationships according to the opinion
exchange.
Jie-Jun Tseng, Chih-Hao Lin, Chih-Ting Lin, Sun-Chong Wang, Sai-Ping Li
posted by Matúš Medo
(9 February 2010)
Real world markets display power-law features in variables such as price
fluctuations in stocks. To further understand market behavior, we have
conducted a series of market experiments on our web-based prediction market
platform which allows us to reconstruct transaction networks among traders.
<br />From these networks, we are able to record the degree of a trader, the size
of a community of traders, the transaction time interval among traders and
other variables that are of interest. The distributions of all these variables
show power-law behavior. On the other hand, agent-based models have been
proposed to study the properties of real financial markets. We here study the
statistical properties of these agent-based models and compare them with the
results from our web-based market experiments. In this work, three agent-based
models are studied, namely, zero-intelligence (ZI), zero-intelligence-plus
(ZIP) and Gjerstad-Dickhaut (GD). Computer simulations of variables based on
these three agent-based models were carried out. We found that although being
the most naive agent-based model, ZI indeed best describes the properties
observed in real market
704
s. Our study suggests that the basic ingredient to
produce the observed properties from real world markets could in fact be the
result of a continuously evolving dynamical system with basic features similar
to the ZI model.