27 research outputs found
Market bubbles and crashes
Episodes of market crashes have fascinated economists for centuries. Although
many academics, practitioners and policy makers have studied questions related
to collapsing asset price bubbles, there is little consensus yet about their
causes and effects. This review and essay evaluates some of the hypotheses
offered to explain the market crashes that often follow asset price bubbles.
Starting from historical accounts and syntheses of past bubbles and crashes, we
put the problem in perspective with respect to the development of the efficient
market hypothesis. We then present the models based on heterogeneous agents and
the limits to arbitrage that prevent rational agents from bursting bubbles
before they inflate. Then, we explore another set of explanations of why
rational traders would be led to actually profit from and surf on bubbles, by
anticipating the behavior of noise traders or by realizing the difficulties in
synchronizing their actions. We then end by discussing a complex system
approach of social imitation leading to collective market regimes like herding
and the phenomenon of bifurcation (or phase transition) that rationalize what
crash can occur in unstable market regimes. The key insight is that diagnosing
bubbles may be feasible when taking into account the positive feedback
mechanisms that give rise to transient "super-exponential" price growth, the
bubbles.Comment: 25 pages, long version of a shorter review written for the
Encyclopedia of Quantitative Finance (Wiley)
http://www.wiley.com//legacy/wileychi/eqf
Statistical properties of absolute log-returns and a stochastic model of stock markets with heterogeneous agents
This paper is intended as an investigation of the statistical properties of
{\it absolute log-returns}, defined as the absolute value of the logarithmic
price change, for the Nikkei 225 index in the 28-year period from January 4,
1975 to December 30, 2002. We divided the time series of the Nikkei 225 index
into two periods, an inflationary period and a deflationary period. We have
previously [18] found that the distribution of absolute log-returns can be
approximated by the power-law distribution in the inflationary period, while
the distribution of absolute log-returns is well described by the exponential
distribution in the deflationary period.\par To further explore these empirical
findings, we have introduced a model of stock markets which was proposed in
[19,20]. In this model, the stock market is composed of two groups of traders:
{\it the fundamentalists}, who believe that the asset price will return to the
fundamental price, and {\it the interacting traders}, who can be noise traders.
We show through numerical simulation of the model that when the number of
interacting traders is greater than the number of fundamentalists, the
power-law distribution of absolute log-returns is generated by the interacting
traders' herd behavior, and, inversely, when the number of fundamentalists is
greater than the number of interacting traders, the exponential distribution of
absolute log-returns is generated.Comment: 12 pages, 5 figure
Statistical mixing and aggregation in Feller diffusion
We consider Feller mean-reverting square-root diffusion, which has been
applied to model a wide variety of processes with linearly state-dependent
diffusion, such as stochastic volatility and interest rates in finance, and
neuronal and populations dynamics in natural sciences. We focus on the
statistical mixing (or superstatistical) process in which the parameter related
to the mean value can fluctuate - a plausible mechanism for the emergence of
heavy-tailed distributions. We obtain analytical results for the associated
probability density function (both stationary and time dependent), its
correlation structure and aggregation properties. Our results are applied to
explain the statistics of stock traded volume at different aggregation scales.Comment: 16 pages, 3 figures. To be published in Journal of Statistical
Mechanics: Theory and Experimen
Volatility clustering and scaling for financial time series due to attractor bubbling
A microscopic model of financial markets is considered, consisting of many
interacting agents (spins) with global coupling and discrete-time thermal bath
dynamics, similar to random Ising systems. The interactions between agents
change randomly in time. In the thermodynamic limit the obtained time series of
price returns show chaotic bursts resulting from the emergence of attractor
bubbling or on-off intermittency, resembling the empirical financial time
series with volatility clustering. For a proper choice of the model parameters
the probability distributions of returns exhibit power-law tails with scaling
exponents close to the empirical ones.Comment: For related publications see http://www.helbing.or
Extrapolation of power series by self-similar factor and root approximants
The problem of extrapolating the series in powers of small variables to the
region of large variables is addressed. Such a problem is typical of quantum
theory and statistical physics. A method of extrapolation is developed based on
self-similar factor and root approximants, suggested earlier by the authors. It
is shown that these approximants and their combinations can effectively
extrapolate power series to the region of large variables, even up to infinity.
Several examples from quantum and statistical mechanics are analysed,
illustrating the approach.Comment: 21 pages, Latex fil
Index Cohesive Force Analysis Reveals That the US Market Became Prone to Systemic Collapses Since 2002
BACKGROUND: The 2007-2009 financial crisis, and its fallout, has strongly emphasized the need to define new ways and measures to study and assess the stock market dynamics. METHODOLOGY/PRINCIPAL FINDINGS: The S&P500 dynamics during 4/1999-4/2010 is investigated in terms of the index cohesive force (ICF--the balance between the stock correlations and the partial correlations after subtraction of the index contribution), and the Eigenvalue entropy of the stock correlation matrices. We found a rapid market transition at the end of 2001 from a flexible state of low ICF into a stiff (nonflexible) state of high ICF that is prone to market systemic collapses. The stiff state is also marked by strong effect of the market index on the stock-stock correlations as well as bursts of high stock correlations reminiscence of epileptic brain activity. CONCLUSIONS/SIGNIFICANCE: The market dynamical states, stability and transition between economic states was studies using new quantitative measures. Doing so shed new light on the origin and nature of the current crisis. The new approach is likely to be applicable to other classes of complex systems from gene networks to the human brain
Super-exponential endogenous bubbles in an equilibrium model of rational and noise traders
We introduce a model of super-exponential financial bubbles with two assets (risky and risk-free), in which rational investors and noise traders co-exist. Rational investors form expectations on the return and risk of a risky asset and maximize their constant relative risk aversion expected utility with respect to their allocation on the risky asset versus the risk-free asset. Noise traders are subjected to social imitation and follow momentum trading. Allowing for random time-varying herding propensity, we are able to reproduce several well-known stylized facts of financial markets such as a fat-tail distribution of returns and volatility clustering. In particular, we observe transient faster-than-exponential bubble growth with approximate log-periodic behavior and give analytical arguments why this follows from our framework. The model accounts well for the behavior of traders and for the price dynamics that developed during the dotcom bubble in 1995-2000. Momentum strategies are shown to be transiently profitable, supporting these strategies as enhancing herding behavior.