2,291 research outputs found

### Anomalous price impact and the critical nature of liquidity in financial markets

We propose a dynamical theory of market liquidity that predicts that the
average supply/demand profile is V-shaped and {\it vanishes} around the current
price. This result is generic, and only relies on mild assumptions about the
order flow and on the fact that prices are (to a first approximation)
diffusive. This naturally accounts for two striking stylized facts: first,
large metaorders have to be fragmented in order to be digested by the liquidity
funnel, leading to long-memory in the sign of the order flow. Second, the
anomalously small local liquidity induces a breakdown of linear response and a
diverging impact of small orders, explaining the "square-root" impact law, for
which we provide additional empirical support. Finally, we test our arguments
quantitatively using a numerical model of order flow based on the same minimal
ingredients.Comment: 16 pages, 7 figure

### On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses

We reformulate the interpretation of the mean-field glass transition scenario
for finite dimensional systems, proposed by Wolynes and collaborators.
This allows us to establish clearly a temperature dependent length xi* above
which the mean-field glass transition picture has to be modified. We argue in
favor of the mosaic state introduced by Wolynes and collaborators, which leads
to the Adam-Gibbs relation between the viscosity and configurational entropy of
glass forming liquids.
Our argument is a mixture of thermodynamics and kinetics, partly inspired by
the Random Energy
Model: small clusters of particles are thermodynamically frozen in low energy
states, whereas large clusters are kinetically frozen by large activation
energies. The relevant relaxation time is that of the smallest `liquid'
clusters. Some physical consequences are discussed.Comment: 8 page

### Rejuvenation in the Random Energy Model

We show that the Random Energy Model has interesting rejuvenation properties
in its frozen phase. Different `susceptibilities' to temperature changes, for
the free-energy and for other (`magnetic') observables, can be computed
exactly. These susceptibilities diverge at the transition temperature, as
(1-T/T_c)^-3 for the free-energy.Comment: 9 pages, 1 eps figur

### Statistical Mechanics of a Two-Dimensional System with Long Range Interaction

We analyse the statistical physics of a two dimensional lattice based gas
with long range interactions. The particles interact in a way analogous to
Queens on a chess board. The long range nature of the interaction gives the
mathematics of the problem a simple geometric structure which simplifies both
the analytic and numerical study of the system. We present some analytic
calculations for the statics of the problem and also we perform Monte Carlo
simulations which exhibit a dynamical transition between a high temperature
liquid regime and a low temperature glassy regime exhibiting aging in the two
time correlation functions.Comment: 9 pages, 8 figure

### A Non-Gaussian Option Pricing Model with Skew

Closed form option pricing formulae explaining skew and smile are obtained
within a parsimonious non-Gaussian framework. We extend the non-Gaussian option
pricing model of L. Borland (Quantitative Finance, {\bf 2}, 415-431, 2002) to
include volatility-stock correlations consistent with the leverage effect. A
generalized Black-Scholes partial differential equation for this model is
obtained, together with closed-form approximate solutions for the fair price of
a European call option. In certain limits, the standard Black-Scholes model is
recovered, as is the Constant Elasticity of Variance (CEV) model of Cox and
Ross. Alternative methods of solution to that model are thereby also discussed.
The model parameters are partially fit from empirical observations of the
distribution of the underlying. The option pricing model then predicts European
call prices which fit well to empirical market data over several maturities.Comment: 37 pages, 11 ps figures, minor changes, typos corrected, to appear in
Quantitative Financ

### Anomalous dynamical light scattering in soft glassy gels

We compute the dynamical structure factor S(q,tau) of an elastic medium where
force dipoles appear at random in space and in time, due to `micro-collapses'
of the structure. Various regimes are found, depending on the wave vector q and
the collapse time. In an early time regime, the logarithm of the structure
factor behaves as (q tau)^{3/2}, as predicted by Cipelletti et al. [1] using
heuristic arguments. However, in an intermediate time regime we rather obtain a
q tau)^{5/4} behaviour. Finally, the asymptotic long time regime is found to
behave as q^{3/2} tau. We also give a plausible scenario for aging, in terms of
a strain dependent energy barrier for micro-collapses. The relaxation time is
found to grow with the age t_w, quasi-exponentially at first, and then as
t_w^{4/5} with logarithmic corrections.Comment: 15 pages, 1 .eps figure. Submitted to EPJ-

### Financial Applications of Random Matrix Theory: a short review

We discuss the applications of Random Matrix Theory in the context of
financial markets and econometric models, a topic about which a considerable
number of papers have been devoted to in the last decade. This mini-review is
intended to guide the reader through various theoretical results (the
Marcenko-Pastur spectrum and its various generalisations, random SVD, free
matrices, largest eigenvalue statistics, etc.) as well as some concrete
applications to portfolio optimisation and out-of-sample risk estimation.Comment: To appear in the "Handbook on Random Matrix Theory", Oxford
University Pres

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