1,574 research outputs found
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
Evidence of Deep Water Penetration in Silica during Stress Corrosion Fracture
We measure the thickness of the heavy water layer trapped under the stress corrosion fracture surface of silica using neutron reflectivity experiments. We show that the penetration depth is 65–85 Å, suggesting the presence of a damaged zone of ~100 Å extending ahead of the crack tip during its propagation. This estimate of the size of the damaged zone is compatible with other recent results
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
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
Multiple scaling regimes in simple aging models
We investigate aging in glassy systems based on a simple model, where a point
in configuration space performs thermally activated jumps between the minima of
a random energy landscape. The model allows us to show explicitly a subaging
behavior and multiple scaling regimes for the correlation function. Both the
exponents characterizing the scaling of the different relaxation times with the
waiting time and those characterizing the asymptotic decay of the scaling
functions are obtained analytically by invoking a `partial equilibrium'
concept.Comment: 4 pages, 3 figure
Dynamics of particles and manifolds in a quenched random force field
We study the dynamics of a directed manifold of internal dimension D in a
d-dimensional random force field. We obtain an exact solution for and a Hartree approximation for finite d. They yield a Flory-like
roughness exponent and a non trivial anomalous diffusion exponent
continuously dependent on the ratio of divergence-free ()
to potential () disorder strength. For the particle (D=0) our results
agree with previous order RG calculations. The time-translational
invariant dynamics for smoothly crosses over to the previously
studied ultrametric aging solution in the potential case.Comment: 5 pages, Latex fil
Delta Hedged Option Valuation with Underlying Non-Gaussian Returns
The standard Black-Scholes theory of option pricing is extended to cope with
underlying return fluctuations described by general probability distributions.
A Langevin process and its related Fokker-Planck equation are devised to model
the market stochastic dynamics, allowing us to write and formally solve the
generalized Black-Scholes equation implied by dynamical hedging. A systematic
expansion around a non-perturbative starting point is then implemented,
recovering the Matacz's conjectured option pricing expression. We perform an
application of our formalism to the real stock market and find clear evidence
that while past financial time series can be used to evaluate option prices
before the expiry date with reasonable accuracy, the stochastic character of
volatility is an essential ingredient that should necessarily be taken into
account in analytical option price modeling.Comment: Four pages; two eps figure
Individual and collective stock dynamics: intra-day seasonalities
We establish several new stylised facts concerning the intra-day
seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the
volatility, we find that the average correlation between stocks increases
throughout the day, leading to a smaller relative dispersion between stocks.
Somewhat paradoxically, the kurtosis (a measure of volatility surprises)
reaches a minimum at the open of the market, when the volatility is at its
peak. We confirm that the dispersion kurtosis is a markedly decreasing function
of the index return. This means that during large market swings, the
idiosyncratic component of the stock dynamics becomes sub-dominant. In a
nutshell, early hours of trading are dominated by idiosyncratic or sector
specific effects with little surprises, whereas the influence of the market
factor increases throughout the day, and surprises become more frequent.Comment: 9 pages, 7 figure
Dynamical ultrametricity in the critical trap model
We show that the trap model at its critical temperature presents dynamical
ultrametricity in the sense of Cugliandolo and Kurchan [CuKu94]. We use the
explicit analytic solution of this model to discuss several issues that arise
in the context of mean-field glassy dynamics, such as the scaling form of the
correlation function, and the finite time (or finite forcing) corrections to
ultrametricity, that are found to decay only logarithmically with the
associated time scale, as well as the fluctuation dissipation ratio. We also
argue that in the multilevel trap model, the short time dynamics is dominated
by the level which is at its critical temperature, so that dynamical
ultrametricity should hold in the whole glassy temperature range. We revisit
some experimental data on spin-glasses in light of these results.Comment: 7 pages, 4 .eps figures. submitted to J. Phys.
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