13 research outputs found
Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions
This paper considers multi-dimensional affine processes with continuous
sample paths. By analyzing the Riccati system, which is associated with affine
processes via the transform formula, we fully characterize the regions of
exponents in which exponential moments of a given process do not explode at any
time or explode at a given time. In these two cases, we also compute the
long-term growth rate and the explosion rate for exponential moments. These
results provide a handle to study implied volatility asymptotics in models
where returns of stock prices are described by affine processes whose
exponential moments do not have an explicit formula.Comment: 36 pages, 5 figure
Non-Supersymmetric Attractors
We consider theories with gravity, gauge fields and scalars in
four-dimensional asymptotically flat space-time. By studying the equations of
motion directly we show that the attractor mechanism can work for
non-supersymmetric extremal black holes. Two conditions are sufficient for
this, they are conveniently stated in terms of an effective potential involving
the scalars and the charges carried by the black hole. Our analysis applies to
black holes in theories with supersymmetry, as well as
non-supersymmetric black holes in theories with supersymmetry.
Similar results are also obtained for extremal black holes in asymptotically
Anti-de Sitter space and in higher dimensions.Comment: 55 pages, LaTeX, 7 eps figures. v3: references and some additional
comments added, minor correction
A C-Function For Non-Supersymmetric Attractors
We present a c-function for spherically symmetric, static and asymptotically
flat solutions in theories of four-dimensional gravity coupled to gauge fields
and moduli. The c-function is valid for both extremal and non-extremal black
holes. It monotonically decreases from infinity and in the static region
acquires its minimum value at the horizon, where it equals the entropy of the
black hole. Higher dimensional cases, involving -form gauge fields, and
other generalisations are also discussed.Comment: References adde
One entropy function to rule them all
We study the entropy of extremal four dimensional black holes and five
dimensional black holes and black rings is a unified framework using Sen's
entropy function and dimensional reduction. The five dimensional black holes
and black rings we consider project down to either static or stationary black
holes in four dimensions. The analysis is done in the context of two derivative
gravity coupled to abelian gauge fields and neutral scalar fields. We apply
this formalism to various examples including minimal supergravity.Comment: 29 pages, 2 figures, revised version for publication, details adde
Arbitrage Opportunities in Misspecified Stochastic volatility Models
There is vast empirical evidence that given a set of assumptions on the real-world dynamics of an asset, the European options on this asset are not efficiently priced in options markets, giving rise to arbitrage opportunities. We study these opportunities in a generic stochastic volatility model and exhibit the strategies which maximize the arbitrage profit. In the case when the misspecified dynamics is a classical Black-Scholes one, we give a new interpretation of the classical butterfly and risk reversal contracts in terms of their (near) optimality for arbitrage strategies. Our results are illustrated by a numerical example including transaction costs.
Rotating Attractors
We prove that, in a general higher derivative theory of gravity coupled to abelian gauge fields and neutral scalar fields, the entropy and the near horizon background of a rotating extremal black hole is obtained by extremizing an entropy function which depends only on the parameters labeling the near horizon background and the electric and magnetic charges and angular momentum carried by the black hole. If the entropy function has a unique extremum then this extremum must be independent of the asymptotic values of the moduli scalar fields and the solution exhibits attractor behaviour. If the entropy function has flat directions then the near horizon background is not uniquely determined by the extremization equations and could depend on the asymptotic data on the moduli fields, but the value of the entropy is still independent of this asymptotic data. We illustrate these results in the context of two derivative theories of gravity in several examples. These include Kerr black hole, Kerr-Newman black hole, black holes in Kaluza-Klein theory, an