Josep Vives

On Lévy processes, Malliavin calculus and market models with jumps

Abstract. Recent work by Nualart and Schoutens (2000), where a kind of chaotic property for Lévy processes has been proved, has enabled us to develop a Malliavin calculus for Lévy processes. For simple Lévy processes some useful formulas for computing Malliavin derivatives are deduced. Applications for option hedging in a jump–diffusion model are given.

Chaos expansions of double intersection local time of Brownian motion in Rd and renormalization

Double intersection local times [alpha](x,.) of Brownian motion which measure the size of the set of time pairs (s, t), s [not equal to] t, for which Wt and Ws + x coincide can be developed into series of multiple Wiener-Ito integrals. These series representations reveal on the one hand the degree of smoothness of [alpha](x,.) in terms of eventually negative order Sobolev spaces with respect to the canonical Dirichlet structure on Wiener space. On the other hand, they offer an easy access to renormalization of [alpha](x,.) as x --> 0. The results, valid for any dimension d, describe a pattern in which the well known cases d = 2, 3 are naturally embedded.

On the Short-Time Behavior of the Implied Volatility for Jump-Diffusion Models With Stochastic Volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

A Duality Formula on the Poisson Space and Some Applications

We establish a duality formula for the chaotic derivative operator on the canonical Poisson space. The adjoint of this operator is proved to coincide with the stochastic integration on predictable processes.

Smoothness of Brownian local times and related functionals

AbstractIn this paper we show that the local time of the Brownian motion belongs to the Sobolev space

Molecular structure of {[Ag13(μ-SC5H9NHMe)16]13+}n, a novel one-dimensional non-molecular silver-thiolate

\mathbb{D}^{\alpha {\text{,}}p}

{Ag5[µ2-S–(CH2)3–NHMe2]3[µ2-S–(CH2)3–NMe2]3}2+, the first thiolate complex of a metal with trigonal bipyramido-M5-trigonal prismo-S6 polyhedral stereochemistry

for any p≥2 and 0<α<1/p. In order to prove this result we first discuss the smoothness and integrability properties of the composition of the Dirac function δα with a Wiener integral W(h), and we show that this composition belongs to