We establish a Krylov's type estimate and an Itô-Krylov's change of variable formula for the solutions of one-dimensional quadratic backward stochastic differential equations (QBSDEs) with a measurable generator and an arbitrary terminal datum. This allows us to prove various existence and uniqueness results for some classes of QBSDEs with a square integrable terminal condition and sometimes a merely measurable generator. It turns out that neither the
existence of exponential moments of the terminal datum nor the continuity of the generator are necessary to the

The purpose of this article is to give a closed Fourier-based valuation
formula for a caplet in the framework of the Lévy forward process model which was
introduced in Eberlein and Özkan (2005) [8]. Afterwards, we compute Greeks by
two approaches which come from totally different mathematical fields. The first is
based on the integration-by-parts formula, which lies at the core of the application
of the Malliavin calculus to finance. The second consists in using Fourier-based

The aim of this paper is to compute Greeks, i.e. price sensitivities in the framework of
the Lévy LIBOR model (LLM) which was introduced in Eberlein and Özkan (2005). Two approaches
are discussed. The first approach is based on the integration–by–parts formula, which lies at the core
of the application of the Malliavin calculus to finance as developed in Fournié et al. (1999). The
second approach consists in using Fourier based methods for pricing derivatives. A recent survey on