Computation of Greeks in LIBOR models driven by time-inhomogeneous Lévy processes
Eddahbi, M. . 2016
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
these methods is presented in Eberlein (2014). We illustrate the result by applying the formula to
a caplet price where the underlying model is driven by a time–inhomogeneous Gamma process and
alternatively by a Variance Gamma process. A comparison between the two approaches which come
from totally different mathematical fields is made.
This paper deals with numerical analysis of solutions to stochastic differential equations
with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is…
In this paper we are interested in solving numerically quadratic SDEs with non-necessary continuous drift of the from
\begin{equation*}
X_{t}=x+\int_{0}^{t}b(s,X_{s})ds+\int_{0}^{t}f(…
We study both Malliavin regularity and numerical approximation schemes for a class of quadratic backward stochastic