arXiv subjects

El Hadj Aly Dia

Publications and source records attributed to El Hadj Aly Dia.

3 recordsLinked to original sources

arXiv2012

Error bounds for small jumps of Lévy processes

The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy measure generally requires either to truncate small jumps or to replace them by a Brownian motion with the same variance. We will derive bounds for the errors generated by these two types of approximation.

q-fin.CP↗

arXiv2010

Continuity correction for barrier options in jump-diffusion models

The aim of this paper is to study the continuity correction for barrier options in jump-diusion models. For this purpose, we express the pay-off a barrier option in terms of the maximum of the underlying process. We then condition with respect to the jump times and to the values of the underlying at the jump times and rely on the connection between the maximum of the Brownian motion and Bessel processes.

math.PR↗

arXiv2010

Connecting discrete and continuous lookback or hindsight options in exponential Lévy models

Motivated by the pricing of lookback options in exponential Lévy models, we study the difference between the continuous and discrete supremum of Lévy processes. In particular, we extend the results of Broadie et al. (1999) to jump-diffusion models. We also derive bounds for general exponential Lévy models.

q-fin.CP↗