Dynamic Lévy Copulas and their Applications in the Pricing of Multidimensional Option with Path Dependence

Abstract

This article presents an alternative to modeling multidimensional options, where the payoffs depend on the paths of the trajectories of the underlying-asset prices. The proposed technique considers Lévy processes, a very ample class of stochastic processes that allows the existence of jumps (discontinuities) in the price process of financial assets, and as a particular case, comprises the Brownian motion. To describe the dependence among Lévy processes, extending the static concepts of the ordinary copulas to the Lévy processes context, considering the Lévy measure, which characterizes the jumps behavior of these processes. A comparison between the Clayton and the Frank dynamic copulas and their impact in asset pricing of Asian type derivatives contracts is studied, considering gamma processes and Monte Carlo simulation procedures.