Alice Pignatelli di Cerchiara

Università Cattolica del Sacro Cuore

Title

American multi-asset option pricing under vine Lévy copulae and the Ballotta-Bonfiglioli model

Author

Alice Pignatelli di Cerchiara

Abstract

In this work, multivariate Lévy processes are discussed focusing on two different characterizations of dependence: the Ballotta-Bonfiglioli method and Lévy copulae (with also their vine extension). The first of the two provides a flexible way of modelling dependence, while the second extends the classic idea of copulae into the world of Lévy processes, with the consequence of a potentially wider and more precise capture of dependence, but at the cost of a reduced analytical tractability. The final aim of our work was to price several multi-asset options while highlighting the effect of dependence between the underlying assets introduced by the two different models. For both the approaches, the analysis focused on the selection of the best marginal stochastic processes and on the construction of a specific dependence structure. These two steps paved the way to the effective identification of robust models which were then used to retrieve the prices of the options by applying the specific payoff conditions. Then, a sensitivity analysis was performed for each method, with the objective of showing how the results could change in terms of pricing if different dependence structures were exploited. Finally, a comparison between the two methods is provided, clearly explaining the fact that different assumptions about marginal stochastic processes and dependence modelling were used.