Multivariate Lévy models: calibration and pricing

The goal of this paper is to investigate how the marginal and dependence structures of a variety of multivariate Lévy models affect calibration and pricing. To this aim, we study the approaches of Luciano and Semeraro (J Comput Appl Math 233:1937–1953, 2010) and Ballotta and Bonfiglioli (Eur J Financ 22:1320–1350, 2016) to construct multivariate processes. We explore several calibration methods that can be used to fine-tune the models, and that deal with the observed trade-off between marginal and correlation fit. We carry out a thorough empirical analysis to evaluate the ability of the models to fit market data, price exotic derivatives, and embed a rich dependence structure. By merging theoretical aspects with the results of the empirical test, we provide tools to make suitable decisions about the models and calibration techniques to employ in a real context.