Lévy Factor Models for Financial Applications

In this thesis we bring a series of contributions to the topic of multivariate asset modelling with

dependence.

In the first part of the thesis (chapters 2, 3 and 4) we look at equity modelling by factor models obtained by multivariate subordination of Lévy basis and discuss multi-asset derivative pricing by Fourier transform methods. More specifically, in the second chapter we propose a construction method for obtaining factor models based on multivariate subordination which extends the results of Barndorff-Nielsen et al. (2001). A lemma describing the characteristic function for the entire class of models is provided which opens the gates for multi-asset derivative pricing by Fourier transform methods under this class of models. Classification, parametrisation and the dependence structure details for the models in this class are then discussed in the second part of the chapter. The chapters 3 and 4 propose each a different three-factor model for the evolution of equity returns and provide the details of martingale asset pricing, calibration and multi-asset derivative pricing methods under

the specific model. The specific applications that are treated are the spread options, in chapter 3 and CVA evaluation for forward contracts, in chapter 4.

In the second part of the thesis (chapter 5) we look at the multi-name credit modelling in the context of factor models built by time-changes. Specifically, we propose a factor extension of the univariate default model proposed in Packham et al. (2013)and then we discuss the calibration and the pricing methodology (including details of their implementation) for single-name and multi-name credit derivatives contracts. The specific applications that are treated are the pricing and calibration on Credit Default Swaps, Credit Index Default Swaps and Index Tranches (synthetic CDOs).