AUTHOR=Law Jimmy , Shek Chun K., Levendorskii Sergei TITLE=Efficient option pricing under Lévy processes, with CVA and FVA JOURNAL=Frontiers in Applied Mathematics and Statistics VOLUME=Volume 1 - 2015 YEAR=2015 URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2015.00006 DOI=10.3389/fams.2015.00006 ISSN=2297-4687 ABSTRACT=We generalize the Piterbarg (2010) model to include 1) bilateral default risk as in Burgard and Kjaer (2012), and 2) jumps in the dynamics of the underlying asset using general classes of L\'evy processes of exponential type. We develop an efficient explicit-implicit scheme for European options and barrier options taking CVA-FVA into account. We highlight the importance of this work in the context of trading, pricing and management a derivative portfolio given the trajectory of regulations.