Efficient option pricing under Lévy processes, with CVA and FVA - Law, Jimmy; Shek, Chun K.; Levendorskii, Sergei (Frontiers in Applied Mathematics and Statistics, 2015)
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.