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=1

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=<p>We generalize the Piterbarg [<xref ref-type="bibr" rid="B1">1</xref>] model to include (1) bilateral default risk as in Burgard and Kjaer [<xref ref-type="bibr" rid="B2">2</xref>], and (2) jumps in the dynamics of the underlying asset using general classes of Lévy 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.</p>