Option prices in exponential L´evy models solve certain partial
integrodifferential equations (PIDEs). This work focuses on a finite
difference scheme that issuitable for solving such PIDEs. The scheme was
introduced in [Cont and Voltchkova, SIAM J. Numer. Anal.,
43(4):1596–1626, 2005]. The main results of this work are new estimates
of the dominating error terms, namely the time and space discretization
errors. In addition, the leading order terms of the error estimates are
determined in computable form. The payoff is only assumed to satisfy an
exponential growth condition, it is not assumed to be Lipschtitz
continuous as in previous works.

If the underlying Lévy process has
infinite jump activity, then the jumps smallerthan some ε> 0 are
approximated by diffusion. The resulting diffusion approximationerror is
also estimated, with leading order term in computable form, as well as
its effecton the space and time discretization errors. Consequently, it
is possible to determine how to jointly choose the space and time grid
sizes and the parameter ε.