  We investigate the extension of the multilevel Monte Carlo path simulation
method to jump-diffusion SDEs. We consider models with finite rate activity,
using a jump-adapted discretisation in which the jump times are computed and
added to the standard uniform dis- cretisation times. The key component in
multilevel analysis is the calculation of an expected payoff difference between
a coarse path simulation and a fine path simulation with twice as many
timesteps. If the Poisson jump rate is constant, the jump times are the same on
both paths and the multilevel extension is relatively straightforward, but the
implementation is more complex in the case of state-dependent jump rates for
which the jump times naturally differ.
