Abstract:
This paper presents new results on strong numerical schemes, which are appropriate
for scenario analysis, filtering and hedge simulation, for stochastic differential equations (SDEs) of
jump-diffusion type. It provides first order strong approximations for jump-diffusion SDEs driven
by Wiener processes and Poisson random measures. The paper covers first order derivative-free,
drift-implicit and jump-adapted strong approximations. Moreover, it provides a commutativity
condition under which the computational effort of first order strong schemes is independent of
the total intensity of the jump measure. Finally, a numerical study on the accuracy of several
strong schemes applied to the Merton model is presented.
