Abstract:
In finance and economics the key dynamics are often specified via
stochastic differential equations (SDEs) of jump-diffusion type. The class of
jump-diffusion SDEs that admits explicit solutions is rather limited. Consequently,
discrete time approximations are required. In this paper we give a
survey of strong and weak numerical schemes for SDEs with jumps. Strong
schemes provide pathwise approximations and therefore can be employed in
scenario analysis, filtering or hedge simulation. Weak schemes are appropriate
for problems such as derivative pricing or the evaluation of risk measures
and expected utilities. Here only an approximation of the probability distribution
of the jump-diffusion process is needed. As a framework for applications
of these methods in finance and economics we use the benchmark approach.
Strong approximation methods are illustrated by scenario simulations. Numerical
results on the pricing of options on an index are presented using weak
approximation methods.
