In this thesis we discuss basket option valuation for jump-diffusion models.
We suggest three new approximate pricing methods. The first approximation
method is the weighted sum of Rogers and Shi’s lower bound and
the conditional second moment adjustments. The second is the asymptotic
expansion to approximate the conditional expectation of the stochastic variance
associated with the basket value process. The third is the lower bound
approximation which is based on the combination of the asymptotic expansion
method and Rogers and Shi’s lower bound. We also derive a forward
partial integro-differential equation (PIDE) for general asset price processes
with stochastic volatilities and stochastic jump compensators. Numerical
tests show that the suggested methods are fast and accurate in comparison
with Monte Carlo and other methods in most cases.