  We consider high-dimensional asset price models that are reduced in their
dimension in order to reduce the complexity of the problem or the effect of the
curse of dimensionality in the context of option pricing. We apply model order
reduction (MOR) to obtain a reduced system. MOR has been previously studied for
asymptotically stable controlled stochastic systems with zero initial
conditions. However, stochastic differential equations modeling price processes
are uncontrolled, have non-zero initial states and are often unstable.
Therefore, we extend MOR schemes and combine ideas of techniques known for
deterministic systems. This leads to a method providing a good pathwise
approximation. After explaining the reduction procedure, the error of the
approximation is analyzed and the performance of the algorithm is shown
conducting several numerical experiments. Within the numerics section, the
benefit of the algorithm in the context of option pricing is pointed out.
