Acceleration techniques for stochastic volatility models in Finance

Abstract

Mixing Monte-Carlo and PDE methods can substantially speed-up computations because it allows use of closed form solutions for some of the components. It can also solve problems like unknown boundary conditions for complex stochastic volatility models. Applying the method combined with Longstaff-Schwartz projection can lead to efficient computations of early exercise contracts. The convergence of the methods will be established with error estimates and we shall report performance on multi-dimensional problems. Further accelerations by using POD will be discussed.