Fast valuation of financial derivatives

ABSTRACT A method for pricing European contingent claims (options) based on Monte Carlo simulation with variance reduction is presented. The evolution of the option price can be formulated as a Kolmogorov final value problem and thus be calculated numerically either by solving the deterministic partial differential equation or by simulating a large number of trajectories of the corresponding stochastic differential equation. The authors discuss a Monte Carlo simulation method combined with variance reduction obtained from a Girsanov transformation of the stochastic differential equation by a correction term that is obtained as a rough solution of the partial differential equation computed by a classical numerical method. The trade-off between these methods is investigated and it is shown that the composite method is more efficient than either the standard Monte Carlo or the classical numerical method.