Path Generation for Quasi-Monte Carlo Simulation of Mortgage-Backed Securities

Monte Carlo simulation is playing an increasingly important role in the pricing and hedging of complex, path dependent financial instruments. Low discrepancy simulation methods offer the potential to provide faster rates of convergence than those of standard Monte Carlo methods; however, in high dimensional problems special methods are required to ensure that the faster convergence rates hold. Indeed, Ninomiya and Tezuka (1996) have shown highdimensional examples, in which low discrepancy methods perform worse than Monte Carlo methods. The principal component construction introduced by Acworth et al. (1998) provides one solution to this problem. However, the computational effort required to generate each path grows quadratically with the dimension of the problem. This article presents two new methods that offer accuracy equivalent, in terms of explained variability, to the principal components construction with computational requirements that are linearly related to the problem dimension. One method is to take into account knowledge about the payoff function, which makes it more flexible than the Brownian Bridge construction. Numerical results are presented that show the benefits of such adjustments. The different methods are compared for the case of pricing mortgage backed securities using the Hull-White term structure model.