Path generation for quasi-Monte Carlo simulation of mortgage-backed securities

Monte Carlo simulation is playing an increasingly important role in the pri cing and hedging of complex, path dependent financial instruments. Low disc repancy simulation methods offer the potential to provide faster rates of c onvergence than those of standard Monte Carlo methods; however, in high dim ensional problems special methods are required to ensure that the faster co nvergence rates hold. Indeed, Ninomiya and Tezuka (1996) have shown high-di mensional examples, in which low discrepancy methods perform worse than Mon te Carlo methods. The principal component construction introduced by Acwort h et al. (1998) provides one solution to this problem. However, the computa tional effort required to generate each path grows quadratically with the d imension of the problem. This article presents two new methods that offer a ccuracy equivalent, in terms of explained variability, to the principal com ponents construction with computational requirements that are Linearly rela ted to the problem dimension. One method is to take into account knowledge about the payoff function, which makes it more flexible than the Brownian B ridge construction. Numerical results are presented that show the benefits of such adjustments. The different methods are compared for the case of pri cing mortgage backed securities using the Hull-White term structure model.