Valuation of Mortgage - Backed Securities in a Distributed Environment

Valuation of Mortgage-Backed Securities in a Distributed Environment Vladimir Surkov Master of Science Graduate Department of Computer Science University of Toronto 2004 Valuation of Mortgage-Backed Securities, regarded as integration in high dimensional space, can be readily performed using Monte Carlo method. The Quasi-Monte Carlo method, by utilizing low discrepancy sequences, has been able to achieve better convergence rates at computational finance problems despite analysis suggesting that the improved convergence comes into effect only at sample sizes growing exponentially with dimension. This may be attributed to the fact that the integrands are of low effective dimension and quasi-random sequences’ good equidistribution properties in low dimensions allow for the faster convergence rates to be attained at feasible sample sizes. The Brownian bridge discretization is traditionally used to reduce the effective dimension although an alternate choice of discretization can produce superior results. This paper examines the standard Brownian bridge representation and offers a reparametrization to further reduce dimension. The performance is compared both in terms of improvement in convergence and reduced effective dimensionality as computed using ANOVA decomposition. Also, porting of the valuation algorithm to a distributed environment using Microsoft .NET is presented.