Distributed quasi-Monte Carlo algorithm for option pricing on HNOWs using mpC

Abstract

Monte Carlo (MC) simulation is one of the popular approaches for approximating the value of options and other derivative securities due to the absence of straightforward closed form solutions for many financial models. However, the slow convergence rate, O(N/sup - 1/2/) for N number of samples of the MC method has motivated research in quasi Monte-Carlo (QMC) techniques. QMC methods use low discrepancy (LD) sequences that provide faster, more accurate results than MC methods. In this paper, we focus on the parallelization of the QMC method on a heterogeneous network of workstations (HNOWs) for option pricing. HNOWs are machines with different processing capabilities and have distinct execution time for the same task. It is therefore important to allocate and schedule the tasks depending on the performance and resources of these machines. We present an adaptive, distributed QMC algorithm for option pricing, taking into account the performances of both processors and communications. The algorithm distributes data and computations based on the architectural features of the available processors at run time. We implement the algorithm using mpC, an extension of ANSI C language for parallel computation on heterogeneous networks. We compare and analyze the performance results with different parallel implementations. The results of our algorithm demonstrate a good performance on heterogenous parallel platforms.