American options and the LSM algorithm: quasi-random sequences and Brownian bridges

Suneal K. Chaudhary

Abstract

ABSTRACT

The least-squares Monte Carlo (LSM) algorithm of Longstaff and Schwartz (2001) is a method for Monte Carlo valuation of the price of American options. We use quasi-random sequences to generate asset prices which follow geometric Brownian motions, and obtain a significant increase in the rate of convergence of American min-puts and American–Bermuda–Asian calls. Using the Brownian-bridge formula, we present a method for reducing the memory requirements from O(N ×M × d) to O(Nd log(M)) for quasi-random sequences, where N is the number of paths, M is the number of timesteps and d is the number of assets, for example, in a min-put.