Least-Squares Monte Carlo for Backward SDEs

Abstract

In this paper we first give a review of the least-squares Monte Carlo approach for approximating the solution of backward stochastic differential equations (BSDEs) first suggested by Gobet et al. (Ann Appl Probab., 15:2172-2202, 2005). We then propose the use of basis functions, which form a system of martingales, and explain how the least-squares Monte Carlo scheme can be simplified by exploiting the martingale property of the basis functions. We partially compare the convergence behavior of the original scheme and the scheme based on martingale basis functions, and provide several numerical examples related to option pricing problems under different interest rates for borrowing and investing. © Springer-Verlag Berlin Heidelberg 2012.