Least-Squares Monte Carlo for Backward SDEs [chapter]

Christian Bender, Jessica Steiner
2012 Springer Proceedings in Mathematics  
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, Lemor, and Warin (Ann. Appl. Probab., 15, 2005, 2172-2202. 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
more » ... ehavior 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.
doi:10.1007/978-3-642-25746-9_8 fatcat:cr4hpgufifac3ac2ynys4p3k6m