A Modified Least-Squares Simulation Approach to Value American Barrier Options

This paper presents the total least squares quasi-Monte Carlo approach (TLSQM) for valuing American barrier options, which modifies the least-squares Monte Carlo method (LSM). The total least squares are applied to estimate the conditional expected payoff to the option holder from continuation, and the quasi-Monte Carlo method is used to simulate the paths of stock prices. We show that the approximations of a set of conditional expectation functions in the TLSQM method converge to the true expectation function under general assumptions. It provides the mathematical foundation for the use of the TLSQM method in the derivatives research. In order to illustrate the high efficiency of the proposed approach, several examples are given to price American barrier options using TLSQM, LSM, and binomial trees, respectively. The numerical analysis demonstrates that the TLSQM method is accurate, and it makes improvements in computational speed and efficiency, compared with the LSM method. Copyright Springer Science+Business Media New York 2014