An improved approach for valuing American options and their greeks by least-squares Monte Carlo simulation

This Paper presents a new methodology to approximate the value of American options by least-squares Monte Carlo simulation. Whereas Longstaff and Schwartz's approach does not utilize the underlying asset price movement, we develop several methods that incorporate the movement into option pricing. One category improves the R-squares from the regressions by using, [1] the weighted the discount factor from the current decision to exercise time. The other category improves the computational speed without sacrificing the convergence level by, [1] terminating early during the backwardation procedure, and [2] decreasing the number of observations for the regressors. Finally, combining both mathods, we can get improved R-squares and computational speed in comparison to Longstaff and Schwartz's approach.