In this paper we suggest two improvements to the Least-Squares Monte-Carlo approach of Longstaff & Schwartz (2001). Both focus on the accuracy and stability of the exercise strategy rather than the Monte-Carlo valuation of the option given a strategy, which is considered in Rasmussen (2002).
The first improvement is achieved by applying control variates to the sampled discounted payoffs used in the least squares projection estimate of the unknown conditional expectation of the discounted payoffs from continuing the option. We show that this produces a more efficient estimate of the continuation value used in determining the strategy.
Te second improvement is achieved by dispersing the initial state variables from which the paths used in the least squares projections are generated. Rather than generating paths from a single initial point, paths are generated from an initial distribution of the state variables. This improves the overall accuracy of the determined exercise region, in particular where few in-the-money paths are generated from the original state variables.
Numerical examples are given for the American single-asset put option. The improved accuracy leads to closer lower and upper bounds on the American option value. A tradeoff can be made to improve the speed of the Least-Squares Monte-Carlo approach, while still obtaining accurate results.
By Nicki Søndergaard Rasmussen