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Convergence of 'exercise boundary fitting' least squares simulation approach

Previously, we introduced a methodology based on exercise boundary fitting in an effort to develop a practical Monte Carlo simulation-based real options approach. We showed that our methodology converges in the case of simple Bermudan and American put options. More recently, we expanded on the model to solve a staged manufacturing problem. As we presented, utilizing boundary fitting allowed us to solve a computationally difficult problem. In another study we explored the use of the boundary fitting methodology for a number of cases, one being a build and abandon mining example. We showed that while the methodology provided good convergence on option value, under certain scenarios, where the optimal exercise boundaries occurred in regions where there were few Monte Carlo paths, the optimization algorithm struggled to converge. The purpose of this paper is to explore convergence issues related to the boundary fitting methodology. Specifically, we develop experiments where we compare our boundary fitting methodology with pseudo-analytical or numerical results for the following cases: Bermudan put option; option to purchase a Bermudan put option; American put option; and build / abandon real option.