An exposition of least square Monte Carlo approach for real options valuation

Abstract

The least square Monte Carlo simulation (LSM) approach is a state-of-the-art approach built upon approximate dynamic programming for the selection of single or multiple exercise options, and it has been extensively used for sequential decision-making and real options valuation. Although it has been broadly discussed and employed in many real-world applications, relatively less attention has been given to some of its implementation details. This paper aims to contribute to an improved understanding of sequential decision-making and real options valuation using the LSM algorithm. In this paper, we illustrate and argue the impact of only including the in-the-money (ITM) paths and the choice of regression functions for a specific example. A simple oil production problem with two common embedded options (shrink versus expands) has been utilized for the analysis.The analyses conducted in this article for the considered decision situation confirm that when at least one of the options (decision alternatives) is relevant to the out-of-the-money (OOTM) paths, it is crucial to consider all the paths to benefit from all the flexibilities. Furthermore, the choice of regression function is shown to have minor effect on the optimal strategies and the expected project value as long as the options are deeply ITM or OOTM. However, when the options are poorly ITM or OOTM, we might reach a different solution than what would have been achieved had we used an exact dynamic programming approach. In addition, excluding OOTM paths from the analysis adversely affects the option valuation part of the LSM for the current application, leading to lower project values. In contrast, the impact of path exclusion on regression performance is less emphasized. This work also verifies the robustness of the LSM approach for the selection of the polynomial order used for tuning the regression function. While some of the findings herein are problem-specific, a similar methodology can be used to evaluate the implementation details and refine problem settings in other real options problems.