The valuation of multidimensional American real options using the LSM simulation method
In this paper we show how a multidimensional American real option may be solved using the LSM simulation method originally proposed by Longstaff and Schwartz [2001, The Review of the Financial Studies 14(1): 113147] for valuing a financial option and how this method can be used in a complex setting. We extend a well-known natural resource real option model, initially solved using finite difference methods, to include a more realistic three-factor stochastic process for commodity prices, more in line with current research. Numerical results show that the procedure may be successfully used for multidimensional models, expanding the applicability of the real options approach. Even though there has been an increasing literature on the benefits of using the contingent claim approach to value real assets, limitations on solving procedures and computing power have often forced academics and practitioners to simplify these real option models to a level in which they loose relevance for real-world decision making. Real option models present a higher challenge than their financial option counterparts because of two main reasons: First, many real options have a longer maturity which makes risk modeling critical and may force considering many risk factors, as opposed to the classic Black and Scholes approach with only one risk factor. Second, real investments many times exhibit a more complex set of interacting American options, which make them more difficult to value. In recent years new approaches for solving American options have been proposed which, coupled with an increasing availability of computing power, have been successfully applied to solving long-term financial options. In this paper we explore the applicability of one the most promising of these new methods in a multidimensional real option setting.
valuation real options simulation natural resources finance