The Valuation of Multidimensional American Real Options using Computer-based Simulation

In this paper we show how a multidimensional American real option may be solved using a computer-based simulation procedure. We implement an approach originally proposed for a financial option and show how it can be used in a much more complex setting. We extend a wellknown natural resource real option model, originally solved using finite difference methods, to include a more realistic 3 factor stochastic process for commodity prices, more in line with current research. We show how complexity may be reduced by adequately choosing the implementation variables. Numerical results show that the procedure may be successfully used for multidimensional models, notably expanding the applicability of the real options approach. Scope and purpose 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 one-factor model. Second, many times real investments have a more complex set of interacting American options available, making 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 and opening new hopes for increasing the use of this modeling approach for valuing real assets. • All Authors Tel.: +56-2-3544272; fax: +56-2-5521608 E-mail: [email protected] (G Cortazar); [email protected] (M Gravet); [email protected] (J Urzua)