Numerical Valuation of the Investment Project with Expansion Options Based on the PDE Approach

Compared to the standard DCF methodology, the real options approach provides a solution to optimal investment decisions that captures the value of flexibilities embedded in a project. In this paper we focus on one specific kind of investment decisions - an option to expand. Assuming values of both the project and the embedded option are determined in terms of time and underlying output price, driven by a relevant stochastic process, one can unify the PDE approach to describe the development of values of the project and options. More precisely, the link is realized through a payoff function enforced at a fixed time. As a result, we obtain a system of relevant governing equations of the Black-Scholes type. Since explicit formulae are known for this type of PDE problem only in specific cases, one must turn to some approximation methods. With reference to the results obtained in valuing financial options, we apply the discontinuous Galerkin method to solve the relevant governing equations. The obtained numerical scheme is applied to a simple illustrative expansion decision problem.