Valuing portfolios of interdependent real options using influence diagrams and simulation-and-regression: A multi-stage stochastic integer programming approach

Abstract

Although real options generally occur within portfolios, most valuation approaches based on either option pricing or decision analysis alone focus on single well-defined options. In this paper we present a new approach for modelling and approximating the value of portfolios of interdependent real options using both influence diagrams and simulation-and-regression. The key feature of this approach is that it translates the interdependencies between real options into a set of constraints and then directly models the dynamics of all underlying uncertainties using (Markovian) stochastic processes. These are then integrated in a portfolio optimisation problem which is formulated as a multi-stage stochastic integer program. Applying a simulation and parametric regression approach to approximate the value of this optimisation problem, we present a transparent valuation algorithm that explicitly takes into account vector-valued exercise decisions and the state variable’s multidimensional resource component. The approach is therefore applicable to a wide range of complex investment projects with both inherent interdependent flexibilities and many underlying uncertainties. The approach is illustrated by evaluating a complex natural resource investment that features both a large portfolio of interdependent real options and four stochastic factors. We analyse the way in which the approximated value of the portfolio and its individual options are affected by the initial copper price as well as by the degrees of production cost and copper price uncertainty.