An Approach for Valuing Portfolios of Interdependent Real Options under both Exogenous and Endogenous Uncertainties

Although the value of portfolios of real options is often affected by both exogenous and endogenous uncertainties, most existing valuation approaches consider only the former and neglect the latter. In this paper we extend our existing approach for modelling and approximating the value of portfolios of interdependent real options to include endogenous, decisionand state-dependent uncertainties, using stochastic processes. In particular, we study a portfolio of options under conditions of four underlying uncertainties. The options are to defer investment, to stage investment, to temporarily halt expansion, to temporarily mothball the operation, and to abandon the project. Two of the underlying uncertainties, decision-dependent cost to completion and state-dependent salvage value, are endogenous, the other two, annual operating revenues and their growth rate, are exogenous. The directly-modelled dynamics of all four uncertainties and the linear integer constraints modelling the real options’ interdependencies are integrated in a multi-stage stochastic integer programme. Using a simulation and regression approach to approximate the value of this optimisation problem, we present an efficient valuation algorithm that is more transparent than those used in existing approaches, as it exploits the problem structure to explicitly account for the path dependencies of the state variables. The applicability of the approach to complex investment projects is illustrated by valuing an urban infrastructure investment in London. In this example we show how the optimal value of the portfolio and its single, well-defined options are affected by the initial level of the annual revenues, and by the degrees of exogenous and endogenous uncertainty.