A General Approach to Real Option Valuation with ... - ICMA Centre

ICMA Centre Discussion Papers in Finance DP2012-04focus on analytic solutions, available only in the exponential case, and neither do we considerexpansion approximations, preferring instead the direct numerical implementation of a veryflexible framework.We develop an approach that is both general in scope and flexible in its applicationto a wide range of investment or divestment decisions. Several numerical examples focus onreal estate investments, from large-scale land development to individual residential propertytransactions. When we assume none of the risk of the project can be hedged in a financialmarket our framework is applicable to decisions faced by private companies, charitable entitiesor individuals. Such decisions can have profound implications for the decision maker’s welfare.Housing may represent a major component of individual wealth and should not be viewedsimply in expected net present value terms, nor should all uncertainties be based on systematicrisk because they are largely unhedgeable. Private development companies may be generatingreturns and risks that have a utility value that is specific to the owners’ outlook. Similarly,charitable entities such as housing trusts may have objectives that are far removed fromwealth maximisation under risk-neutrality.We provide a coherent analytical framework for computing the relative values of differentreal options under discrete decisions, for example at a monthly or quarterly meeting of theboard of directors. The decision maker’s utility function is applied to value every opportunitybut the decision maker’s subjective views about the evolution of the market price and anyfuture rents or development costs are specific to each location. A variety of processes for aforward market price under the investor’s (subjective) physical measure could be employed.Here we consider only one-factor models: geometric Brownian motion (GBM), mean-reversionand boom-bust market price scenarios. Extensions to jumps in prices and stochastic volatilityare an interesting topic for further research.An option strike can be predetermined, as is commonly assumed in the real optionliterature, or the investment cost can be stochastic, but then it will be perfectly correlatedwith the market price because we consider only one source of uncertainty. In the latter casethe problem falls squarely into the realm of decision analysis. Indeed, the standard riskneutraloption price will be zero, yet a risk-averse investor would still place a positive valueon the decision opportunity. Assumptions about the structure of investment costs turn outto be crucial for the ranking of alternative opportunities and for this ranking’s sensitivityanalysis to the investor’s views on market prices and cash flows.Standard risk-neutral real option prices are captured within our approach on assumingthat the investment cost is predetermined, the forward asset price follows a GBM with totalreturn equal to the risk-free rate, the investor applies a linear utility (equivalently, he hasCopyright c○ 2012 Alexander and Chen 2