Extending Real Options Theory to Account for Property Investment under Conditions of Uncertainty and Incomplete Markets

The literature on real options theory is both diverse and rapidly expanding. Now standard techniques for the pricing of derivatives given a stochastic process for the price of underlying assets, are increasingly applied to the case of real investment in productive assets, including property development (Trigeorgis, 1996). Typically, this latter class of investments is represented as a set of options over deferment of a project, termination and salvage, switching of inputs and/or outputs, spawning of related projects, and the expansion, contraction, and temporary shut-down of projects. Concurrently, finance theorists have drawn on the mathematical literature on risksensitive and robust control theory under norm bounds and relative entropy constraints as one vehicle for accommodating uncertainty and market incompleteness (Andersen, Hansen, and Sargent 1999; McEneaney, W.M., 1997; Tornell, A., 2000). This paper provides a heuristic understanding of the relationship between these two bodies of research by examining recent work that establishes range bounds over option prices in incomplete markets (eg, that arising due to the stochastic volatility of stock prices or the existence of a stochastic interest rate) through the application of “gooddeal” bounds over the Sharpe ratios and gain-loss ratios of basis assets (Bernardo and Ledoit, 2000; Cochrane and Saa-Requejo, 2000). By varying the stipulated bound, the valuer can move along a spectrum ranging from the set of non-arbitrage bounds through to the uniquely defined option price that is associated with the pricing kernel of a chosen asset pricing model. The “good-deal” bound can thus be interpreted as a measure of investor uncertainty relative to a reference probability distribution for the equilibrium asset-pricing model. The paper identifies the precise relationship holding between the sup-norm bound on the pricing kernel, minimum cross entropy (Stutzer, 1995), and the stochastic uncertainty constraint that is adopted in certain robust control problems. In addition, it examines the derivation of martingale measures and the role of entropy techniques in Generalized Method of Moments estimation. As such, it sets out an agenda for future research into real options-based valuation of investment under uncertainty. _____________________________________________________________________