Risk management with substitution options: Valuing flexibility in small-scale energy systems

Several features of small-scale energy systems make them more easily adapted to a changing operating environment than large centralized designs. This flexibility is often manifested as the ability to substitute inputs. This research explores the value of this substitution flexibility and the marginal value of becoming a "little more flexible" in the context of real project investment in developing countries.; The elasticity of substitution is proposed as a stylized measure of flexibility and a choice variable. A flexible alternative (elasticity > 0) can be thought of as holding a fixed-proportions "nflexible" asset plus a sequence of exchange options---the option to move to another feasible "recipe" each period.; Substitutability derives value from following a contour of anticipated variations and from responding to new information. Substitutability value, a "cost savings option", increases with elasticity and price risk. However, the required premium to incrementally increase flexibility can in some cases decrease with an increase in risk.; Variance is not always a measure of risk. Tools from stochastic dominance are newly applied to real options with convex payoffs to correct some misperceptions and clarify many common modeling situations that meet the criteria for increased variance to imply increased risk.; The behavior of the cost savings option is explored subject to a stochastic input price process. At the point where costs are identical for all alternatives, the stochastic process for cost savings becomes deterministic, with savings directly proportional to elasticity of substitution and price variance. The option is also formulated as a derivative security via dynamic programming. The partial differential equation is solved for the special case of Cobb-Douglas (elasticity = 1) (also shown are linear (infinite elasticity), Leontief (elasticity = 0)).; Risk aversion is insufficient to prefer a more flexible alternative with the same expected value. Intertemporal links convert the sequence of independent options to a single compound option and require an expansion of the flexibility concept. Additional options increase the value of the project but generally decrease flexibility value.; The framework is applied to case study in India: an urban industry electricity strategy decision with reliability risk.