A framework for pricing multiple-exercise option contracts for water (Texas)

Quality and quantity of water supplies are emerging as pressing concerns in many areas of the U.S. and the world, making efficient allocation of water a crucial issue for economic analysis. Water allocation mechanisms must be flexible enough to respond to changes in quality, quantity, location, and timing of both water supply and water demand. Historically the policy response to excess demand for water was to build dams, find new water sources, or construct storage facilities. More recently, markets for water have been developing in the western U.S. and elsewhere. Option contracts for water are emerging in some U.S. states as institutional and legal modifications allow water users to devise new mechanisms to increase reliability of water supply in dry years. Option contracts for water, though, are structurally distinct from financial derivatives and often entail a lengthy lifespan and the opportunity for multiple exercise. The Black-Scholes option-valuation framework is appropriate for options with simple payoffs but the complicated structure of water options requires an innovative computational algorithm. Adoption of the Black-Scholes assumption of geometric Brownian motion in the underlying asset price is also questionable in the scenario of water markets. In this thesis I present the framework and results of a finite-horizon, discrete-time, stochastic dynamic programming methodology for valuing multiple-exercise option contracts. The analysis examines a call option that can be exercised in any seven of fifteen years, but not more than once per year. I use data from short-term water markets in the Texas Lower Rio Grande to estimate parameters for two different price processes: mean reversion and geometric Brownian motion. Nonsychronous trading effects in the data are addressed through simulation and through the Scholes and Williams (1977) technique. Key findings of the analysis include: (1) non-zero contract values for both price processes, (2) higher contract values under geometric Brownian motion than under mean reversion, (3) greater sensitivity to price process parameters than to discount rate in the mean reverting case, and (4) greater sensitivity to price process volatility than to discount rate for low initial water prices under geometric Brownian motion.