Stochastic Water Quality: The Timing and Option Value of Treatment

An option-pricing model is developed to rank investments that might improve water quality. The model presumes that two investment options exist that have the potential to alter the stochastic drift of a pollutant. The investments have capital and operating costs and are irreversible once constructed. The stochastically evolving pollutant induces stochastic damage. An option-pricing model provides a criterion for determining when it is optimal to adopt the investment with the highest option value. Option value, in this model, measures the expected present value in reduced damage, relative to doing nothing. If the investments are mutually exclusive, it is possible to obtain closed-form solutions for the barriers which would trigger investment. If the investments can be sequentially adopted, a methodology is developed to calculate option values for all possible combinations of adoption dates. To illustrate the optionpricing approach, a stylized analysis of investments to protect New York City’s water supply is presented. Watershed management dominates filtration and, in the case of mutually exclusive investments, is initiated when the concentration of phosphorus reaches 22.80 μg/L.