Abstract

What is the optimal timing of inventory investment for a firm when its forecasts of demand and price improve with time but are correlated with the prices of traded assets in the financial markets? We consider this problem using a single period inventory model where demand and price are realized at time T and the stocking decision may be made at any time in the interval [0, T]. The processes for the firm’s value as well as that of the market evolve as geometric Brownian motions. We show that the right to make the optimal inventory decision is a modified American-style option. However, since the stochastic variables defining the forecasts of demand and price are not tradeable, we cannot use standard dynamic hedging arguments in the Black-Scholes-Merton sense. Therefore, we use a risk-adjusted valuation approach for incomplete markets to determine the optimal timing strategy. Our model provides results regarding the value of the option to postpone inventory procurement as a function of the key parameters: the market price of risk, the volatilities of price and demand, the correlation between these two variables and the return on the market portfolio, and the procurement cost. We illustrate the empirical validity of our model by testing it on firms in the gold mining industry. Thus, we shows that our model provides new evidence on the correlation between days of inventory and price volatility.

Citations