Hysteresis Models of Investment with Multiple Uncertainties and Exchange Rate Risk

In this article we use the hysteresis model of investment developed by Brennan and Schwartz, and Dixit, and we extend it to capture the impact of interacting uncertainties on a firm with foreign operations. We develop a three-country, four-factor model where both continuous revenues and continuous costs are stochastic and are generated in countries other than the home country of the investor, who has to carry foreign currencies' risk. All four state-variables follow geometric Brownian motion processes. A critical assumption is made that the capital outlays for switching between the idle and the active states are constant fractions of the costs. An efficient numerical solution is used to demonstrate applications of the model on a multinational corporation facing operating and exchange rate risks in a multistage investment setting with interacting investment and operating options.