Review of Quantitative Finance and Accounting, 16: 251–267, 2001
2001 Kluwer Academic Publishers. Manufactured in The Netherlands.
Hysteresis Models of Investment with Multiple
Uncertainties and Exchange Rate Risk
SPIROS H. MARTZOUKOS
Department of Public and Business Administration, University of Cyprus
Abstract. 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.
Key words: hysteresis, multiplicative uncertainties, exchange rate risk, compound (real) option, ﬂexibility
JEL Classiﬁcation: D92, F23, G13
Partial irreversibility was ﬁrst introduced in the literature by Brennan and Schwartz (1985);
soon thereafter Dixit (1989a, 1989b, 1989c) generalized their results and coined the term
hysteresis for the zone of inaction. Speciﬁcally, this zone is the area between the upper and
the lower critical asset price. The upper critical price deﬁnes when we should invest, thereby
incurring capital cost, receiving variable revenues, and paying variable costs. The lower
critical price deﬁnes when we should disinvest, similarly incurring (closing) capital costs.
In the zone in between, if we have not invested, we remain so; likewise, if we have invested,
we remain invested. Thus, crossing either the upper or the lower boundary determines an
action (to invest or to disinvest), that depends on the previous state. This path dependency
makes the valuation of such investment options difﬁcult. Under the assumption of inﬁnitely
lived opportunities we arrive at the solution of a system of four highly nonlinear equations.
Brennan and Schwartz (1985) valued natural resource investments and demonstrated that
the classic Net Present Value (NPV) rule fails under uncertainty and irreversibility-inducing
sunk costs. Dixit (1989a) used the model to show the hysteresis effects in a simpliﬁed two-
sector economy with costly capital mobility, and also demonstrated that the hysteresis band
can arise even under certainty. Uncertainty widens this band. Dixit (1989b) used the model
Please address correspondence to: Spiros H. Martzoukos, University of Cyprus, Department of Public and Business
Administration, 75 Kallipoleos Str., P.O. Box 20537, CY 1678 Nicosia–Cyprus.