Economic hysteresis effects and hitting time densities for CIR diffusions

Using the so-called mean-reverting square-root process of Cox et al. (1985b) we generalize the work of Dias and Shackleton (2005) by introducing the mean reversion feature into the economic hysteresis analysis under stochastic interest rates and show that such issue highlights a tendency for a widening effect on the range of inaction, though both thresholds have risen when compared with the no mean-reverting case. In addition, using the work of Linetsky (2004) we compute the hitting time densities in order to have an idea of how long does it take for a current interest rate to revert and hit the investment thresholds that would induce idle firms to invest.

Introduction:
Decisions made in an uncertain economic environment where it is costly to reverse in-vestment decisions will lead to an intermediate range of the state variable, known as the hysteretic band, where inaction is the optimal policy. Several models of entry and exit decisions have shown that the range of inaction can be remarkably large for many economic applications [see, for example, Brennan and Schwartz (1985), Dixit (1989a,b) and Abel and Eberly (1996)]. In such literature it is usually assumed that discount rates remain constant. However, since interest rates are also an important determinant of investment and disinvestment decisions it is important to analyze the economic hysteresis effect under stochastic interest rates.

Author: Dias Jose Carlos and Shackleton Mark

Source: Lancaster University Management School

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