Hysteresis due to irreversible exit: Addressing the option to mothball

This paper analyses the following hitherto understudied feature in real switching options: a firm has a mothballing option and an option to permanently abandon. If the firm finds itself in an operating mode with a price just above the abandonment threshold, it is unclear whether to exercise the abandonment option or to exercise the mothballing option. If the price goes down, the firm may exit, but, surprisingly, if it goes up, it may mothball. We find that two different strategies could be optimal: one where mothballing is not a viable option and one where mothballing does occur. In the latter case a hysteresis region arises in which the firm produces at a loss, while a further price decrease induces exit and a sufficient price increase results in the firm entering the mothballing stage. Mothballing being optimal requires sufficiently large values of the price trend and the uncertainty parameter.