General option exercise rules, with applications to embedded options and monopolistic expansion

This paper provides a general framework for pricing of real options in continuous time for wide classes of payoff streams that are functions of Levy processes. As applications, we calculate the option values of multi-stage investment/disinvestment problems (sequences of embedded options, which we call Russian dolls), and study two models of expansion of a monopoly. In the first model, each time when the stochastic demand reaches the boundary of the inaction region or crosses it, the monopoly increases capital stock but uses the same production technology. We assume that above a certain level, the stochastic demand factor increases slower than in the standard geometric Levy models, and demonstrate that then the investment threshold is lower than in the standard models. Moreover, in the intermediate range between the regimes of the fast and slower growth, the monopoly may find it optimal to simultaneously increase the capital stock and decrease the output price. The second model is driven by two factors: one factor follows a process with upward jumps and describes the dynamics of the frontier technology, the other - demand uncertainty. The impact of these factors on new technology adoption is analyzed. It is shown that depending on the situation and type of uncertainty, the diffusion uncertainty and jump uncertainty can produce opposite effects.