Optimal Sequential Investment Decision-Making with Jump Risk

Abstract

This paper uses the real-option approach to find the optimal amount and time of investment in a real project. This approach is better than the net present value approach because it captures the uncertainty in the future expected cash flow. The real option has been applied to many industries; for example, oil and gas, telecommunications, and large-scale energy projects. The model introduced in this paper adds two features to the standard real options. The first feature is the two-stage investment. In reality, it is common for the project manager to not invest all budget at once. The second feature is the early termination event. The finding is that such a sudden death event causes the waiting period to be longer for both one-stage and two-stage investments. With low volatility, the lower optimal investment proportion of the total project budget is expected, when the mean arrival rate of the jump downside risk is higher. With medium or higher volatility, the higher optimal proportion is associated with a higher probability of jump risk. When the rate of one-time event is constant, volatility increases the optimal investment amount and increases the waiting time. The project has more value when the investment is divided into two stages rather than one stage. All other things being equal, the waiting time of one-stage is shorter than the waiting time of the first stage but longer than that of the second stage.