Investment under Joint Cost and Interest Rate Uncertainty: A Stochastic Control Approach

The present paper analyses irreversible investment decisions when there is joint uncertainty in the cost of investments and in the stochastic interest rates. A continuous-time real options model is constructed by us where the value of a project is a perpetual cash flow discounted by a stochastic short rate and investment costs track a correlated stochastic process. The problem of optimal stopping as a two-dimensional Hamilton-Jacobi-Bellman variational inequality has its time-varying investment problem formulated in the firm. We define analytical valuation characteristics of the value function such as existence, smooth-pasting and curvature and derive constraints on the shape of the optimal investment frontier. Unlike models that have deterministic discounting, we demonstrate that as project value is negatively associated with interest rates, constrained financial conditions decrease net present value and decrease the optimal investment trigger. Cost-interest-rate correlation changes the level of the investment boundary but leaves its monotonicity the same. It is numerically verified that correlation transforms the region of investment. Monte Carlo simulation also shows that correlation has a dominant influence on the spread of time of investment waiting and not on the average. On the whole, the model gives a single theoretical and quantitative framework of explaining investment delays with stochastic discounting and correlated macro-financial uncertainty and implications on monetary policy transmission and investment dynamics.