Getting Real with Real Options: A Utility–Based Approach for Finite–Time Investment in Incomplete Markets
提出一种基于效用的方法，为不完全市场中有限期投资机会估值，发现即使项目风险无法对冲，时间灵活性本身仍能带来期权价值，但该价值随风险厌恶和低相关性而快速消失。
Abstract: We apply a utility–based method to obtain the value of a finite–time investment opportunity when the underlying real asset is not perfectly correlated to a traded financial asset. Using the comparison principle for the associated variational inequality, we establish several qualitative properties of the optimal investment boundary, in particular its dependence on correlation and risk aversion. We then use a discrete–time algorithm to calculate the indifference value for this type of real option and present numerical examples for the corresponding investment thresholds. We verify that even in the zero correlation case, whereby none of the risk in the project can be hedged in a financial market, the paradigm of real options can still be applied to value an investment decision, since the opportunity to invest still carries an option value above its net present value. In other words, it is time flexibility itself, more than the possibility of replication, that is the source of the extra value of an investment opportunity. This value, however, quickly erodes at higher levels of risk aversion, and even more so when the project is weakly correlated to financial markets.