Optimal Investment with Two-Factor Uncertainty

This paper presents a real options model to value the option to invest in a new project, whose value is contingent on two multiplicative stochastic factors behaving accordingly to correlated geometric Brownian motions. A general sensitivity analysis is conducted highlighting the importance of the variance and correlation between the two variables. A higher correlation is shown to increase always the values of the trigger, the active project and the option. The impact of uncertainty is more complex and depends on the assumption about which variables adjust and the correlation between the variables and the market as a whole. Uncertainty can, for some cases, decrease the trigger and the option values, namely when the correlation with the market is negative and the growth rates are fixed, and when the two stochastic variables are highly negatively correlated