Investment timing and implied option value for risk-aversion entrepreneurs under macroeconomic risk

We explore how risk-aversion entrepreneurs make firm's investment decision with macroeconomic risk which alternates via a Markov chain. In this paper, we analytically derive the implied option values and investment timings during economic boom and recession. We find that in contrast with the case with no macroeconomic risk, the macroeconomic risk leads to both underinvestment and overinvestment, and has both positive effect and negative effect on the implied option values, which depend on the risk aversion of entrepreneur and the volatility of the project's cash flows. This paper shows that the implied option value in boom is higher than that in recession when the volatility in recession is enough lower, however, the result is opposite when the volatility in recession is enough higher.