Uncertain Growth Options and Asset Pricing
thesisposted on 22.07.2021, 19:41 by Brian G HogleBrian G Hogle
We develop a growth option and asset pricing model that incorporates uncertain cash flow volatility by way of a bounded quadratic diffusion. Using different measures of risk uncertainty, we study the combined effects of risk and its associated uncertainty on project values, firm investment, and the resulting returns. Uncertain cash flow volatility is modeled by a Jacobi process, and our main interest is the effect of the max uncertainty arising from the diffusion term. For comparison, we also model the volatility by a CIR process. In regards to the Jacobi process, we consider upper and lower bounds on cash flow volatility as measures of uncertainty. For the max uncertainty and upper bound, we find that higher uncertainty leads to less investment, higher returns, and lower project values. In the case of the lower bound, we find that higher uncertainty leads to more investment, lower returns, and higher project values. Comparatively, using a CIR process in place of the Jacobi process yields differences in returns and growth option values, showing the importance of the diffusion term in the volatility process. Finally, we have reduced the computational complexity of the simulation. This allows the user to generate long time series and run cross sectional regressions with many firms.