Investment opportunity strategy in a double-mean-reverting 4/2 stochastic volatility environment

Abstract

The investment-timing problem and the valuation of the right to take certain business initiatives in a given project (called a “real option”) have been considered by many authors under the assumption that volatility of the present value of the expected future net cash flows is stochastic. In this paper, we re-tackle these problems by assuming that the present value of the expected future net cash flows follows the double-mean-reverting 4/2 stochastic volatility model, proposed recently by Cao et al. (2023). Applying an asymptotic analysis approach outlined by Fouque et al. (2011), we obtain two approximation formulas for the value of the real option and the investment threshold, respectively. We conduct numerical experiments on sensitivity analysis of the formulas with respect to the model parameters (“Heston”- and “3/2”-factors) and the associated variables. Furthermore, we also conduct the least square Monte Carlo (LSM) simulation proposed by Longstaff and Schwartz (2001), and compare the real option values from our approximation formula with those from the LSM simulation. Our analysis shows that the relative errors are less than 0.3% in most of our cases, which justifies the appropriateness of our asymptotic approach for the model.