The valuation of real options for risky barrier to entry with hybrid stochastic and local volatility and stochastic investment costs

Real options are a type of investment choice that supports decision-makers in making better strategic management decisions while simultaneously reducing uncertainty in investments. This study presents a new model to help investors flexibly handle uncertain investment environments. First, we adopt a hybrid stochastic and local volatility model to efficiently describe the uncertain effects of the external environment on the project value in decision-making cases. Second, we set the investment cost (or sunk cost) as a geometric Brownian motion (GBM) to illustrate the opportunity costs that originating from discarding alternatives to invest in complex decision-making circumstances. We derive partial differential equations (PDEs) for the value of real options, and then use asymptotic analysis to obtain analytical solutions. Additionally, we analyze the price accuracy of the approximate formulas compared with that of the solutions obtained from a Monte Carlo simulation. Finally, we investigate the numerical effects of various parameters related to stochastic volatility on real options to observe their economic implications.