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. In this paper, we present a new model to help investors handle uncertain investment environments flexibly. First, we adopt a hybrid stochastic and local volatility model to efficiently describe the external environment's uncertain effects on 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 arise from giving up 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 to solutions obtained from Monte-Carlo simulation. Finally, we investigate the numerical effects of various parameters related to stochastic volatility on real options to observe their economic implications