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.

实物期权是一种投资选择，可以支持决策者做出更好的战略管理决策，同时减少投资的不确定性。本研究提出了一种新模型，帮助投资者灵活应对不确定的投资环境。首先，我们采用混合随机和局部波动率模型来有效地描述决策案例中外部环境对项目价值的不确定性影响。其次，我们将投资成本（或沉没成本）设置为几何布朗运动（GBM），以说明在复杂的决策环境下放弃投资替代方案所产生的机会成本。我们推导出实物期权价值的偏微分方程（PDE），然后使用渐近分析来获得解析解。此外，我们还分析了近似公式与蒙特卡罗模拟获得的解的价格准确性。最后，我们研究与随机波动性相关的各种参数对实物期权的数值影响，以观察其经济影响。