An external barrier option has a random variable which determines whether the option is knock-in or knock-out. In this paper, we deal with the pricing of the external barrier option under a stochastic volatility model incorporated by a fast mean-reverting process. By using a singular perturbation method (asymptotic analysis) on the given partial differential equation for the option price, and applying the double Mellin transform technique and the method of images, we derive the corrected option price, which is an explicit analytical approximated solution for the external barrier option. For numerical experiments, we verify the price accuracy of the external barrier option with a stochastic volatility model by comparing the approximated option price with the option price obtained by Monte Carlo simulation. Finally, we investigate the behavior and sensitivity of option prices to model parameters.

外部障碍期权具有随机变量，该随机变量确定期权是敲入还是敲出。在本文中，我们通过快速均值回复过程并入的随机波动率模型来处理外部障碍期权的定价。通过对给定的期权价格偏微分方程使用奇异摄动法（渐近分析），并应用双重Mellin变换技术和图像方法，得出校正后的期权价格，这是对期权价格的显式解析近似解。外部屏障选项。对于数值实验，我们通过比较近似期权价格和通过蒙特卡洛模拟获得的期权价格，用随机波动率模型验证了外部障碍期权的价格准确性。最后，