翻译 我们创建了不同的期权定价函数, 有基于BS模型和monte carlo模型的, 同时通过consistency checks. 为了进一步验证, 我们使用mone carlo模拟得出来的价格与BS模型得出的价格进行比较. 此外, 为了提高蒙特卡洛的效率,我们还利用stepping methods来创建单个路径.

We have created different option pricing functions based on both the Black-Scholes model and Monte Carlo model, while conducting consistency checks. To further validate our results, we compared the prices obtained from Monte Carlo simulations with those obtained from the Black-Scholes model. Additionally, in order to improve the efficiency of Monte Carlo simulations, we utilized stepping methods to generate individual paths.