The Application and Challenges of Monte Carlo Simulation in Financial Derivatives Pricing

The Monte Carlo simulation is a powerful numerical method based on random sampling. Renowned for its flexibility in handling high-dimensional problems, it serves as a cornerstone of modern finance. However, it faces a fundamental challengeslow convergence and high computational cost limit its application in pricing financial derivatives. This paper explores the application of Monte Carlo simulation in option pricing, focusing on its benchmark role for European options and how the LSM algorithm addresses backward pricing in American options. Numerical experiments were conducted under the geometric Brownian motion model. Monte Carlo priced European options, while LSM priced American options. Results show Monte Carlo effectively prices European options, with error convergence matching theory (1/N). For American options, LSM performs excellently, providing accurate estimates. However, its accuracy and stability depend heavily on the choice of basis functions and number of paths. Moreover, the computational complexity is higher than European pricing methods. It increases cost and amplifies pre-existing limitations. In summary, this study highlights the flexibility of Monte Carlo but also the persistence of its challenges in sophisticated applications like LSM. The findings offer insights regarding parameter selection and contribute to understanding trade-offs in accuracy, stability, efficiency and cost.