Pricing Asian Options Using Numerical Methods: A Comparison of Monte Carlo Simulation and Binomial Tree Model

This paper presents a comprehensive comparative analysis of Monte Carlo simulation and binomial tree models for pricing geometric Asian options. In the process of evaluations, the Tesla (TSLA) stock is the underlying asset for the options, and the modified Black-Scholes model serves as the benchmark for comparisons of pricing accuracy, Greeks calculation. Besides, this research also analyzes the difference between the two methods in terms of computational efficiency. According to the simulations, the binomial tree model shows a higher accuracy compared to the Monte Carlo simulation. For Greeks calculations, both methods illustrate consistency in Delta and Gamma values, and the binomial tree model shows almost perfect Vega precision. At the same time, the Monte Carlo simulation offers computational advantages with near-linear complexity, making it ideal for real-time applications. The binomial tree model, despite exponential complexity growth, remains ideal for high-precision requirements. Therefore, these results offer a guideline for the application of these two methods, in which one can determine the usage based on the tradeoff between accuracy and computational speed.