Evaluation of GBM model performance with barrier options, Asian options and European options based on Tesla

Geometric Brownian motion is a kind of financial model which is used in simulating stock prices with an assumption of a constant volatility. In order to evaluate the performance of the model, we price and investigate the differences between barrier options (knock-in and knock-out), Asian options, and European options based on the Tesla stock-taking from NASDAQ100. We carry out Monte-Carlo simulations 1000 times and price the options correspondingly. According to the analysis, the knock-in option is better for high volatility underlying assets like Tesla stock. These results shed light on a better understanding of option pricing with GBM model and point out its shortcomings in reality.