Compare the Black-Scholes Model, Monte Carlo Model, One Step Binomial Tree Model through the European options of Apple

In this article, there are three Models, including Black-Scholes Model, Monte Carlo Model and the One-Step Model for Binomial Tree used to estimate the option premium of Apple, finding the most fitted model for estimating the European call and put options. Using the historical data of Apple in the recent year, the data of three models are found in Yahoo Finance. Simulating the possible outcomes in the future for 1000 steps and calculating the integral for the partial differential equation, spreadsheet is used for calculating the European call and put option premium by using the three models. Comparing the outcomes of three models, Black-Scholes Model provide a more accurate estimations on the European Options compared with the other two. The result indicates the pros and cons of three models, explaining specifically for the Monte Carlo Model, Black-Scholes Model, and One Step Binomial Model in both perspective of finance and mathematics.