Pricing European Call Options with Visualization Based on the Binomial Model, Monte-Carlo Simulation, and Classical Black-Scholes Model

Abstract

After the emergence of financial derivatives, pricing has been focused by a considerable number of mathematicians. With stochastic analysis and some classic probability theories, many new pricing formulas appeared in the quantitative finance field. The improvement of pricing methods of different financial securities has essentially made prices more precise and more strict, thus greatly promoting the development of modern financial markets. In this research paper, the author reviewed three significant option pricing models in mathematical finance, which are the binomial model, classical Black-Scholes model, and Monte-Carlo simulation, and applied these three models to give the price of European options. Based on the results of these three models, the author conducted some visualization work and statistical work to compare the differences of the models. Furthermore, in order to determine the most suitable model in this case, the machine learning technique is applied to classify the price data by analyzing the confusion matrices in each model.