The Black-Scholes Model Analysis and Comparison

Abstract

Mathematical or Quantitative model-based trading is evolving and has become more and more popular nowadays. The Black-Scholes model is one of the most widely used models in option pricing. In this article, the researcher wants to find a better option pricing model compared to the Black-Scholes model. In research question 1 and research question3, the researcher compares the binary tree model and the Back- Propagating model which is included in machine learning to the Black-Scholes model with the real world’s call option prices to find whether one of them can win the Black-Scholes model. In research question 2, the researcher analyses the volatility simile caused by the Black-Scholes model in the real world and observes its yield distribution to see its shape features. For these research questions, the researcher uses MATLAB and Python to do the numerical experiments and visualize results in these three questions and do descriptive statistics for them by STATA. Finally, the researcher finds that the performance of the Black-Scholes model and the Binary Tree model are both well in predicting options’ price. However, the BP model only performs well when the price is around zero. Besides, for the research question 2, the result is that the yield distribution of the volatility smile is slim and right-biased. Therefore, the Black-Scholes model can be used in most of the cases in options pricing and the Binary tree model is also a good choice which is simpler than the Black-Scholes model with fewer assumptions. For the BP model, if the user has enough training data for option pricing, it will be a good choice with its excellent learning ability for a short period of predicting. For the volatility smile, the Black-Scholes model’s use is one of the reasons for it. The volatility will perform differently with different options. The user can use some hedging skills to deal with it. For example, using different ways to build a portfolio.