Options Pricing Comparison between the Black-Scholes Model and the Binomial Tree Model: A Case Study of American Equity Option and European-style Index Option

Abstract

In recent years, quantitative researchers used a wide range of models to price options, from the Black-Scholes model to more complex models such as the Heston model. This paper aims to analyze the effectiveness of the Black-Scholes model and the Binomial Tree model by using them to price Berkshire Hathaway’s equity options and European-style S&P 100 index options. The method used in this paper is gathering the market data of the options first. Second, using the data gathered to price the options by applying the Black-Scholes and Binomial Tree models. Third, comparing the derived theoretical price with the market price by getting the Sum of Square Errors. Lastly, determining the best model for each type of option. Through this research, the author found that comparing the two models, the Binomial Tree model derives a smaller Sum of Square Errors when pricing European-style index options, and the Black-Scholes model derives a smaller Sum of Square Errors when pricing American equity options. Thus, the Binomial Tree model is a better model to price European-style index options, and the Black-Scholes model is more effective when pricing American equity options.