The comparison between different option pricing models: evidence from Black-Scholes model and Leland model

Abstract

The Black-Scholes (B-S) and Leland models play an important role in option pricing. This paper investigates the differences between the Black-Scholes model and the Leland model from aspects of option pricing in real markets with or without transaction costs. Specifically, the results of the B-S models and Leland model performance differently when transaction costs are introduced. The paper demonstrates the differences between the two models by selecting the relevant prices of four stocks for the last ten days and calculating their theoretical prices based on the relevant algorithms of the two models. According to the analysis, every change on conditions has the potential to affect the pricing of options in the market. Based on these results, we have focused on the differences in option pricing after the implementation of transaction costs, though some realistic factors that may affect the results have been ignored in the calculation process for both models. Overall, the greater the transaction costs, the larger the deviation from the analytical results of the two models. These results shed light on option pricing in a real market.