Comparing the Payoff Differences Between the Barrier and European Options Based on the Black-sholes Model

Abstract

As more people want to invest in the options market, there are basic traditional options in the futures market, such as European options. Still, there are also some exotic options like the barrier option that is conditional on the stock price before expiration and is called a barrier (1). This paper analyzes the payoffs of European and barrier options based on the Black Scholes model by calculating them and comparing them. This study analysis of the results shows that the price of the barrier option is lower than that of the European option. The barrier option is essentially close to the European option under conditions. This article helps newcomers to the options and those unfamiliar with exotic options to understand the differences between barrier options and European options in terms of payoff.