Barrier Options Pricing: The Black-Scholes Model vs. The Merton Jump Model

Abstract

This dissertation critically investigates barrier options pricing, contrasting the traditional Black- Scholes Model (BSM) with the Merton Jump Model. Recognizing the limitations of the BSM, particularly its inability to account for sudden stock price ’jumps’, the studt explores the Merton Jump Model as a more realistic reflection of market dynamics. Employing the Monte Carlo simulation and the Euler-Maruyama method, the dissertation presents empirical results that highlight the advantages and potential superiority of the Merton model over the BSM in certain market conditions. This comparative analysis aims to bridge theoretical concepts with their practical implications in barrier options pricing.