Empirical comparison of S&P 500 index options: Black-Scholes-Merton model and Heston model

• Main Author: Marques, Duarte Miguel da Cunha Domingues Amador
• Publication Date: 2023
• Format: Master thesis
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/10071/30851
• topic: Black-Scholes-Merton model; Heston model; Stochastic volatility; Modelo Black-Scholes-Merton; Modelo Heston; Volatilidade estocástica

Option pricing has been a fundamental problem in financial engineering for several decades, and it has a wide range of applications in various fields, including investments, risk management, and portfolio optimization. The Black-Scholes-Merton model has been the cornerstone of option pricing theory since its introduction in 1973. However, empirical studies have shown that the model has some limitations, including assuming constant volatility and ignoring stochastic volatility, which leads to a mismatch between model predictions and actual market prices. In contrast, the Heston model, introduced in 1993, is a more advanced option pricing model that incorporates stochastic volatility, which makes it more realistic and accurate. The Black-Scholes-Merton model and the Heston model are two of the most widely used models in quantitative finance for pricing financial derivatives. Both models make use of stochastic calculus to model the dynamics of asset prices, but they differ in the assumptions they make about the underlying asset. The purpose of this master thesis is to compare and contrast the Black-Scholes-Merton model and the Heston model, with a focus on their strengths and weaknesses in different market environments. The thesis will begin with a brief overview of the two models, followed by a discussion of their key assumptions and parameters. The thesis will then present a comprehensive analysis of the performance of the two models, using S&P500 options real-world financial data and a variety of evaluation metrics.