Predicting option prices: From the Black-Scholes model to machine learning methods

Abstract

In the ever-changing landscape of financial markets, accurate option pricing remains critical for investors, traders and financial institutions. Traditionally, the Black-Scholes (B&S) model has been the cornerstone for option pricing, providing a solid framework based on mathematical and physical principles. Nevertheless, the B&S model has some limitations, such as the restriction to European options, the absence of dividends, constant volatility, etc. Studies and academic literature on the application of machine learning models in the financial sector are rapidly increasing. The main objective of this paper is to provide a comprehensive comparative analysis between the traditional B&S model and the most commonly used machine learning algorithms such as Artificial Neural Networks (ANNs). The rationale is twofold. First, to examine the assumptions of the B&S model, such as constant volatility and a perfectly efficient market, in light of the complexity of the real world, even though it is recognized that the model has been known as a pillar for decades. Secondly, to emphasize that the proliferation of big data and advances in computing power have fuelled the rise of machine learning techniques in finance. These algorithms have remarkable capabilities in discovering non-linear patterns and extracting information from large data sets, providing a compelling alternative to traditional quantitative methods. Machine learning offers a new way to capture and model such complex financial dynamics, which can lead to more accurate pricing models. By comparing the B&S model and some machine learning approaches, this paper aims to shed light on their respective strengths, weaknesses and applicability in the context of options pricing using real data. Through rigorous empirical analyses and performance metrics, our results demonstrate the importance of using machine learning techniques that can outperform or complement the established B&S model in predicting option prices by achieving higher prediction accuracy.