Using Neural Networks for Option Pricing and Hedging

Abstract

This thesis scrutinises the efficacy of conventional and sophisticated models for option pricing and hedging within financial markets, advocating for the integration of artificial neural networks to surmount their inherent limitations. Traditional models such as the Black-Scholes assume constant volatility — an assumption often at odds with the fluctuating volatilities observed in real-world markets. To bridge this gap, stochastic models like the Heston model, and the Variance-Gamma model are introduced. Beyond these stochastic frameworks, this study harnesses the capabilities of neural networks to detect and exploit both linear and nonlinear patterns in market data, which conventional models typically overlook. Employing a robust dataset of European call and put options on the S&P 500, this research benchmarks these neural network models against the classic Black-Scholes, Heston, and Variance-Gamma frameworks. The evaluation focuses on their precision in replicating observed market prices, capturing the volatility smile, and adapting to evolving market conditions. We find that the FNN model maintains low pricing errors, especially in put contract pricing, with consistent performance across different subsets of the out-of-sample data, and compelling results in the pricing of long maturity contracts. However, the model struggles with accurately capturing the volatility smile, particularly at extreme strike prices, indicating a need for further refinement to enhance its sensitivity to market dynamics. A Hybrid neural network approach is employed to explore risk management efficacy for the hedging objective. Central to this approach is the optimisation of the delta hedging ratio, 𝛿, essential for managing the risk exposures of option contracts. The model aims to minimise the mean squared hedging error of the hedged portfolio, advocating for a delta-neutral term that mitigates sensitivity to minor fluctuations in the underlying asset, crucial in the efforts of enhancing the relevance and accuracy of risk management. The performance evaluation of our model against traditional benchmarks reveals compelling results, especially for medium to long-term maturities and in-the-money put contracts. These results highlight the model's adeptness at adjusting to underlying market changes. Moreover, the Hybrid model demonstrates robust stability and consistency across varied market conditions, particularly during periods in the out-of-sample data characterised by heightened volatility, outperforming benchmark models in overall hedging efficacy.