International Journal of Science, Engineering and TechnologyAuthors: Tawanda Laston Makombe, Walter Gachira, Obert Chahele, Edington Shumbashava
Abstract: Accurately modelling implied volatility surfaces is critical for derivative pricing, risk management, and informed trading decisions. Traditional parametric models such as Black-Scholes and SABR often fall short in capturing the complex, nonlinear behavior of market-implied volatilities, especially under stressed conditions. This research introduces a hybrid modelling framework that integrates B-Spline interpolation with Physics-Informed Deep B-Spline Networks (PI-DeepBSNs), combining the flexibility of spline methods with the expressive power of deep learning. The model was developed using options market data, focusing on strike prices and time to maturity. The PI-DeepBSN architecture embeds domain-specific constraints, such as no-arbitrage conditions and smoothness, within a neural network framework trained using PyTorch. The study demonstrates that PI-DeepBSNs outperform traditional B-Spline models in capturing the nuanced structure of the implied volatility surface. Empirical results show that the model achieves a Mean Absolute Error (MAE) of 0.0699 and Root Mean Squared Error (RMSE) of 0.0208. While the model fits well in moderate-volatility regions, it tends to underpredict in high-volatility zones, highlighting the need for more diverse data and further refinement. This research contributes a novel, interpretable, and data-driven approach for modelling implied volatility surfaces. It underscores the value of integrating financial theory with deep learning and opens pathways for real-time forecasting tools in derivative markets. Future enhancements may involve extending the model’s maturity coverage and deploying it as a web-based financial analytics tool.
DOI: http://doi.org/10.5281/zenodo.18324291
