Volatility Surface Reconstruction using Deep Learning under No-Arbitrage Constraints
For quantitative finance practitioners, this provides a data-driven alternative to parametric SVI models that better handles sparse data while enforcing financial constraints.
Deep learning models, especially Transformers and U-Nets, reconstruct implied volatility surfaces from sparse option quotes with high accuracy, and soft no-arbitrage penalties reduce violations by over 50% with only a 5-10% increase in reconstruction error.
We study the reconstruction of implied volatility surfaces from sparse and noisy option quotes using deep learning models under no-arbitrage constraints. We compare multiple neural architectures, including multilayer perceptrons, convolutional networks, U-Nets, variational autoencoders, and Transformer-based models against classical SVI parameterizations on option market data. Results show that Transformer and U-Net architectures achieve strong reconstruction accuracy, particularly under sparse observation regimes, while soft arbitrage penalties significantly reduce arbitrage violations with moderate impact on reconstruction error. We further analyze the trade-off between accuracy and arbitrage consistency across architectures and regularization strengths.