Using an Attention-Based Permutation-Invariant VAE to Model Volatility Surfaces

Sammanfattning

This thesis investigates whether a variational autoencoder (VAE) can be trained directly on raw, ir- regularly sampled option quotes rather than on pre-interpolated volatility surfaces. A Raw Set VAE is proposed, combining a Set Transformer encoder with a pointwise decoder to process unordered, variable-length sets of SPX option contracts without requiring prior grid construction. To isolate the contribution of the attention-based encoder architecture, two grid-based models are implemented and compared against each other on fixed interpolated surfaces: an MLP-VAE replicating prior work and a Grid Set VAE using the Set Transformer encoder. All models are evaluated on their ability to reconstruct full volatility surfaces from a small number of observed contracts. When evaluated head- to-head on identical raw market data, the Raw Set VAE outperforms the MLP-VAE as the number of observed contracts increases, achieving a relative MAE improvement of approximately 10% at 40 observed points. The two grid-based models perform nearly identically across all settings, suggesting that attention-based aggregation provides limited benefit when the input structure is fixed and regular, and that permutation invariance is simply not a relevant property for structured grid data. Arbitrage compliance is achieved through soft penalty regularization, whereby the constrained model produces e!ectively arbitrage-free surfaces across the full validation period. Latent space analysis reveals that the model organizes market information in a structured and interpretable manner, with the dominant latent dimensions capturing volatility level and term structure. The results demonstrate that it is possible to train and deploy a generative model for implied volatility surfaces without constructing pre-interpolated inputs, eliminating a significant preprocessing dependency