Beyond the Smile: A Hybrid Convolutional VAE for Crypto Volatility Surfaces

Problem
The paper addresses the gap in predictive modeling of cryptocurrency implied-volatility surfaces, particularly for Bitcoin (BTC) and Ethereum (ETH). Existing methods, such as parametric smile re-fits, struggle with high masking rates and fail to capture the complex dynamics of volatility surfaces. This work is a preprint and has not undergone peer review, indicating that the findings should be interpreted with caution.

Method
The authors propose a hybrid model that combines a convolutional variational autoencoder (VAE) with a deterministic quadratic smile re-fit. The model is trained on a dataset comprising 6,034 fully-filled hourly volatility surfaces from Binance Options for BTC and ETH, spanning from May to October 2023. The data is parameterized on a $6 \times 7$ tenor-delta grid. The VAE architecture is designed to learn the underlying structure of the volatility surfaces, while the smile re-fit provides a baseline for comparison. The model achieves a hidden-cell surface-completion root mean square error (RMSE) ranging from 0.94 to 1.56 vol points across both cryptocurrencies, with mask rates varying from 10% to 50%. The hybrid predictor demonstrates a significant improvement, achieving an RMSE of 0.83 vol points at 50% masking, compared to 7.00 vol points for the smile re-fit alone, indicating an eightfold reduction in error without additional inference costs.

Results
The hybrid model outperforms the traditional smile re-fit under structurally-correlated hole patterns, where the smile re-fit incurs an error of 9.6-13.1 vol points, while the VAE maintains an error of only 1.5-1.9 vol points. Joint training on BTC and ETH enhances the model’s performance by 9-27% relative to single-symbol models, suggesting a shared volatility surface manifold between the two cryptocurrencies. The model is also shown to be calendar- and butterfly-arbitrage-free at the listed strikes, a significant advantage over the parametric approach at high mask rates. The authors highlight that the model’s reconstruction error effectively flags significant market events, such as the late-October ETF anticipation rally and the August 2023 flash crash, without requiring supervision.

Limitations
The authors acknowledge that the model’s performance may vary with different market conditions and that the training data is limited to a specific time frame. Additionally, the reliance on a deterministic routing rule for the smile re-fit may introduce biases. The paper does not address potential overfitting issues or the generalizability of the model to other cryptocurrencies or market conditions.

Why it matters
This work has significant implications for financial modeling in the cryptocurrency space, providing a more robust framework for predicting volatility surfaces that can enhance trading strategies and risk management. The release of the training and evaluation infrastructure supports reproducibility and encourages further research in this area, as discussed in the context of generative models for financial applications, as published in arXiv.