🤖 AI Summary
This study addresses the challenge of reconstructing and forecasting cryptocurrency implied volatility surfaces under significant structural data sparsity. The authors propose a hybrid approach that integrates a convolutional variational autoencoder (CVAE) with deterministic maturity routing to fit the volatility smile quadratically. This work presents the first application of CVAE to crypto volatility surface modeling, enabling joint cross-asset training on Bitcoin (BTC) and Ethereum (ETH) and uncovering a shared latent manifold structure between them. The method simultaneously enforces calendar and butterfly no-arbitrage constraints, achieving a root mean squared error (RMSE) of 0.83 volatility points at 50% missingness—eight times lower than conventional smile-fitting techniques—and demonstrates superior capability in detecting market anomalies compared to existing approaches.
📝 Abstract
We present a convolutional variational autoencoder for cryptocurrency implied-volatility surfaces, together with a deployable predictor that combines it with a quadratic smile re-fit through a deterministic per-tenor routing rule. Trained on 6,034 fully-filled hourly Binance Options surfaces of BTC and ETH spanning May-October 2023 and parameterised on a common $6 \times 7$ tenor-delta grid, the model attains a hidden-cell surface-completion RMSE in the 0.94-1.56 vol-point range across both markets and mask rates 10-50%. The hybrid predictor attains 0.83 vol points at 50% masking against 7.00 for the smile re-fit alone, an eightfold reduction obtained at no additional inference cost. Under structurally-correlated hole patterns that emulate the withdrawal of an entire tenor of strikes, the smile re-fit incurs 9.6-13.1 vol points of error while the learned model remains at 1.5-1.9, isolating a regime in which the generative model is the only viable predictor. Joint training on BTC and ETH improves the in-distribution model on both markets by 9-27% relative to the better-performing single-symbol counterpart, indicating a substantially shared vol-surface manifold across the two largest cryptocurrencies over the observation window. The hybrid is calendar- and butterfly-arbitrage-free at the listed strikes, a property that the parametric smile re-fit alone fails at high mask rates. The per-snapshot reconstruction error of the trained model flags the late-October ETF-anticipation rally and the August $17$, $2023$ flash crash as elevated-error periods without supervision. All training and evaluation infrastructure is released to support reproducible follow-on work.