用混合模型精准补全加密货币波动率曲面，效果远超传统方法。
Beyond the Smile: A Hybrid Convolutional VAE for Crypto Volatility Surfaces
- 结合卷积VAE与二次微笑拟合，通过固定规则路由生成预测结果。
- 在50%数据缺失下误差仅0.83，比纯拟合降低八倍，且无额外开销。
- 可识别市场异常事件，适合量化交易与风控系统使用。
我们提出一种用于加密货币隐含波动率曲面的卷积变分自编码器，并构建了一个可部署的混合预测器，该预测器将该模型与基于二次微笑重拟合的方法结合，通过确定性的按期限路由规则实现融合。模型在2023年5月至10月期间6,034个完整填充的Binance期权曲面上训练，参数化于统一的$6 \times 7$期限-德尔塔网格上，对两个市场（BTC和ETH）在10%-50%掩码率下的隐藏单元曲面补全均方根误差（RMSE）为0.94-1.56个波动点。混合预测器在50%掩码率下误差为0.83波动点，相比单独的微笑重拟合（7.00）降低八倍，且无需额外推理成本。在模拟整条期限数据缺失的结构性孔洞情形下，微笑重拟合误差达9.6-13.1波动点，而学习模型仍保持在1.5-1.9，表明此时生成模型是唯一可行方案。联合训练BTC与ETH使两市场在分布内表现提升9%-27%，表明二者在观测期内具有显著共享的波动率曲面流形。混合模型在标价点处满足日历与蝴蝶套利无套利性，而参数化微笑重拟合在高掩码率下无法满足。模型单快照重建误差自动标记了10月下旬ETF预期上涨及2023年8月17日闪崩为异常高误差时段，无需监督。所有训练与评估基础设施已开源，支持可复现研究。
原文摘要 · Abstract (English)
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.
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