用深度学习重建波动率曲面，确保无套利且精度高。
Volatility Surface Reconstruction using Deep Learning under No-Arbitrage Constraints
- 采用Transformer和U-Net模型，结合无套利约束进行曲面重建。
- 在数据稀疏情况下，模型误差低于传统方法，套利违规减少70%以上。
- 适合金融工程、量化交易人员用于高精度波动率建模。
本文研究在无套利约束下，利用深度学习从稀疏且含噪的期权报价中重建隐含波动率曲面。对比了多层感知机、卷积网络、U-Net、变分自编码器及基于Transformer的模型与经典SVI参数化方法在真实期权市场数据上的表现。结果表明，Transformer与U-Net架构在数据稀疏条件下表现出色，重建精度显著优于传统方法；引入软套利惩罚后，套利违规率大幅降低，对重建误差影响较小。进一步分析了不同模型与正则化强度下的精度与无套利一致性权衡。
原文摘要 · Abstract (English)
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.
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