用路径签名提升非马尔可夫波动率模型下的期权对冲效果
Hedging with memory: shallow and deep learning with signatures
- 用路径签名作特征，替代LSTM，训练耗能低得多
- 签名模型对冲误差更小，跨不同收益和波动场景更稳定
- 适合量化金融中需要高效对冲的从业者
我们研究在非马尔可夫随机波动率模型下，利用路径签名进行奇异期权对冲的机器学习方法。在深度学习设置中，将签名作为前馈神经网络的输入特征，结果显示其性能普遍优于LSTM，且训练计算量低几个数量级。在浅层学习设置中，比较两种回归方法：第一种直接从价格过程的期望签名学习对冲策略；第二种通过签名波动率模型拟合波动率动态，该模型基于波动率期望签名进行校准。在已校准的签名波动率模型中求解对冲问题，得到的结果在不同收益结构和波动率动态下均更精确且更稳定。
原文摘要 · Abstract (English)
We investigate the use of path signatures in a machine learning context for hedging exotic derivatives under non-Markovian stochastic volatility models. In a deep learning setting, we use signatures as features in feedforward neural networks and show that they outperform LSTMs in most cases, with orders of magnitude less training compute. In a shallow learning setting, we compare two regression approaches: the first directly learns the hedging strategy from the expected signature of the price process; the second models the dynamics of volatility using a signature volatility model, calibrated on the expected signature of the volatility. Solving the hedging problem in the calibrated signature volatility model yields more accurate and stable results across different payoffs and volatility dynamics.
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