arXiv 1906.050652019-06q-fin.PRcs.LGstat.ML

隐含波动率曲面的深度平滑

Deep Smoothing of the Implied Volatility Surface

UBS（瑞银集团）；Swiss Data Science Center（瑞士数据科学中心）；Columbia University（哥伦比亚大学）

Damien Ackerer, Natasa Tagasovska, Thibault Vatter

备注：: forthcoming NeurIPS 2020

摘要：

本文提出了一种神经网络拟合和预测隐含波动率曲面的方法。与标准NN应用程序不同，金融行业从业者同样使用这些模型来复制市场价格并对其他金融工具进行估值。换句话说，低训练损失与泛化能力一样重要。重要的是，IVS模型需要产生现实的无仲裁期权价格，这意味着没有任何投资组合可以带来无风险利润。我们提出了一种方法，保证没有套利机会，惩罚损失使用软约束。此外，我们的方法可以结合标准的IVS模型在量化金融，从而提供了一个基于神经网络的校正时，这些模型无法复制观察到的市场价格。这使得从业者可以将我们的方法作为经典方法之上的插件来使用。实证结果表明，这种方法是特别有用的，当只有稀疏或错误的数据。我们还量化了模型预测的不确定性，在很少或没有观测的地区。我们进一步探讨了较深的NN如何比较浅的NN改进，以及网络架构的其他属性。我们基准我们的方法对标准的IVS模型。通过在训练集和测试集上评估我们的方法，我们强调了它们再现观察价格和预测新价格的能力。

英文摘要：

We present a neural network (NN) approach to fit and predict implied volatility surfaces (IVSs). Atypically to standard NN applications, financial industry practitioners use such models equally to replicate market prices and to value other financial instruments. In other words, low training losses are as important as generalization capabilities. Importantly, IVS models need to generate realistic arbitrage-free option prices, meaning that no portfolio can lead to risk-free profits. We propose an approach guaranteeing the absence of arbitrage opportunities by penalizing the loss using soft constraints. Furthermore, our method can be combined with standard IVS models in quantitative finance, thus providing a NN-based correction when such models fail at replicating observed market prices. This lets practitioners use our approach as a plug-in on top of classical methods. Empirical results show that this approach is particularly useful when only sparse or erroneous data are available. We also quantify the uncertainty of the model predictions in regions with few or no observations. We further explore how deeper NNs improve over shallower ones, as well as other properties of the network architecture. We benchmark our method against standard IVS models. By evaluating our method on both training sets, and testing sets, namely, we highlight both their capacity to reproduce observed prices and predict new ones.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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