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.
翻译:我们提出了一个适应和预测隐含的波动表面(IVS)的神经网络(NN)方法。相对于标准的NN应用,金融业从业人员同样使用这类模型来复制市场价格和估价其他金融工具。换句话说,低培训损失与一般化能力一样重要。重要的是,IVS模型需要产生现实的无套利选择价格,这意味着没有组合能够带来没有风险的利润。我们提出了一个方法,通过利用软约束来惩罚损失,来保证没有套利机会。此外,我们的方法可以与标准IVS在定量融资方面的模型结合起来,从而在这类模型复制观察到的市场价格失败时提供基于NNN的校正。这让实践者利用我们的方法作为传统方法的顶端的插座。经验性结果显示,当只有零散或错误的数据时,这种做法特别有用。我们还用很少或没有观察的观察来量化模型预测的不确定性。我们进一步探索NS在较浅的模型以及网络结构的其他特性方面有何更深的改进。我们用标准IVS模型来衡量我们的方法,也就是我们所观察到的复制能力,我们用的方法来衡量。