Deep Smoothing of the Implied Volatility Surface
This work addresses the need for accurate and arbitrage-free IVS models in quantitative finance, offering a plug-in correction for practitioners, but it is incremental as it builds on existing methods with neural network enhancements.
The authors tackled the problem of fitting and predicting implied volatility surfaces (IVSs) with neural networks, ensuring arbitrage-free option prices through soft constraints, and showed that their method improves over standard models, especially with sparse or erroneous data, by quantifying uncertainty and benchmarking performance.
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.