Deep Smoothing of the Implied Volatility Surface

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.