Incorporating Prior Financial Domain Knowledge into Neural Networks for Implied Volatility Surface Prediction

Abstract

In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are embedded into the loss function. This is one of the very first studies which discuss a methodological framework that incorporates prior financial domain knowledge into neural network architecture design and model training. The proposed model outperforms the benchmarked models with the option data on the S&P 500 index over 20 years. More importantly, the domain knowledge is satisfied empirically, showing the model is consistent with the existing financial theories and conditions related to implied volatility surface.

Black-Box Model Risk in Finance

“…Drawing from the review by Ruf and Wang (2020), methods that adjust the architectural design of neural networks include models that incorporate a homogeneity hint by training a neural network in two parts, the first part controls for moneyness, and the other for time-to-maturity (Garcia and Gençay, 1998). Other methods restrict the shape of outputs (Dugas et al, 2001) or enforce noarbitrage conditions such as the convexity of a neural network pricing function and monotonicity (Zheng et al, 2019).…”