# Incorporating prior financial domain knowledge into neural networks for implied volatility surface prediction

## TL;DR

This paper introduces a neural network model for implied volatility surface prediction that integrates financial domain knowledge through a novel activation function and loss function constraints, improving accuracy and theoretical consistency.

## Contribution

It presents a new neural network architecture that incorporates prior financial knowledge, such as volatility smile and arbitrage constraints, into both the model design and training process.

## Key findings

- Outperforms benchmark models on S&P 500 data over 20 years.
- Model aligns with financial theories and conditions.
- Demonstrates the effectiveness of domain knowledge integration.

## 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.