  Predicting volatility is important for asset predicting, option pricing and
hedging strategies because it cannot be directly observed in the financial
market. The Black-Scholes option pricing model is one of the most widely used
models by market participants. Notwithstanding, the Black-Scholes model is
based on heavily criticized theoretical premises, one of which is the constant
volatility assumption. The dynamics of the volatility surface is difficult to
estimate. In this paper, we establish a novel architecture based on
physics-informed neural networks and convolutional transformers. The
performance of the new architecture is directly compared to other well-known
deep-learning architectures, such as standard physics-informed neural networks,
convolutional long-short term memory (ConvLSTM), and self-attention ConvLSTM.
Numerical evidence indicates that the proposed physics-informed convolutional
transformer network achieves a superior performance than other methods.
