Physics-informed convolutional transformer for predicting volatility surface

Abstract

Predicting volatility is important for asset predicting, option pricing and hedging strategies because it cannot be directly observed in the financial market. 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.

Keywords:

• Volatility
• Black–Scholes model
• Physics-informed neural networks
• Convolutional LSTM
• Attention mechanism
• Convolutional transformer

Acknowledgments

The authors thank the anonymous referees for their helpful comments that improved the quality of the manuscript.

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

The work of S. Kim was supported by URP program by Korea Foundation for the Advancement of Science and Creativity. S.-B. Yun has been supported by Samsung Science and Technology Foundation under Project Number SSTF-BA1801-02. H. Bae is supported by the Basic Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education and Technology (NRF-2021R1A2C1093383). The work of Y. Hong was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2021R1A2C1093579) and by the Korea government (MSIT) (RS-2023-00219980).