Physics-informed convolutional transformer for predicting volatility surface

References

• Andersen, L. and Brotherton-Ratcliffe, R., The equity option volatility smile: An implicit finite difference approach. J. Comput. Finance, 1998, 1, 5–37.
   Google Scholar
• Anwar, N. and Sazzad Andallah, L., A study on numerical solution of Black–Scholes model. J. Math. Finance, 2018, 8, 372–381.
   Google Scholar
• Avellaneda, M., Friedman, C., Holmes, R. and Samperi, D., Calibrating volatility surfaces via relative-entropy minimization. Appl. Math. Finance, 1997, 4(1), 37–64.
   Google Scholar
• Azad, R., Asadi-Aghbolaghi, M., Fathy, M. and Escalera, S., Bi-directional ConvLSTM U-Net with densley connected convolutions. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, Oct 2019.
   Google Scholar
• Berestycki, H., Busca, J. and Florent, I., Asymptotics and calibration of local volatility models. Quant. Finance, 2002, 2(1), 61–69.
   Google Scholar
• Black, F.S. and Scholes, M.S., The valuation of option contracts and a test of market efficiency. J. Finance, 1972, 27(2), 399–417.
   Web of Science ®Google Scholar
• Black, F.S. and Scholes, M.S., The pricing of options and corporate liabilities. J. Polit. Econ., 1973, 81(3), 637–654.
   Web of Science ®Google Scholar
• Bondarenko, M. and Bondarenko, V., Calibration of Dupire local volatility model using genetic algorithm of optimization. Neuro-Fuzzy Model. Tech. Econ., 2018, 7(1), 1–20.
   Google Scholar
• Cen, Z. and Le, A., A robust and accurate finite difference method for a generalized Black–Scholes equation. J. Comput. Appl. Math., 2011, 235(13), 3728–3733.
   Web of Science ®Google Scholar
• Cont, R. and Da Fonseca, J., Dynamics of implied volatility surfaces. Quant. Finance, 2002, 2(1), 45–60.
   Google Scholar
• de Boor, C., A practical guide to splines. In Applied Mathematical Sciences, 1978.
   Google Scholar
• Derman, E. and Kani, I., Riding on a smile. Risk, 1994, 7(2), 32–39.
   Google Scholar
• Dupire, B., Pricing with a smile. Risk, 1994, 7(1), 18–20.
   Google Scholar
• Garman, M.B. and Kohlhagen, S.W., Foreign currency option values. J. Int. Money Finance, 1983, 2(3), 231–237.
   Web of Science ®Google Scholar
• Granger, C.W.J. and Poon, S.-H., Forecasting volatility in financial markets: A review. J. Econ. Lit., 2003, 41(2), 478–539.
   Web of Science ®Google Scholar
• Guo, I., Loeper, G. and Wang, S., Local volatility calibration by optimal transport. arXiv preprint arXiv:1709.08075v4, 2018.
   Google Scholar
• Heston, S.L., A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud., 1993, 6(2), 327–343.
   Web of Science ®Google Scholar
• Huang, W., Hu, W., Yeung, Y.T. and Chen, X., Conv-transformer transducer: Low latency, low frame rate, streamable end-to-end speech recognition. In Proc. Interspeech 2020, pp. 5001–5005, 2020.
   Google Scholar
• Hull, J.C., Options, Futures, and Other Derivatives, 2003 (Prentice Hall).
   Google Scholar
• Hull, J.C. and White, A., The pricing of options on assets with stochastic volatilities. J. Finance, 1987, 42, 281–300.
   Web of Science ®Google Scholar
• Jagtap, A.D. and Karniadakis, G.E., Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations. Commun. Comput. Phys., 2020, 28(5), 2002–2041.
   Web of Science ®Google Scholar
• Jiang, G.J. and Tian, Y.S., The model-free implied volatility and its information content. Rev. Financ. Stud., 2005, 18(4), 1305–1342.
   Web of Science ®Google Scholar
• Jin, Y., Wang, J., Kim, S., Heo, Y., Yoo, C., Kim, Y., Kim, J. and Jeong, D., Reconstruction of the time-dependent volatility function using the Black–Scholes model. Discrete Dyn. Nat. Soc., 2018, 2018, 1–9.
   Web of Science ®Google Scholar
• Kanniainen, J., Lin, B. and Yang, H., Estimating and using GARCH models with VIX data for option valuation. J. Bank. Finance, 2014, 43, 200–211.
   Web of Science ®Google Scholar
• Karniadakis, G.E., Kevrekidis, I.G., Lu, L., Perdikaris, P., Wang, S. and Yang, L., Physics-informed machine learning. Nat. Rev. Phys., 2021, 3(6), 422–440.
   Google Scholar
• Kissas, G., Yang, Y., Hwuang, E., Witschey, W.R., Detre, J.A. and Perdikaris, P., Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks. Comput. Methods Appl. Mech. Eng., 2020, 358, 112623.
   Web of Science ®Google Scholar
• Lagaris, I.E., Likas, A. and Fotiadis, D.I., Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans. Neural Netw., 1998, 9(5), 987–1000.
   PubMedGoogle Scholar
• Li, W., Bazant, M.Z. and Zhu, J., A physics-guided neural network framework for elastic plates: Comparison of governing equations-based and energy-based approaches. Comput. Methods Appl. Mech. Eng., 2021a, 383, 113933.
   Web of Science ®Google Scholar
• Li, B., Tang, B., Deng, L. and Zhao, M., Self-attention ConvLSTM and its application in RUL prediction of rolling bearings. IEEE Trans. Instrum. Meas., 2021b, 70, 1–11.
   PubMed Web of Science ®Google Scholar
• Lin, Z., Li, M., Zheng, Z., Cheng, Y. and Yuan, C., Self-attention ConvLSTM for spatiotemporal prediction. Proc. AAAI Conf. Artif. Intell., 2020, 34(7), 11531–11538.
   Google Scholar
• Liu, Z., Luo, S., Li, W., Lu, J., Wu, Y., Sun, S., Li, C. and Yang, L., Convtransformer: A convolutional transformer network for video frame synthesis. arXiv preprint arXiv:2011.10185v2, 2021.
   Google Scholar
• Malliaris, M. and Salchenberger, L., Using neural networks to forecast the S&P 100 implied volatility. Neurocomputing, 1996, 10, 183–195.
   Web of Science ®Google Scholar
• Mathews, A., Francisquez, M., Hughes, J.W., Hatch, D.R., Zhu, B. and Rogers, B.N., Uncovering turbulent plasma dynamics via deep learning from partial observations. Phys. Rev. E, Aug 2021, 104, 025205.
   PubMed Web of Science ®Google Scholar
• Merton, R.C., Theory of rational option pricing. Bell J. Econ. Manag. Sci., 1973, 4(1), 141–183.
   Google Scholar
• Mixon, S., Factors explaining movements in the implied volatility surface. J. Futures Mark., 2002, 22(10), 915–937.
   Web of Science ®Google Scholar
• Moishin, M., Deo, R.C., Prasad, R., Raj, N. and Abdulla, S., Designing deep-based learning flood forecast model with ConvLSTM hybrid algorithm. IEEE Access, 2021, 9, 50982–50993.
   Google Scholar
• Noh, J., Engle, R.F. and Kane, A., Forecasting volatility and option prices of the S&P 500 index. J. Deriv., 1994, 2, 17–30.
   Google Scholar
• Raissi, M., Perdikaris, P. and Karniadakis, G.E., Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys., 2019, 378, 686–707.
   Web of Science ®Google Scholar
• Raissi, M., Yazdani, A. and Karniadakis, G.E., Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. Science, 2020, 367(6481), 1026–1030.
   PubMed Web of Science ®Google Scholar
• Shi, X., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W.-K. and Woo, W.-C., Convolutional LSTM network: A machine learning approach for precipitation nowcasting. In NIPS 2015, pp. 802–810, 2015.
   Google Scholar
• Shinde, A.S. and Takale, K.C., Study of Black–Scholes model and its applications. Procedia Eng., 2012, 38, 270–279.
   Google Scholar
• Wiecha, P.R., Arbouet, A., Girard, C. and Muskens, O.L., Deep learning in nano-photonics: inverse design and beyond. Photon. Res., May 2021, 9(5), B182–B200.
   Google Scholar