Solving the Black-Scholes partial differential equation using physically - informed neural networks
Resolución de la ecuación diferencial parcial de Black-Scholes mediante redes neuronales físicamente informadas
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Abstract
Commemorative article for the 50th anniversary of the Black-Scholes model, presenting the derivation of the partial differential equation for pricing in the context of a continuous-time market model. The use of a physically informed neural network (PINN) is proposed as a resolution method, as a novel technique in the field of scientific machine learning, which allows solving these types of equations without the need for a large amount of training data. The article includes the implementation of the method and the valuation results for the case of European call options.
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Bellman, R. (1966). Dynamic programming. Science, 153(3731), 34-37. https://doi.org/10.1126/science.153.3731.34
Black, F., y Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654. https://doi.org/10.1086/260062
Lagaris, I. E., Likas, A., y Fotiadis, D. I. (1998). Artificial neural networks for solving ordinary and partial differential equations. IEEE Transactions on Neural Networks, 9(5), 987-1000. https://doi.org/10.1109/72.712178
Lagaris, I. E., Likas, A. C., y Papageorgiou, D. G. (2000). Neural-network methods for boundary value problems with irregular boundaries. IEEE Transactions on Neural Networks, 11(5), 1041-1049. https://doi.org/110.1109/72.870037
Lee, H., y Kang, I. S. (1990). Neural algorithm for solving differential equations. Journal of Computational Physics, 91(1), 110-131. https://doi.org/10.1016/0021-9991(90)90007-N
Merton, R. C. (1973). Theory of rational option pricing. The Bell Journal of Economics and Management Science, 141-183.
Raissi, M., Perdikaris, P., y Karniadakis, G. E. (2017a). Physics informed deep learning (part i): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv:1711.10561.
Raissi, M., Perdikaris, P., y Karniadakis, G. E. (2017b). Physics informed deep learning (part ii): Data-driven solutions of nonlinear partial differential equations. arXiv preprint arXiv:1711.10566.
Raissi, M., Perdikaris, P., y Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707. https://doi.org/10.1016/j.jcp.2018.10.045
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