Penyelesaian persamaan diferensial parsial Black-Scholes dengan physics-informed neural network = Solving partial differential equation Black-Scholes using physics-informed neural network

Utomo, Jennifer (2024) Penyelesaian persamaan diferensial parsial Black-Scholes dengan physics-informed neural network = Solving partial differential equation Black-Scholes using physics-informed neural network. Bachelor thesis, Universitas Pelita Harapan.

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Abstract

Seiring berkembangnya zaman, pencarian solusi persamaan diferensial parsial (PDP) dengan bantuan komputer semakin dibutuhkan, salah satunya adalah physics-informed neural network (PINN). PINN merupakan teknik pembelajaran mesin yang mengaproksimasi nilai PDP dengan melatih neural network untuk meminimalkan loss function. Pada tugas akhir ini, PINN diimplementasikan untuk menyelesaikan PDP Black-Scholes untuk European dan American option. PINN dilatih dengan menggunakan fungsi aktivasi tanh, swish, SELU, dan GELU. Selain itu, diterapkan juga model PINN dengan meningkatkan learning rate, model transformer layer untuk PINN, dan model PINN gabungan. Keakuratan model dianalisis dengan menggunakan root mean square error (RMSE). Model berhasil mengaproksimasi solusi Black-Scholes dengan baik untuk European dan American option. Model terbaik diperoleh dengan menggunakan fungsi aktivasi GELU untuk European call dan tanh untuk European put. / As time progresses, solving partial differential equations using computers have become more essential, one of them is physics-informed neural networks (PINN). PINN is a machine learning technique which approximate PDE by training neural network to minimize loss function. In this thesis, PINN is implemented to solve Black-Scholes PDE for European and American options. PINN is trained using tanh, swish, SELU, and GELU activation functions. Furthermore, PINN with enhanced learning rate, transformer layer for PINN, and combined PINN are implemented as well. The accuracy of the model is analyzed using root mean square error (RMSE). The model successfully approximates Black-Scholes solution well for both European and American option. The best performing model is achieved by using GELU activation function for European call and tanh activation function for European put.

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