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When Physics Meets Finance: Using AI to Solve Black-Scholes
- Physics-Informed Neural Networks (PINNs) combine physics with artificial intelligence to predict complex systems like financial models.
- In the finance world, the Black-Scholes model uses a differential equation to price call options for a risk-free portfolio.
- PINNs aim to match both data and physics principles, ensuring accurate predictions while respecting underlying equations.
- An example implementation involves training a PINN on the Black-Scholes model using Python, Torch, and object-oriented programming.
- The config.json file sets parameters for simulations, data generation, and model training in the Python implementation.
- The main script, black_scholes.py, data.py, loss.py, and model.py are crucial components for building and training the PINN model.
- Results show a good match between the PINN predictions and real-world data, adhering to both financial observations and the Black-Scholes equation.
- The implementation allows for parameter tweaking, synthetic data generation, and exploration of model predictions at different time points.
- The article provides insights into the integration of physics, finance, and AI, offering a detailed Python-based solution for solving the Black-Scholes equation.
- Author Piero Paialunga, a Ph.D. candidate in Aerospace Engineering, presents a practical application of PINNs in financial modeling.
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