# Neural Network Learning of Black-Scholes Equation for Option Pricing

arXiv: https://arxiv.org/abs/2405.05780 · HTML: https://mlsanity.com/paper/2405.05780/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 47 references that are in the map.
- First posted on arXiv 9 May 2024.

## Builds on (most cited first, 2 of 2)

- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [Neural network stochastic differential equation models with applications to financial data forecasting](https://mlsanity.com/paper/2111.13164/) (2021)

## Abstract (arXiv)

One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model. The present work proposes an approach based on Neural Networks to solve the Black-Scholes Equations. Real-world data from the stock options market were used as the initial boundary to solve the Black-Scholes Equation. In particular, times series of call options prices of Brazilian companies Petrobras and Vale were employed. The results indicate that the network can learn to solve the Black-Sholes Equation for a specific real-world stock options time series. The experimental results showed that the Neural network option pricing based on the Black-Sholes Equation solution can reach an option pricing forecasting more accurate than the traditional Black-Sholes analytical solutions. The experimental results making it possible to use this methodology to make short-term call option price forecasts in options markets.