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Deep Learning vs. Black-Scholes: Option Pricing Performance on Brazilian Petrobras Stocks

Joao Felipe Gueiros, Hemanth Chandravamsi, Steven H. Frankel

TL;DR

The paper addresses the problem of pricing European Petrobras options more accurately than the Black-Scholes model in the Brazilian market. It adopts a residual neural network trained on eight years of B3 data using a hybrid loss that blends market prices with Black-Scholes benchmarks, and evaluates performance across different expirations and price ranges. The main finding is a 64.3% reduction in mean absolute error within the 3–19 BRL price range on the test set, with improved accuracy for longer-dated options, though limitations remain for extreme price scenarios. The work demonstrates the practical potential of deep learning in financial modeling under resource constraints and points to future work on range-specific models to further boost accuracy and robustness.

Abstract

This paper explores the use of deep residual networks for pricing European options on Petrobras, one of the world's largest oil and gas producers, and compares its performance with the Black-Scholes (BS) model. Using eight years of historical data from B3 (Brazilian Stock Exchange) collected via web scraping, a deep learning model was trained using a custom built hybrid loss function that incorporates market data and analytical pricing. The data for training and testing were drawn between the period spanning November 2016 to January 2025, using an 80-20 train-test split. The test set consisted of data from the final three months: November, December, and January 2025. The deep residual network model achieved a 64.3\% reduction in the mean absolute error for the 3-19 BRL (Brazilian Real) range when compared to the Black-Scholes model on the test set. Furthermore, unlike the Black-Scholes solution, which tends to decrease its accuracy for longer periods of time, the deep learning model performed accurately for longer expiration periods. These findings highlight the potential of deep learning in financial modeling, with future work focusing on specialized models for different price ranges.

Deep Learning vs. Black-Scholes: Option Pricing Performance on Brazilian Petrobras Stocks

TL;DR

The paper addresses the problem of pricing European Petrobras options more accurately than the Black-Scholes model in the Brazilian market. It adopts a residual neural network trained on eight years of B3 data using a hybrid loss that blends market prices with Black-Scholes benchmarks, and evaluates performance across different expirations and price ranges. The main finding is a 64.3% reduction in mean absolute error within the 3–19 BRL price range on the test set, with improved accuracy for longer-dated options, though limitations remain for extreme price scenarios. The work demonstrates the practical potential of deep learning in financial modeling under resource constraints and points to future work on range-specific models to further boost accuracy and robustness.

Abstract

This paper explores the use of deep residual networks for pricing European options on Petrobras, one of the world's largest oil and gas producers, and compares its performance with the Black-Scholes (BS) model. Using eight years of historical data from B3 (Brazilian Stock Exchange) collected via web scraping, a deep learning model was trained using a custom built hybrid loss function that incorporates market data and analytical pricing. The data for training and testing were drawn between the period spanning November 2016 to January 2025, using an 80-20 train-test split. The test set consisted of data from the final three months: November, December, and January 2025. The deep residual network model achieved a 64.3\% reduction in the mean absolute error for the 3-19 BRL (Brazilian Real) range when compared to the Black-Scholes model on the test set. Furthermore, unlike the Black-Scholes solution, which tends to decrease its accuracy for longer periods of time, the deep learning model performed accurately for longer expiration periods. These findings highlight the potential of deep learning in financial modeling, with future work focusing on specialized models for different price ranges.
Paper Structure (13 sections, 10 equations, 7 figures, 3 tables)

This paper contains 13 sections, 10 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Data Collection and Processing
  3. Data Selection
  4. Accessing and Cleaning up the Data
  5. Data Combination for Training
  6. Methodology
  7. Machine Learning Model
  8. Loss Function and Training
  9. Results and discussion
  10. Hyperparameter optimization and final training losses
  11. Comparison with the Black-Scholes Solution
  12. Discussion
  13. Summary

Figures (7)

  • Figure 1: (Left) Deep neural network architecture adapted from CS230_2019, where the input features represent key financial variables, and the output corresponds to the call option price. (Right) The residual deep neural network used in this work, featuring a residual connection between Layer 1 and Layer 2. Abbreviations: FC – Fully Connected Layer, BN – Batch Normalization, LReLU – Leaky ReLU Activation.
  • Figure 2: Epoch vs. loss plots for each hyperparameter trail performed using optuna with the validation dataset.
  • Figure 3: Evolution of training and test loss during the final training.
  • Figure 4: Comparison of overall error for validation and test sets
  • Figure 5: Comparison of mean absolute errors for the validation (top) and test (bottom) sets, based on option expiration time and strike price.
  • ...and 2 more figures