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A comparative analysis of option pricing models: Black–Scholes, Bachelier, and artificial neural networks

Author

Listed:
  • Eden Gross

    (University of the Witwatersrand)

  • Ryan Kruger

    (University of Cape Town)

  • Francois Toerien

    (University of Cape Town)

Abstract

Practitioners and academics alike have applied the Black–Scholes model when pricing options practically since its introduction in 1973. The COVID-19 pandemic and the oil futures price crash of April 2020 caused major markets to briefly switch to the less widely known Bachelier model to price derivatives, as the model allows for negative strikes on the underlying. This study evaluates the predictive ability and accuracy of the Bachelier model and the Black–Scholes model when pricing European call options on the Standard & Poor’s 500 index using five volatility estimation methods. Moreover, it compares the forecasts of the two parameterized models to a deep feed-forward artificial neural network (ANN) which is also used to price such options. Overall, the ANN is statistically superior in its predictive ability relative to both parameterized models, and there is no statistical difference in predictive ability between the Black–Scholes and Bachelier models. These results are of relevance to both academics and participants in the options markets.

Suggested Citation

  • Eden Gross & Ryan Kruger & Francois Toerien, 2025. "A comparative analysis of option pricing models: Black–Scholes, Bachelier, and artificial neural networks," Risk Management, Palgrave Macmillan, vol. 27(2), pages 1-16, May.
    • Handle: RePEc:pal:risman:v:27:y:2025:i:2:d:10.1057_s41283-025-00160-0
    DOI: 10.1057/s41283-025-00160-0
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