Option pricing and machine learning: a comparison of black-scholes, bachelier, and artificial neural networks - Gross, Eden (School of Management Studies, 2023)
Practitioners and academics alike have applied the Black-Scholes model (or derivatives thereof) when pricing options practically since the introduction of the model in 1973. The recent coronavirus pandemic and the oil futures price crash of April 2020 have 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 both the Bachelier model and the Black-Scholes model when pricing European call options on the Standard & Poor's (S&P) 500 Index using five different volatility estimation methods. Moreover, it then compares the forecasts of the two parametrised models to a deep feed-forward artificial neural network which is also used to price such options. Overall, the artificial neural network is statistically superior in its predictive ability relative to both of the parameterised models, and the Black-Scholes model is statistically superior in its predictive ability to the Bachelier model.