Option Pricing Error: Evidence from Nonlinear Markets based on Probabilistic Neural Networks and Multilayer Perceptron

This sudy aims to compare the pricing error of Barles-Soner and Bakstein-Howison equation, in the S&P500 index option market. Option pricing equations are solved using Lie algebra. Using the historical data of the S&P500 index from August 18, 2022, to August 18, 2023, the price of this asset has been calculated with each model considered. In the sequel, the obtained data are classified using multilayer Perceptron and Probabilistic neural networks. The networks show which model is closest to the real market. In addition, the prices obtained from Lie algebra have been compared with the actual values of the options in the market. PNN and MLP have been tested with statistical data after August 18, 2023. Two assumed models were priced with the same data and then compared with the real market. In testing the networks, MLP put 60% of the test data and PNN put all the data into the Barels-Soner category. By calculating the difference between the results of the Lie groups and the real data, 80% of the data were less different from the Barrels-Soner model. With the results obtained in S&P option pricing, the Barels-Soner model has less error than other models.