Option Pricing Based on Modular Neural Network

Hedging the risk caused by price volatility using options relies on an accurate and appropriate valuation of those options. Therefore, the purpose of this research is to value the options traded on the Tehran Stock Exchange using modular neural networks. The study will also compare the performance of these modular neural networks with the most renowned options valuation models, namely the Black-Scholes-Merton model and the multi-layer perceptron neural network model.

For this research, data on call options traded on the Tehran Stock Exchange from March 2018 to March 2022 were utilized. Initially, after removing outlier data, 80% of the dataset was designated as training data, while the remaining 20% was set aside as test data. To facilitate a comparison of results obtained from different models, these two subsets of data remained constant throughout the research. In this study, the theoretical prices generated by each model were compared with the market prices traded on the Tehran Stock Exchange using MSPE, RMSPE, and MAPE statistical criteria. To calculate the prediction error for the Black-Scholes-Merton model, the theoretical price of options was first obtained using its pricing formula. Subsequently, the theoretical prices derived from the Black-Scholes-Merton equation were compared with their corresponding market prices. In the neural network models, option prices were predicted using Python and its machine learning algorithms. Finally, the predicted prices from the models were compared with the market prices of the same options. To assess the significant differences between each model and the others, the Paired Sample Test of the mean percentage of errors was employed.

This research showed that, from the perspective of the RMSPE criterion, the developed neural network model with implied volatility has the lowest error and has the best performance in valuing call options across all monetary positions and periods compared to other investigated models. However, the performance of the developed multi-layer perceptron neural network model with implied volatility has been slightly better than that of its modular counterpart. Following this, the neural networks developed with historical volatility, the neural networks with discrete data, the Black-Scholes and Merton model, and the modular neural network model proposed by Gradoevich et al. (2009) have been the most accurate, respectively. From the perspective of the MAPE criterion, the developed neural network model with implied volatility has performed the best; however, among all the neural network models, the multi-layer perceptron neural network has outperformed the modular model.

Modular neural network models can outperform the Black-Scholes and Merton models. Incorporating implied volatility enhances the performance of neural networks in options valuation. However, when considering the RMSPE criterion, modular neural networks trained with historical volatility perform better than multi-layer perceptron neural networks. In contrast, for models using implied volatility, the modular neural network does not achieve better performance than the multi-layer perceptron neural network. Overall, neural networks utilizing implied volatility—whether in modular or multi-layer perceptron configurations—exhibit superior performance in long-term periods and in ITM (in-the-money) moneyness situations.