Option Pricing Based on Modular Neural Network

Objective: Hedging the risk caused by price volatility by using options will depend on accurate and appropriate valuation for options. For this reason, the purpose of this research is to value the options traded in the Tehran Stock Exchange with modular neural networks and compare the performance of each of these modular neural networks with the most famous options valuation model, i.e. Black, Scholes and Merton model and the multi-layer perceptron neural network model.

Methods: For this research, the data of call options traded in the Tehran Stock Exchange from March 2018 to March 2022 have been used. At first, after removing the outlier data, 80% of the data were considered as training data and the remaining 20% as test data. For the possibility of comparing the results obtained from different models, these two parts of the data were constant during the research. In this research, using MSPE, RMSPE and MAPE statistical criteria, the theoretical price obtained from each model was compared with the prices traded in the Tehran Stock Exchange. To calculate the prediction error in the Black, Scholes and Merton model, first, by using its pricing formula, the theoretical price of options was obtained, and then the theoretical prices obtained from the Black, Scholes and Merton equation were compared with their market prices. In neural network models, the price of options was first predicted using Python and its machine learning algorithms, and finally, the price predicted by the models was compared with the market price of the same option. In the end, to check the significant difference of each model with other models, the Paired Sample Test of the mean percentage of errors was used.

Results: This research showed that from the perspective of RMSPE criterion, the developed neural networks model with implied volatility has the lowest error and It has the best performance in valuing the Call options in all monetary positions and time 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 its modular state. After that, 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, Genjai and Kokolaj (2009) have been the most accurate, respectively. from the perspective of MAPE criterion, the developed neural networks model with implied volatility have performed the best, but in all the neural network models, the multi-layer perceptron neural network has performed better than the modular mode.

Conclusion: Modular neural network models can perform better than Black, Scholes and Merton model. Implied volatility can improve the performance of neural networks in options valuation. On the other hand, from the perspective of RMSPE criterion, in the developed neural network models with historical volatility, the modular neural network will perform better than the multi-layer perceptron neural network. But in the developed neural network models with implied volatility, the modular neural network cannot register a better performance than the multi-layer perceptron neural network. In general, neural networks developed with implied volatility in both modular and multi-layer perceptron modes have performed best in long-term time periods as well as in ITM moneyness situations.