The Using Neural Network and Finite Difference Method for Option Pricing under Black-Scholes-Vasicek Model

Subject Areas : Financial Engineering

Mahdiye Mohmmadi ¹ , Elham Dastranj ² , Abdolmajid Abdolbaghi Ataabadi ^{3 *} , Hossein Sahebi fard ⁴

1 - Department of Mathematics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
2 - Department of Mathematics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
3 - Department of Management, Faculty of Industrial Engineering and Management, Shahrood University of Technolo-gy, Shahrood, Semnan, Iran
4 - Department of Mathematics, Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran

Received: 2024-05-01 Accepted : 2024-12-11 Published : 2025-01-17

Keywords: Option Pricing , Neural Networks , Finite Difference Method , Black-Scholes-Vasicek Model,

Abstract :

In this paper, the European option pricing is done using neural networks in the Black-Scholes-Vasicek market. The general purpose of this research is to compare the accuracy of neural network and Black-Scholes-Vasicek models for the pricing of call options. In the sequel, the finite difference method is applied to find approximate solutions of partial differential equation related to option pricing in the considered market. In the design of the artificial neural network required for this research, the parameters of the Black-Scholes-Vasicek model have been used as network inputs, as well as 720 data from the daily price of stock options available in the Tehran Stock Exchange market (in 1400) as the network output. The approximate solutions obtained in this article, which were carried out by two methods of neural networks and finite differences on the Tehran stock exchange based on the daily price of stock options, are shown that neural networks are more accurate method comparing with finite difference. The comparison of pricing results using neural networks with real prices in the assumed market is presented and shown via diagram, as well. In this paper, the European option pricing is done using neural networks in the Black-Scholes-Vasicek market. The general purpose of this research is to compare the accuracy of neural network and Black-Scholes-Vasicek models for the pricing of call options. In the sequel, the finite difference method is applied to find approximate solutions of partial differential equation related to option pricing in the considered market. In the design of the artificial neural network required for this research, the parameters of the Black-Scholes-Vasicek model have been used as network inputs, as well as 720 data from the daily price of stock options available in the Tehran Stock Exchange market (in 1400) as the network output. The approximate solutions obtained in this article, which were carried out by two methods of neural networks and finite differences on the Tehran stock exchange based on the daily price of stock options, are shown that neural networks are more accurate method comparing with finite difference. The comparison of pricing results using neural networks with real prices in the assumed market is presented and shown via diagram, as well.

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