Application of stochastic differential equations in predicting stock price behavior

Subject Areas : Financial Economics

Behrouz Piri Iranshahi ¹ , Davood Jafari Seresht ^{2 *} , Ali Akbar Golizadeh ³ , Seyed Ehsan Hosseinidoust ⁴

1 - Ph.D. Candidate, Department of Economics, Faculty of Economics and Social Sciences, University of Bu-Ali Sina, Hamedan, Iran, [e-mail]
2 - Assistant Professor, Department of Economics and Social Sciences, University of Bu-Ali Sina, Hamedan, Iran. (Corresponding Author), [e-mail]
3 - Associate Professor, Department of Economics and Social Sciences, University of Bu-Ali Sina, Hamedan, Iran, [e-mail]
4 - Assistant Professor, Department of Economics and Social Sciences, University of Bu-Ali Sina, Hamedan, Iran, [e-mail]

Received: 2024-04-18 Accepted : 2024-07-29 Published : 2024-08-14

Keywords: Keywords: Stochastic Differential Equations, Stock Price, Prediction, Bourse, Stock Exchange, Mellat Bank JEL Classification: C15, C22, C58, G10, G17,

Abstract :

The aim of this research is to examine the efficiency of stochastic differential equation models in predicting stock prices. To evaluate the accuracy of these models, a comparative study has been conducted between these models and conventional time series models. In this domain, Geometric Brownian Motion and Heston models have been reviewed. For this study, the shares of Mellat Bank with the ticker symbol ‘VBMELLAT’ listed on the Tehran Stock Exchange have been examined as a case study; for this purpose, the study has been conducted on the price data of these shares from the beginning of 2015 to the beginning of 2023. Before modeling the stock, price and making predictions, the possibility of recurring patterns and self-similarity in the price movement trend has been examined. The results indicate that Mellat Bank’s shares have long-term memory, which makes it somewhat possible to predict their behavior. Subsequently, the stock price prediction for the ‘VBMELLAT’ ticker symbol has been carried out, and the research findings show that the Heston stochastic differential model, based on most post-test evaluation criteria, performs better in predicting stock prices; such that this model only showed a 0.0464 percent absolute error in predictions. The AR time series model also performed acceptably with the key assumption that past patterns will repeat in the future. This assumption is consistent with the presence of long-term memory and stability in the overall index, which places the AR model second in the evaluation criteria after the Heston model. According to the results obtained, stochastic differential equation models are efficient models for modeling and predicting stock prices.

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