A quantum Model for the stock Market
الموضوعات :Neda Allahyaribeik 1 , Hashem Nikoomaram 2 , Sara Allahyaribeik 3 , Fraydoon Rahnamay Roodposhti 4
1 - Department of Accounting, Faculty of Management and Economics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Accounting, Faculty of Management and Economics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Marine Sciences, Faculty of Natural Resources and Environment, Science and Research Branch, Islamic Azad University, Tehran, Iran
4 - Department of Accounting, Faculty of Management and Economics, Science and Research Branch, Islamic Azad University, Tehran, Iran
الکلمات المفتاحية: Price return, P/E ratio, Joint quantum potential, Bohmian quantum mechanics,
ملخص المقالة :
Price return and P/E are two interesting factors for a lot of investors; The Bohmian quantum mechanics used referring to the time correlation of return and P/E of the stock market under consideration. In this study, we extend the quantum potential concept to determine the behaviour of P/E and also price return in two different industry of Tehran stock market during a time interval of April. 2008 to march 2019. The obtained results show that the quantum potential behaves in the same manner for P/E and price return, also confines the variations of the P/E and price return into a specific domain. Furthermore, a joint quantum potential as a function of return and P/E is derived by the probability distribution function (PDF) constructed by the real data of a given market. It serves as a suitable instrument to investigate the relationship between these variables. The resultant PDF and the corresponding joint quantum potential illustrate that where we have light points in joint quantum potential chart, the probability of those amount of P/E and price return are more than other points. In addition, because of the rectangular shape of the joint quantum potential chart we can say that these two variables behave as two independent variables in the Market.
[1] Lo, A. W., Wang, J., Trading volume: Definitions, data analysis, and implications of portfolio theory, Rev. Financ. Stud, 2000, 13, P.257-300. Doi: 10.1093/rfs/13.2.257
[2] Granger C. W. J., Morgenstern, O., Spectral analysis of New York stock market prices, Kyklos, 1963, 16, P.1-27. Doi: 10.1111/j.1467-6435. 1963.tb00270.x
[3] Campbell, J. Y., Grossman, S. J., Wang, J., Trading volume and serial correlation in stock returns, Q. J. Econ., 1993, 108, P.905-939. Doi: 10. 2307/2118454
[4] Tripathi, S., Application of mathematics in financial management, Advances in mathematical finance and applications, 2019, 4, P.1-14. Doi:10.2203/amfa.2019.583576.1169.
[5] Habib, N. M., Trade volume and returns in emerging stock markets an empirical study: The Egyptian market, Int. J. Humanit. Soc. Sci., 2011, 1, P.302-312.
[6] Todorova, N., Soucek, M., The impact of trading volume, number of trades and overnight returns on forecasting the daily realized range, Econ. Model, 2014, 36, P.332–334.
[8] Chakraborti, A., Muni Toke, I., Patriarca, M., Abergel, F., Econophysics: Empirical facts and agent-based models, 2009, ArXiv e-prints.
[9] Chen, J., The Unity of Science and Economics: A New Foundation of Economic Theory, SSRN Electronic Journal, 2014, 15, P.26-29, Doi: 10.2139/ssrn.2516607
[10] Baaquie, B. E., Statistical microeconomics, Physica A, 2013, 392, P.4400-4416.
[11] Baaquie, B. E., Du, X., Bhanap, J., Option pricing: Stock price stock velocity and the acceleration lagrangian, Physica A, 2014, 416, P. 564-581. Doi: 10.1016/j.physa.2014.09.019
[12] Choustova, O. A., Khrennikov, A., Pilot wave quantum model for the stock market in Quantum Theory, Reconsideration of Foundations, Ser. Math. Model, 2002, 2, P.41-58.
[13] Tahmasebi, F., Meskinimood, S., Namaki, A., Farahani, S.V., Jalalzadeh, S., Jafari, G. R., Financial market images: A practical approach owing to the secret quantum potential, EPL (Europhysics Letters), 2015, 109(3), Doi: 10.1209/0295-5075/109/30001
[14] Shen, C., Haven, E., Using Empirical Data to Estimate Potential Functions in Commodity Markets: Some Initial Results, International Journal of Theoretical Physics, 2017, 56(12), P.4092-4104. Doi: 10.1007/s10773-017-3446-z
[15] Nasiri, S., Bektas, E., Jafari, G. R., Risk information of stock market using quantum potential constraints, In: 3rd International Conference on Banking and Finance Perspectives, 2018.
[16] Black, F., Scholes, M., The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 1973, 81(3), P. 637-654. Doi: 10.1086/260062
[17] Chakraborti, A., Toke, I. M., Patriarca, M., Abergel, F., Econophysics review: II. agent-based models, Quant. Finance, 2011, 11, P. 1013-1041, Doi: 10.1080/14697688.2010.539249
[18] Chen, J., The Unity of Science and Economics: A New Foundation of Economic Theory, 2015, first ed., Springer-Verlag, New York, Doi: 10. 1007/978-1-4939-3466-9
[19] Khrennikov, A., Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social, and anomalous phenomena, Found. Phys., 1999, 29, P. 1065-1098. Doi: 10.1023/A:101888563
[20] Izadikhah, M. Financial Assessment of Banks and Financial Institutes in Stock Exchange by Means of an Enhanced Two stage DEA Model. Advances in Mathematical Finance and Applications, 2021, 6(2), P. 207-232. Doi: 10.22034/amfa.2020.1910507.1491
[21] Zanjirdar, M., Overview of Portfolio Optimization Models. Advances in Mathematical Finance and Applications, 2020, 5(4), P. 419-435. Doi: 10.22034/amfa.2020.674941
[22] Choustova, O., Bohmian mechanics for financial processes, Journal of Modern Optics,
2004, 51, P.6-7. Doi: 10.1080/09500340408233645
[23] Choustova, O., Quantum model for the price dynamics: The problem of smoothness of trajectories, J. Math. Anal. Appl., 2008, 346, P. 296-304. Doi: 10.1016/j.jmaa.2008.04.072
[24] Choustova, O., Quantum probability and financial market, Information Sciences, 2009, 179(5), P. 478-484. Doi: 10.1016/j.ins.2008.07.001
