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A wave function for stock market returns

Author

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  • Ataullah, Ali
  • Davidson, Ian
  • Tippett, Mark

Abstract

The instantaneous return on the Financial Times-Stock Exchange (FTSE) All Share Index is viewed as a frictionless particle moving in a one-dimensional square well but where there is a non-trivial probability of the particle tunneling into the well’s retaining walls. Our analysis demonstrates how the complementarity principle from quantum mechanics applies to stock market prices and of how the wave function presented by it leads to a probability density which exhibits strong compatibility with returns earned on the FTSE All Share Index. In particular, our analysis shows that the probability density for stock market returns is highly leptokurtic with slight (though not significant) negative skewness. Moreover, the moments of the probability density determined under the complementarity principle employed here are all convergent — in contrast to many of the probability density functions on which the received theory of finance is based.

Suggested Citation

  • Ataullah, Ali & Davidson, Ian & Tippett, Mark, 2009. "A wave function for stock market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 455-461.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:4:p:455-461
    DOI: 10.1016/j.physa.2008.10.035
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    Citations

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    Cited by:

    1. Kartono, Agus & Solekha, Siti & Sumaryada, Tony & Irmansyah,, 2021. "Foreign currency exchange rate prediction using non-linear Schrödinger equations with economic fundamental parameters," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Zhang, Chao & Huang, Lu, 2010. "A quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5769-5775.
    3. Ana Njegovanović, 2023. "The Importance of Quantum Information in the Stock Market and Financial Decision Making in Conditions of Radical Uncertainty," International Journal of Social Science Studies, Redfame publishing, vol. 11(1), pages 54-71, January.
    4. Bagarello, F. & Haven, E., 2014. "The role of information in a two-traders market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 224-233.
    5. Chao Zhang & Lu Huang, 2010. "A quantum model for the stock market," Papers 1009.4843, arXiv.org, revised Oct 2010.
    6. Pedram, Pouria, 2012. "The minimal length uncertainty and the quantum model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2100-2105.
    7. Pouria Pedram, 2011. "The minimal length uncertainty and the quantum model for the stock market," Papers 1111.6859, arXiv.org, revised Jan 2012.
    8. Jasmina Jekni'c-Dugi'c & Sonja Radi' c & Igor Petrovi'c & Momir Arsenijevi'c & Miroljub Dugi'c, 2018. "Quantum Brownian oscillator for the stock market," Papers 1901.10544, arXiv.org.
    9. Ryu, Inug & Jang, Hanwool & Kim, Dongshin & Ahn, Kwangwon, 2021. "Market Efficiency of US REITs: A Revisit," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Haoran Zheng & Jing Bai, 2024. "Quantum Leap: A Price Leap Mechanism in Financial Markets," Mathematics, MDPI, vol. 12(2), pages 1-27, January.
    11. Li Lin, 2024. "Quantum Probability Theoretic Asset Return Modeling: A Novel Schr\"odinger-Like Trading Equation and Multimodal Distribution," Papers 2401.05823, arXiv.org.

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