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Quantum finance

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  • Schaden, Martin

Abstract

Quantum theory is used to model secondary financial markets. Contrary to stochastic descriptions, the formalism emphasizes the importance of trading in determining the value of a security. All possible realizations of investors holding securities and cash is taken as the basis of the Hilbert space of market states. The temporal evolution of an isolated market is unitary in this space. Linear operators representing basic financial transactions such as cash transfer and the buying or selling of securities are constructed and simple model Hamiltonians that generate the temporal evolution due to cash flows and the trading of securities are proposed. The Hamiltonian describing financial transactions becomes local when the profit/loss from trading is small compared to the turnover. This approximation may describe a highly liquid and efficient stock market. The lognormal probability distribution for the price of a stock with a variance that is proportional to the elapsed time is reproduced for an equilibrium market. The asymptotic volatility of a stock in this case is related to the long-term probability that it is traded.

Suggested Citation

  • Schaden, Martin, 2002. "Quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 511-538.
    • Handle: RePEc:eee:phsmap:v:316:y:2002:i:1:p:511-538
    DOI: 10.1016/S0378-4371(02)01200-1
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    Citations

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    Cited by:

    1. 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.
    2. Jack Sarkissian, 2016. "Spread, volatility, and volume relationship in financial markets and market making profit optimization," Papers 1606.07381, arXiv.org.
    3. Shi, Leilei, 2006. "Does security transaction volume–price behavior resemble a probability wave?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 419-436.
    4. Xiangyi Meng & Jian-Wei Zhang & Jingjing Xu & Hong Guo, 2014. "Quantum spatial-periodic harmonic model for daily price-limited stock markets," Papers 1405.4490, arXiv.org.
    5. Jack Sarkissian, 2016. "Quantum theory of securities price formation in financial markets," Papers 1605.04948, arXiv.org, revised May 2016.
    6. Bucsa, G. & Jovanovic, F. & Schinckus, C., 2011. "A unified model for price return distributions used in econophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3435-3443.
    7. 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.
    8. Meng, Xiangyi & Zhang, Jian-Wei & Xu, Jingjing & Guo, Hong, 2015. "Quantum spatial-periodic harmonic model for daily price-limited stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 154-160.
    9. F. Bagarello & E. Haven, 2014. "Towards a formalization of a two traders market with information exchange," Papers 1412.8725, arXiv.org.
    10. Gao, Tingting & Chen, Yu, 2017. "A quantum anharmonic oscillator model for the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 307-314.
    11. Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantum Game Theory in Finance," Departmental Working Papers 19, University of Bialtystok, Department of Theoretical Physics.
    12. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034, Decembrie.

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