Skip to main content
SpringerLink
Log in

Financial Payoff Functions and Potentials

  • Conference paper
  • First Online:
Quantum Interaction (QI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8951))

Included in the following conference series:

Abstract

This paper attempts to argue that when considering a financial payoff function as a potential, one can begin to model how ‘private’ information is. Private information is probably best understood by juxtaposing it against the concept of ‘public’ information, i.e. information which is widely available via various freely accessible media platforms. The very simple model presented here allows us to make a case to compare public with private information. In economics and academic finance, a comparison of both such notions of information can prove to be a useful exercise especially in models where a more formal approach to information is needed. The argument made in this paper is based on using Fisher information and its relationship with a probability density function which itself is related to a wave function. The comparison between the level of available public information (proxied by total energy) and the payoff function (proxied by the potential function) is an important driver in determining the decay of the wave function.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Arbitrage profits are realized when the risk incurred to realize such profits is nil.

  2. 2.

    To avoid any un-necessary financial vocabulary, a box spread combines a ‘bull’ spread and a ‘bear’ spread. The spreads themselves combine financial option contracts. The bull spread requires the buying of an option at a certain (strike) price; and the selling of another option at a higher (strike) price. The bear spread buys the option at the higher strike, but sells the option at the lower strike price. A strike price can be seen as a contractually determined price. When the time comes, to ‘exercise the option’, the market price can be higher or lower than that price.

  3. 3.

    \(m\) being mass and \(\hbar \) being the Planck constant.

References

  1. Aerts, D., Gabora, L., Sozzo, S.: Concepts and their dynamics: a quantum-theoretic modelling of human thought. Top. Cogn. Sci. 5, 737–772 (2013)

    Google Scholar 

  2. Asano, M., Basieva, I., Khrennikov, A., Ohya, M., Tanaka, Yu., Yamato, I.: Quantum-like model of diauxie in escherichia coli: operational description of precultivation effect. J. Theor. Biol. 314, 130–137 (2012)

    Article  Google Scholar 

  3. Atmanspacher, H., Filk, T.: A proposed test of temporal nonlocality in bistable perception. J. Math. Psychol. 54(3), 314–321 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. Baaquie, B.: Interest rates in quantum finance: the Wilson expansion and Hamiltonian. Phys. Rev. E 80, 046119 (2009)

    Article  Google Scholar 

  5. Bouchaud, J.P.: An introduction to statistical finance. Physica A 313, 238–251 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bouchaud, J.P., Potters, M.: Theory of Financial Risks. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  7. Busemeyer, J., Bruza, P.: Quantum Models of Cognition and Decision. Cambridge University Press, Cambridge (2012)

    Book  Google Scholar 

  8. Cohen, T., Schvaneveldt, R., Widdows, D.: Reflective random indexing and indirect inference: a scalable method for discovery of implicit connections. J. Biomed. Inform. 43(2), 240–256 (2010)

    Article  Google Scholar 

  9. Dzhafarov, E.N., Kujala, J.V.: Selectivity in probabilistic causality: where psychology runs into quantum physics. J. Math. Psychol. 56, 54–63 (2012a)

    Article  MATH  MathSciNet  Google Scholar 

  10. Haven, E., Khrennikov, A.: Quantum Social Science. Cambridge University Press, Cambridge (2013)

    Book  Google Scholar 

  11. Haven, E., Khrennikov, A.: Quantum-like tunnelling and levels of arbitrage. Int. J. Theor. Phys. 52(11), 4083–4099 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  12. Haven, E.: Private information and the ‘Information Function’: a survey of possible uses. Theor. Decis. 64(2–3), 193–228 (2007)

    MathSciNet  Google Scholar 

  13. Hawkins, R.J., Frieden, B. R.: Fisher Information and Quantization in Financial Economics. ESRC (The Economic and Social Research of the United Kingdom) Seminar Series: Financial Modelling Post 2008: Where Next? (University of Leicester), January 2014

    Google Scholar 

  14. Hawkins, R.J., Frieden, B.R.: Asymmetric information and quantization in financial economics. Int. J. Math, Math. Sci. (2012). doi:10.1155/2012/470293

  15. Jaynes, E.T.: Information theory and statistical mechanics. Phys. Rev. 106, 620–630 (1957)

    Article  MATH  MathSciNet  Google Scholar 

  16. Jaynes, E.T.: Information theory and statistical mechanics II. Phys. Rev. 108, 171–191 (1957)

    Article  MathSciNet  Google Scholar 

  17. Khrennikov, A.Y.: Classical and quantum mechanics on information spaces with applications to cognitive, psychological, social and anomalous phenomena. Found. Phys. 29, 1065–1098 (1999)

    Article  MathSciNet  Google Scholar 

  18. Khrennikov, A.Y.: Ubiquitous Quantum Structure: from Psychology to Finance. Springer, Heidelberg (2010)

    Book  Google Scholar 

  19. Li, Y., Zhang, J.E.: Option pricing with Weyl-Titchmarsh theory. Quant. Financ. 4(4), 457–464 (2004)

    Article  Google Scholar 

  20. Mantegna, R., Stanley, H.E.: An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (1999)

    Book  Google Scholar 

  21. Reginatto, M.: Derivation of the equations of nonrelativistic quantum mechanics using the principle of minimum fisher information. Phys. Rev. A 58(3), 1775–1778 (1998)

    Article  Google Scholar 

  22. Zhang, J.E., Li, Y.: New analytical option pricing models with Weyl-Titchmarsh theory. Quant. Financ. 12(7), 1003–1010 (2010). doi:10.1080/14697688.2010.503659

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Leicester, Leicester, LE1 7RH, UK

    Emmanuel Haven

Authors
  1. Emmanuel Haven
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Emmanuel Haven .

Editor information

Editors and Affiliations

  1. ETH Zürich, Zürich, Switzerland

    Harald Atmanspacher

  2. Universitätsspital Bern, Bern, Switzerland

    Claudia Bergomi

  3. University of Freiburg, Freiburg, Germany

    Thomas Filk

  4. Queensland University of Technology, Brisbane, Queensland, Australia

    Kirsty Kitto

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Haven, E. (2015). Financial Payoff Functions and Potentials. In: Atmanspacher, H., Bergomi, C., Filk, T., Kitto, K. (eds) Quantum Interaction. QI 2014. Lecture Notes in Computer Science(), vol 8951. Springer, Cham. https://doi.org/10.1007/978-3-319-15931-7_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-15931-7_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15930-0

  • Online ISBN: 978-3-319-15931-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation