A non-Gaussian option pricing model based on Kaniadakis exponential deformation

  • Enrico Moretto
  • Sara Pasquali
  • Barbara Trivellato
Regular Article

Abstract

A way to make financial models effective is by letting them to represent the so called “fat tails”, i.e., extreme changes in stock prices that are regarded as almost impossible by the standard Gaussian distribution. In this article, the Kaniadakis deformation of the usual exponential function is used to define a random noise source in the dynamics of price processes capable of capturing such real market phenomena.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    F. Black, M. Scholes, J. Polit. Econ. 81, 637 (1973) MathSciNetCrossRefGoogle Scholar
  2. 2.
    E. Platen, R. Rendek, J. Stat. Theory Pract. 2, 233 (2008) MathSciNetCrossRefGoogle Scholar
  3. 3.
    S.L. Heston, Rev. Financ. Stud. 6, 327 (1993) CrossRefGoogle Scholar
  4. 4.
    J.C. Cox, J.E. Ingersoll, S.A. Ross, Econometrica 53, 385 (1985) MathSciNetCrossRefGoogle Scholar
  5. 5.
    R.C. Merton, J. Financ. Econ. 3, 125 (1976) CrossRefGoogle Scholar
  6. 6.
    D.S. Bates, Rev. Financ. Stud. 9, 69 (1996) CrossRefGoogle Scholar
  7. 7.
    B. Eraker, M. Johannes, N. Polson, J. Financ. 58, 1269 (2003) CrossRefGoogle Scholar
  8. 8.
    F. D’Ippoliti, E. Moretto, S. Pasquali, B. Trivellato, Int. J. Theor. Appl. Financ. 13, 901 (2010) CrossRefGoogle Scholar
  9. 9.
    D.G. Hobson, L.C. Rogers, Math. Financ. 8, 7 (1998) CrossRefGoogle Scholar
  10. 10.
    C. Tsallis, J. Stat. Phys. 52, 479 (1988) ADSCrossRefGoogle Scholar
  11. 11.
    G. Kaniadakis, Physica A 296, 405 (2001) ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    G. Kaniadakis, Phys. Rev. E 72, 036108 (2005) ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    G. Kaniadakis, Eur. Phys. J. B 70, 3 (2009) ADSCrossRefGoogle Scholar
  14. 14.
    G. Kaniadakis, Entropy 15, 3983 (2013) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    F. Clementi, M. Gallegati, G. Kaniadakis, Eur. Phys. J. B 57, 187 (2007) ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    F. Clementi, M. Gallegati, G. Kaniadakis, J. Stat. Mech. Theor. Exp. 2009, P02037 (2009) CrossRefGoogle Scholar
  17. 17.
    B. Trivellato, Int. J. Theor. Appl. Financ. 15, 1250038 (2012) MathSciNetCrossRefGoogle Scholar
  18. 18.
    B. Trivellato, Entropy 15, 3471 (2013) ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    P.G. Popescu, V. Preda, E.I. Slusanschi, Physica A 413, 280 (2014) ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    V. Preda, S. Dedu, C. Gheorghe, Physica A 436, 925 (2015) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    V. Preda, S. Dedu, M. Sheraz, Physica A 407, 350 (2014) ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    E. Moretto, S. Pasquali, B. Trivellato, Physica A 446, 246 (2016) MathSciNetCrossRefGoogle Scholar
  23. 23.
    L. Borland, Quant. Financ. 2, 415 (2002) MathSciNetGoogle Scholar
  24. 24.
    L. Borland, Phys. Rev. Lett. 89, 098701 (2002) ADSCrossRefGoogle Scholar
  25. 25.
    M. Vellekoop, H. Nieuwenhuis, Quant. Financ. 7, 563 (2007) CrossRefGoogle Scholar
  26. 26.
    M.L. Bertotti, G. Modanese, Eur. Phys. J. B 85, 1 (2012) CrossRefGoogle Scholar
  27. 27.
    A.R. Plastino, A. Plastino, Physica A 222, 347 (1995) ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    J. Naudts, Generalised thermostatistics (Springer Science & Business Media, London, 2011) Google Scholar
  29. 29.
    T. Wada, A.M. Scarfone, Eur. Phys. J. B 70, 65 (2009) ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    T. Wada, A.M. Scarfone, On the non-linear Fokker–Planck equation associated with κ-entropy, in AIP Conference Proceedings, edited by A. Sumiyoshi et al. (AIP, Catania, Italy, 2007), Vol. 965, p. 1 Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Dipartimento di Economia, Universià dell’InsubriaVareseItaly
  2. 2.CNR-IMATIMilanoItaly
  3. 3.Dipartimento di Matematica, Politecnico di TorinoTorinoItaly

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