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Option pricing under deformed Gaussian distributions

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  • Moretto, Enrico
  • Pasquali, Sara
  • Trivellato, Barbara

Abstract

In financial literature many have been the attempts to overcome the option pricing drawbacks that affect the Black and Scholes model. Starting from the Tsallis deformation of the usual exponential function, this paper presents, in a complete market setup, a class of deformed geometric Brownian motions flexible enough to reproduce fat tails and to capture the volatility behavior observed in models that consider both stochastic volatility and jumps.

Suggested Citation

  • Moretto, Enrico & Pasquali, Sara & Trivellato, Barbara, 2016. "Option pricing under deformed Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 246-263.
    • Handle: RePEc:eee:phsmap:v:446:y:2016:i:c:p:246-263
    DOI: 10.1016/j.physa.2015.11.026
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    References listed on IDEAS

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    1. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    2. L. Borland & J. P. Bouchaud, 2004. "A Non-Gaussian Option Pricing Model with Skew," Papers cond-mat/0403022, arXiv.org, revised Mar 2004.
    3. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    4. Eckhard Platen & Renata Rendek, 2007. "Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices," Research Paper Series 194, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Papers cond-mat/0204331, arXiv.org, revised Sep 2002.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. David G. Hobson & L. C. G. Rogers, 1998. "Complete Models with Stochastic Volatility," Mathematical Finance, Wiley Blackwell, vol. 8(1), pages 27-48, January.
    9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    10. Michel Vellekoop & Hans Nieuwenhuis, 2007. "On option pricing models in the presence of heavy tails," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 563-573.
    11. Lisa Borland & Jean-Philippe Bouchaud, 2004. "A non-Gaussian option pricing model with skew," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 499-514.
    12. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    13. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    14. Preda, Vasile & Dedu, Silvia & Gheorghe, Carmen, 2015. "New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 925-932.
    15. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
    16. Plastino, A.R. & Plastino, A., 1995. "Non-extensive statistical mechanics and generalized Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 222(1), pages 347-354.
    17. Popescu, P.G. & Preda, V. & Sluşanschi, E.I., 2014. "Bounds for Jeffreys–Tsallis and Jensen–Shannon–Tsallis divergences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 280-283.
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    Cited by:

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