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Martingale Option Pricing

Author

Listed:
  • J. L. McCauley
  • G. H. Gunaratne
  • K. E. Bassler

Abstract

We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the case of the Gaussian logarithmic returns model by Harrison and Kreps, but we prove it for much a much larger class of returns models where the diffusion coefficient depends on both returns x and time t. That option prices blow up if fat tails in logarithmic returns x are included in the market dynamics is also explained.

Suggested Citation

  • J. L. McCauley & G. H. Gunaratne & K. E. Bassler, 2006. "Martingale Option Pricing," Papers physics/0606011, arXiv.org, revised Feb 2007.
    • Handle: RePEc:arx:papers:physics/0606011
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    Citations

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    Cited by:

    1. Jovanovic, Franck & Schinckus, Christophe, 2016. "Breaking down the barriers between econophysics and financial economics," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 256-266.
    2. Ausloos, Marcel & Jovanovic, Franck & Schinckus, Christophe, 2016. "On the “usual” misunderstandings between econophysics and finance: Some clarifications on modelling approaches and efficient market hypothesis," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 7-14.
    3. Lasko Basnarkov & Viktor Stojkoski & Zoran Utkovski & Ljupco Kocarev, 2019. "Option Pricing With Heavy-Tailed Distributions Of Logarithmic Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-35, November.
    4. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2008. "Martingales, detrending data, and the efficient market hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 202-216.
    5. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2013. "Log Student’s t -distribution-based option sensitivities: Greeks for the Gosset formulae," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1289-1302, July.
    6. Bassler, Kevin E. & Gunaratne, Gemunu H. & McCauley, Joseph L., 2007. "Empirically Based Modeling in the Social Sciences and Spurious Stylized Facts," MPRA Paper 5813, University Library of Munich, Germany.
    7. Daniel T. Cassidy & Michael J. Hamp & Rachid Ouyed, 2010. "Student's t-Distribution Based Option Sensitivities: Greeks for the Gosset Formulae," Papers 1003.1344, arXiv.org, revised Jul 2010.
    8. McCauley, Joseph L. & Bassler, Kevin E. & Gunaratne, Gemunu H., 2008. "Martingales, nonstationary increments, and the efficient market hypothesis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3916-3920.
    9. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
    10. Jovanovic, Franck & Mantegna, Rosario N. & Schinckus, Christophe, 2019. "When financial economics influences physics: The role of Econophysics," International Review of Financial Analysis, Elsevier, vol. 65(C).
    11. Bassler, Kevin E. & Gunaratne, Gemunu H. & McCauley, Joseph L., 2008. "Empirically based modeling in financial economics and beyond, and spurious stylized facts," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 767-783, December.
    12. Cassidy, Daniel T., 2011. "Describing n-day returns with Student’s t-distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(15), pages 2794-2802.
    13. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    14. McCauley, Joseph L., 2007. "Fokker-Planck and Chapman-Kolmogorov equations for Ito processes with finite memory," MPRA Paper 2128, University Library of Munich, Germany.
    15. Cassidy, Daniel T. & Hamp, Michael J. & Ouyed, Rachid, 2010. "Pricing European options with a log Student’s t-distribution: A Gosset formula," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5736-5748.
    16. McCauley, Joseph L., 2007. "Ito Processes with Finitely Many States of Memory," MPRA Paper 5811, University Library of Munich, Germany.

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