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New analytic approach to address Put - Call parity violation due to discrete dividends

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  • Alexander Buryak
  • Ivan Guo

Abstract

The issue of developing simple Black-Scholes type approximations for pricing European options with large discrete dividends was popular since early 2000's with a few different approaches reported during the last 10 years. Moreover, it has been claimed that at least some of the resulting expressions represent high-quality approximations which closely match results obtained by the use of numerics. In this paper we review, on the one hand, these previously suggested Black-Scholes type approximations and, on the other hand, different versions of the corresponding Crank-Nicolson numerical schemes with a primary focus on their boundary condition variations. Unexpectedly we often observe substantial deviations between the analytical and numerical results which may be especially pronounced for European Puts. Moreover, our analysis demonstrates that any Black-Scholes type approximation which adjusts Put parameters identically to Call parameters has an inherent problem of failing to detect a little known Put-Call Parity violation phenomenon. To address this issue we derive a new analytic approximation which is in a better agreement with the corresponding numerical results in comparison with any of the previously known analytic approaches for European Calls and Puts with large discrete dividends.

Suggested Citation

  • Alexander Buryak & Ivan Guo, 2014. "New analytic approach to address Put - Call parity violation due to discrete dividends," Papers 1407.7328, arXiv.org.
  • Handle: RePEc:arx:papers:1407.7328
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    2. Amaro de Matos, Joao & Dilao, Rui & Ferreira, Bruno, 2006. "The exact value for European options on a stock paying a discrete dividend," MPRA Paper 701, University Library of Munich, Germany.
    3. M. H. Vellekoop & J. W. Nieuwenhuis, 2006. "Efficient Pricing of Derivatives on Assets with Discrete Dividends," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(3), pages 265-284.
    4. Matthias Ehrhardt & Ronald E. Mickens, 2008. "A Fast, Stable And Accurate Numerical Method For The Black–Scholes Equation Of American Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(05), pages 471-501.
    5. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893, October.
    6. Carlos Veiga & Uwe Wystup, 2009. "Closed Formula for Options with Discrete Dividends and Its Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(6), pages 517-531.
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