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An efficient binomial approach to the pricing of options on stocks with cash dividends

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  • Martina Nardon

    () (Department of Applied Mathematics, University of Venice)

  • Paolo Pianca

    () (Department of Applied Mathematics, University of Venice)

Abstract

In this contribution, we consider options written on stocks which pay cash dividends. Dividend payments have an effect on the value of options: high dividends imply lower call premia and higher put premia. While exact solutions to problems of evaluating both European and American call options and European put options are available in the literature, for American-style put options early exercise may be optimal at any time prior to expiration even in the absence of dividends. In this case numerical techniques, such as lattice approaches, are required. Discrete dividends produce a shift in the tree; as a result, the tree is no longer reconnecting beyond any dividend date. Methods based on non-recombining trees give consistent results, but they are computationally expensive. We analyze binomial algorithms and performed some empirical experiments.

Suggested Citation

  • Martina Nardon & Paolo Pianca, 2008. "An efficient binomial approach to the pricing of options on stocks with cash dividends," Working Papers 178, Department of Applied Mathematics, Universit√† Ca' Foscari Venezia.
  • Handle: RePEc:vnm:wpaper:178
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    References listed on IDEAS

    as
    1. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    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. Geske, Robert, 1981. "Comments on Whaley's note," Journal of Financial Economics, Elsevier, vol. 9(2), pages 213-215, June.
    5. Antonella Basso & Martina Nardon & Paolo Pianca, 2004. "A two-step simulation procedure to analyze the exercise features of American options," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 27(1), pages 35-56, August.
    6. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Options on stocks; discrete dividends; binomial lattices;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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