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The Exact Value for European Options on a Stock Paying a Discrete Dividend

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  • Jo~ao Amaro de Matos
  • Rui Dil~ao
  • Bruno Ferreira

Abstract

In the context of a Black-Scholes economy and with a no-arbitrage argument, we derive arbitrarily accurate lower and upper bounds for the value of European options on a stock paying a discrete dividend. Setting the option price error below the smallest monetary unity, both bounds coincide, and we obtain the exact value of the option.

Suggested Citation

  • Jo~ao Amaro de Matos & Rui Dil~ao & Bruno Ferreira, 2006. "The Exact Value for European Options on a Stock Paying a Discrete Dividend," Papers math/0609212, arXiv.org.
    • Handle: RePEc:arx:papers:math/0609212
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    References listed on IDEAS

    as
    1. Merton, Robert C, 1976. "The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns," Journal of Finance, American Finance Association, vol. 31(2), pages 333-350, May.
    2. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    3. 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.
    4. Roll, Richard, 1977. "An analytic valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 5(2), pages 251-258, November.
    5. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
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    Cited by:

    1. Martina Nardon & Paolo Pianca, 2012. "Extracting information on implied volatilities and discrete dividends from American options prices," Working Papers 2012_25, Department of Economics, University of Venice "Ca' Foscari".
    2. Alexander Buryak & Ivan Guo, 2014. "New analytic approach to address Put - Call parity violation due to discrete dividends," Papers 1407.7328, arXiv.org.
    3. 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, Università Ca' Foscari Venezia.

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    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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