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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

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    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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