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An accurate approximation formula for pricing European options with discrete dividend payments

Journal Article


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Abstract


  • In this article, two relevant problems related to pricing European options with discrete dividend under

    the classic Black–Scholes framework are considered. For the case when a discrete dividend payment is

    proportional to the underlying asset value, we discuss an interesting phenomenon observed; the option

    price is independent of the dividend payment date. This appears to be at odds with one’s intuition that

    dividend amount, as well as the dividend date, should both affect the price of a European call or put option.

    We reveal the fundamental reasons, from both mathematical and financial viewpoints, why this occurs.

    When the amount of the discrete dividend is fixed, we provide an approximation formula for European

    option prices, with only one-dimensional integrals involved. It should be noted that our formula is a general

    one since it can not only be applied when there is only a single dividend, but also be suitable for the case

    of multiple dividends.

Publication Date


  • 2016

Citation


  • Zhu, S. & He, X. (2016). An accurate approximation formula for pricing European options with discrete dividend payments. IMA Journal of Management Mathematics, Online First 1-14.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7591&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6561

Number Of Pages


  • 13

Start Page


  • 1

End Page


  • 14

Volume


  • Online First

Place Of Publication


  • United Kingdom

Abstract


  • In this article, two relevant problems related to pricing European options with discrete dividend under

    the classic Black–Scholes framework are considered. For the case when a discrete dividend payment is

    proportional to the underlying asset value, we discuss an interesting phenomenon observed; the option

    price is independent of the dividend payment date. This appears to be at odds with one’s intuition that

    dividend amount, as well as the dividend date, should both affect the price of a European call or put option.

    We reveal the fundamental reasons, from both mathematical and financial viewpoints, why this occurs.

    When the amount of the discrete dividend is fixed, we provide an approximation formula for European

    option prices, with only one-dimensional integrals involved. It should be noted that our formula is a general

    one since it can not only be applied when there is only a single dividend, but also be suitable for the case

    of multiple dividends.

Publication Date


  • 2016

Citation


  • Zhu, S. & He, X. (2016). An accurate approximation formula for pricing European options with discrete dividend payments. IMA Journal of Management Mathematics, Online First 1-14.

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7591&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6561

Number Of Pages


  • 13

Start Page


  • 1

End Page


  • 14

Volume


  • Online First

Place Of Publication


  • United Kingdom