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Abstract: The incorporation of a dividend yield in the classical option pricing modelof Black- Scholes results in a minor modification of the Black-Scholes formula,since the lognormal dynamic of the underlying asset is preserved. However,market makers prefer to work with cash dividends with fixed value instead of adividend yield. Since there is no closed-form solution for the price of aEuropean Call in this case, many methods have been proposed in the literatureto approximate it. Here, we present a new approach. We derive an exact analyticformula for the sensitivity to dividends of an European option. We use thisresult to elaborate a proxy which possesses the same Taylor expansion around 0with respect to the dividends as the exact price. The obtained approximation isvery fast to compute the same complexity than the usual Black-Scholes formulaand numerical tests show the extreme accuracy of the method for all practicalcases.



Autor: Arnaud Gocsei, Fouad Sahel

Fuente: https://arxiv.org/







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