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Analysis of the sensitivity to discrete dividends : A new approach for pricing vanillas

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  • Arnaud Gocsei
  • Fouad Sahel

Abstract

The incorporation of a dividend yield in the classical option pricing model of 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 a dividend yield. Since there is no closed-form solution for the price of a European Call in this case, many methods have been proposed in the literature to approximate it. Here, we present a new approach. We derive an exact analytic formula for the sensitivity to dividends of an European option. We use this result to elaborate a proxy which possesses the same Taylor expansion around 0 with respect to the dividends as the exact price. The obtained approximation is very fast to compute (the same complexity than the usual Black-Scholes formula) and numerical tests show the extreme accuracy of the method for all practical cases.

Suggested Citation

  • Arnaud Gocsei & Fouad Sahel, 2010. "Analysis of the sensitivity to discrete dividends : A new approach for pricing vanillas," Papers 1008.3880, arXiv.org.
  • Handle: RePEc:arx:papers:1008.3880
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    File URL: http://arxiv.org/pdf/1008.3880
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