Analysis of the sensitivity to discrete dividends : A new approach for pricing vanillas
AbstractThe 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1008.3880.
Date of creation: Aug 2010
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-03 (All new papers)
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