2010/08/23 by Arnaud Gocsei, Gocsei, Arnaud, Fouad Sahel +1
Decision Sciences · Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Capital Investment and Risk Analysis #Computational Finance (q-fin.CP) #FOS: Economics and business #Probability and Risk Models #Stochastic processes and financial applications #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1008.3880
openalex publication_date 2010/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.