Title
Closed formula for options with discrete dividends and its derivatives Closed formula for options with discrete dividends and its derivatives
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
London ,
Subject
Economics
Mathematics
Source (journal)
Applied mathematical finance. - London
Volume/pages
16(2009) :6 , p. 517-531
ISSN
1350-486X
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
We present a closed pricing formula for European options under the BlackScholes model as well as formulas for its partial derivatives. The formulas are developed making use of Taylor series expansions and a proposition that relates expectations of partial derivatives with partial derivatives themselves. The closed formulas are attained assuming the dividends are paid in any state of the world. The results are readily extensible to time-dependent volatility models. For completeness, we reproduce the numerical results in Vellekoop and Nieuwenhuis, covering calls and puts, together with results on their partial derivatives. The closed formulas presented here allow a fast calculation of prices or implied volatilities when compared with other valuation procedures that rely on numerical methods.
E-info
https://repository.uantwerpen.be/docman/iruaauth/713ede/8ba15c45010.pdf