Closed formula for options with discrete dividends and its derivatives
We present a closed pricing formula for European options under the BlackScholes model and formulas for its partial derivatives. The formulas are developed making use of Taylor series expansions and by expressing the spatial derivatives as expectations under special measures, as in Carr, together with an unusual change of measure technique that relies on the replacement of the initial condition. The closed formulas are attained for the case where no dividend payment policy is considered. Despite its small practical relevance, a digital dividend policy case is also considered which yields approximation formulas. The results are readily extensible to time dependent volatility models but no so for local-vol type models. For completeness, we reproduce the numerical results in Vellekoop and Nieuwenhuis using the formulas here obtained. 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.
|Date of creation:||2008|
|Date of revision:|
|Contact details of provider:|| Postal: Sonnemannstraße 9-11, 60314 Frankfurt am Main|
Phone: 069 154008-0
Web page: http://www.frankfurt-school.de/content/en/cpqf
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Wollersheim, Jutta & Barthel, Erich, 2008. "Kulturunterschiede bei Mergers & Acquisitions: Entwicklung eines Konzeptes zur Durchführung einer Cultural Due Diligence," Frankfurt School - Working Paper Series 94, Frankfurt School of Finance and Management.
- Bannier, Christina E., 2007.
"Heterogeneous multiple bank financing: does it reduce inefficient credit-renegotation incidences?,"
Frankfurt School - Working Paper Series
83, Frankfurt School of Finance and Management.
- Christina Bannier, 2007. "Heterogeneous multiple bank financing: does it reduce inefficient credit-renegotiation incidences?," Financial Markets and Portfolio Management, Springer, vol. 21(4), pages 445-470, December.
- Ansgar Belke & Thorsten Polleit, 2006.
"How the ECB and the US Fed Set Interest Rates,"
Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim
269/2006, Department of Economics, University of Hohenheim, Germany.
- Ansgar Belke & Thorsten Polleit, 2005. "(How) Do Stock Market Returns React to Monetary Policy? - An ARDL Cointegration Analysis for Germany," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 253/2005, Department of Economics, University of Hohenheim, Germany.
- Bannier, Christina E. & Hänsel, Dennis N., 2007. "Determinants of banks' engagement in loan securitization," Frankfurt School - Working Paper Series 85, Frankfurt School of Finance and Management.
When requesting a correction, please mention this item's handle: RePEc:zbw:cpqfwp:16. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (ZBW - German National Library of Economics)
If references are entirely missing, you can add them using this form.