Stochastic Expansion for the Pricing of Call Options with Discrete Dividends
In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black--Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal proxy model. The final formulae are, respectively, first-, second- and third- order approximations w.r.t. the fixed part of the dividends. Using Cameron--Martin transformations, we provide explicit representations of the correction terms as Greeks in the Black--Scholes model. The use of Malliavin calculus enables us to provide tight error estimates for our approximations. Numerical experiments show that this approach yields very accurate results, in particular compared with known approximations of Bos, Gairat and Shepeleva (2003, Dealing with discrete dividends, Risk Magazine , 16, pp. 109--112) and Veiga and Wystup (2009, Closed formula for option with discrete dividends and its derivatives, Applied Mathematical Finance, 16(6), pp. 517--531), and quicker than the iterated integration procedure of Haug, Haug and Lewis (2003, Back to basics: a new approach to the discrete dividend problem, Wilmott Magazine, pp. 37--47) or than the binomial tree method of Vellekoop and Nieuwenhuis (2006, Efficient pricing of derivatives on assets with discrete dividends, Applied Mathematical Finance, 13(3), pp. 265--284).
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 19 (2012)
Issue (Month): 3 (August)
|Contact details of provider:|| Web page: http://www.tandfonline.com/RAMF20|
|Order Information:||Web: http://www.tandfonline.com/pricing/journal/RAMF20|
When requesting a correction, please mention this item's handle: RePEc:taf:apmtfi:v:19:y:2012:i:3:p:233-264. 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: (Michael McNulty)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.