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).
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 references are entirely missing, you can add them using this form.