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Stochastic Expansion for the Pricing of Call Options with Discrete Dividends

37 Pages Posted: 7 Oct 2010  

Pierre Etore

affiliation not provided to SSRN

Emmanuel Gobet

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees

Date Written: October 5, 2010

Abstract

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 the current approach yields very accurate results, in particular compared to known approximations of [BGS03,VW09], and quicker than the iterated integration procedure of [HHL03] or than the binomial tree method of [VN06].

Keywords: equity option, discrete dividend, stochastic approximation, analytic formula

Suggested Citation

Etore, Pierre and Gobet, Emmanuel, Stochastic Expansion for the Pricing of Call Options with Discrete Dividends (October 5, 2010). Available at SSRN: https://ssrn.com/abstract=1687590 or http://dx.doi.org/10.2139/ssrn.1687590

Pierre Etore

affiliation not provided to SSRN ( email )

Emmanuel Gobet (Contact Author)

Ecole Polytechnique, Paris - Centre de Mathematiques Appliquees ( email )

Palaiseau Cedex, 91128
France

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