Stochastic expansion for the pricing of call options with discrete dividends

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].
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Applied Mathematical Finance, Taylor & Francis (Routledge): SSH Titles, 2012, 19 (3), pp.233-264. 〈10.1080/1350486X.2011.620397〉
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https://hal.archives-ouvertes.fr/hal-00507787
Contributeur : Emmanuel Gobet <>
Soumis le : samedi 31 juillet 2010 - 23:31:13
Dernière modification le : mardi 28 octobre 2014 - 18:34:02
Document(s) archivé(s) le : mardi 23 octobre 2012 - 11:56:37

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Pierre Etore, Emmanuel Gobet. Stochastic expansion for the pricing of call options with discrete dividends. Applied Mathematical Finance, Taylor & Francis (Routledge): SSH Titles, 2012, 19 (3), pp.233-264. 〈10.1080/1350486X.2011.620397〉. 〈hal-00507787〉

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