Stochastic expansion for the pricing of call options with discrete dividends

Pierre Etoré () and Emmanuel Gobet ()
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Pierre Etoré: MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique
Emmanuel Gobet: MATHFI - Mathématiques financières - LJK - Laboratoire Jean Kuntzmann - UPMF - Université Pierre Mendès France - Grenoble 2 - UJF - Université Joseph Fourier - Grenoble 1 - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - CNRS - Centre National de la Recherche Scientifique

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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: analytic formula; stochastic approximation; discrete dividend; Equity option (search for similar items in EconPapers)
Date: 2012-06
Note: View the original document on HAL open archive server: https://hal.science/hal-00507787v1
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Citations: View citations in EconPapers (2)

Published in Applied Mathematical Finance, 2012, 19 (3), pp.233-264. ⟨10.1080/1350486X.2011.620397⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00507787

DOI: 10.1080/1350486X.2011.620397

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