PRICING DOUBLE BARRIER OPTIONS ON HOMOGENEOUS DIFFUSIONS: A NEUMANN SERIES OF BESSEL FUNCTIONS REPRESENTATION

Igor V. Kravchenko (), Vladislav V. Kravchenko (), Sergii M. Torba () and José Carlos Dias
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Igor V. Kravchenko: Instituto Universitário de Lisboa (ISCTE-IUL), Edifício II, Av. Prof. Aníbal Bettencourt, 1600-189 Lisboa, Portugal
Vladislav V. Kravchenko: Departamento de Matemáticas, CINVESTAV del IPN, Unidad Querétaro, Libramiento Norponiente No. 2000, Fracc. Real de Juriquilla, Querétaro, Qro. C.P. 76230, México
Sergii M. Torba: Departamento de Matemáticas, CINVESTAV del IPN, Unidad Querétaro, Libramiento Norponiente No. 2000, Fracc. Real de Juriquilla, Querétaro, Qro. C.P. 76230, México
José Carlos Dias: Instituto Universitário de Lisboa (ISCTE-IUL), Business Research Unit (BRU-IUL), Edifício II, Av. Prof. Aníbal Bettencourt, 1600-189 Lisboa, Portugal

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 06, 1-24

Abstract: This paper develops a novel analytically tractable Neumann series of Bessel functions representation for pricing (and hedging) European-style double barrier knock-out options, which can be applied to the whole class of one-dimensional time-homogeneous diffusions, even for the cases where the corresponding transition density is not known. The proposed numerical method is shown to be efficient and simple to implement. To illustrate the flexibility and computational power of the algorithm, we develop an extended jump to default model that is able to capture several empirical regularities commonly observed in the literature.

Keywords: Double barrier options; default; Neumann series of Bessel functions; Sturm–Liouville equations; spectral decomposition; transmutation operators (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500304

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