A Mellin transform approach to barrier option pricing. (20th December 2018)

• Record Type: Journal Article
• Authors: Guardasoni, Chiara; Rodrigo, Marianito R; Sanfelici, Simona
• Is Part Of: IMA journal of management mathematics. Volume 31:Number 1(2020)
• Page Start: 49
• Page End: 67
• Publication Date: 2018-12-20
• Subjects: barrier options -- partial differential equations -- Mellin transform; Management -- Mathematical models -- Periodicals; Management science -- Mathematical models -- Periodicals; Business mathematics -- Periodicals; 650.01513
• DOI: 10.1093/imaman/dpy016
• Languages: English
• ISSNs: 1471-678X

Abstract

Abstract: A barrier option is an exotic path-dependent option contract that, depending on terms, automatically expires or can be exercised only if the underlying asset ever reaches a predetermined barrier price. Using a partial differential equation approach, we provide an integral representation of the barrier option price via the Mellin transform. In the case of knock-out barrier options, we obtain a decomposition of the barrier option price into the corresponding European option value minus a barrier premium. The integral representation formula can be expressed in terms of the solution to a system of coupled Volterra integral equations of the first kind. Moreover, we suggest some possible numerical approaches to the problem of barrier option pricing.