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.
A Mellin transform approach to barrier option pricing / Guardasoni, Chiara; Rodrigo, Marianito R.; Sanfelici, Simona. - In: IMA JOURNAL OF MANAGEMENT MATHEMATICS. - ISSN 1471-6798. - 31:1(2018), pp. 49-67. [10.1093/imaman/dpy016]
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