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A Mellin transform approach to barrier option pricing

Journal Article


Abstract


  • © 2019 The Author(s). 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.

UOW Authors


  •   Guardasoni, Chiara (external author)
  •   Rodrigo, Marianito R.
  •   Sanfelici, Simona (external author)

Publication Date


  • 2020

Citation


  • Guardasoni, C., Rodrigo, M. & Sanfelici, S. (2020). A Mellin transform approach to barrier option pricing. IMA Journal of Management Mathematics, 31 (1), 49-67.

Scopus Eid


  • 2-s2.0-85079232294

Number Of Pages


  • 18

Start Page


  • 49

End Page


  • 67

Volume


  • 31

Issue


  • 1

Place Of Publication


  • United Kingdom

Abstract


  • © 2019 The Author(s). 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.

UOW Authors


  •   Guardasoni, Chiara (external author)
  •   Rodrigo, Marianito R.
  •   Sanfelici, Simona (external author)

Publication Date


  • 2020

Citation


  • Guardasoni, C., Rodrigo, M. & Sanfelici, S. (2020). A Mellin transform approach to barrier option pricing. IMA Journal of Management Mathematics, 31 (1), 49-67.

Scopus Eid


  • 2-s2.0-85079232294

Number Of Pages


  • 18

Start Page


  • 49

End Page


  • 67

Volume


  • 31

Issue


  • 1

Place Of Publication


  • United Kingdom