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A decomposition approach via Fourier sine transform for valuing American knock-out options with rebates

Journal Article


Abstract


  • We present an innovative decomposition approach for computing the price and

    the hedging parameters of American knock-out options with a time-dependent rebate.

    Our approach is built upon: (i) the Fourier sine transform applied to the

    partial differential equation with a finite time-dependent spatial domain that governs

    the option price, and (ii) the decomposition technique that partitions the price of the

    option into that of the European counterpart and an early exercise premium. Our

    analytic representations can generalize a number of existing decomposition formulas

    for some European-style and American-style options. A complexity analysis of the

    method, together with numerical results, show that the proposed approach is significantly

    more efficient than the state-of-the-art adaptive finite difference methods,

    especially in dealing with spot prices near the barrier. Numerical results are also

    examined in order to provide new insight into the significant effects of the rebate on

    the option price, the hedging parameters, and the optimal exercise boundary.

    Keywords. American barrier options, decomposition, Fourier sine transform, rebate,

    optimal exercise boundary, heat equation, time-dependent spatial domain.

Authors


  •   Le, Nhat Tan (external author)
  •   Dang, Duy-Minh (external author)
  •   Khanh, Tran Vu

Publication Date


  • 2017

Citation


  • Le, N., Dang, D. & Khanh, T. (2017). A decomposition approach via Fourier sine transform for valuing American knock-out options with rebates. Journal of Computational and Applied Mathematics, 317 652-671.

Scopus Eid


  • 2-s2.0-85009074951

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6360

Number Of Pages


  • 19

Start Page


  • 652

End Page


  • 671

Volume


  • 317

Abstract


  • We present an innovative decomposition approach for computing the price and

    the hedging parameters of American knock-out options with a time-dependent rebate.

    Our approach is built upon: (i) the Fourier sine transform applied to the

    partial differential equation with a finite time-dependent spatial domain that governs

    the option price, and (ii) the decomposition technique that partitions the price of the

    option into that of the European counterpart and an early exercise premium. Our

    analytic representations can generalize a number of existing decomposition formulas

    for some European-style and American-style options. A complexity analysis of the

    method, together with numerical results, show that the proposed approach is significantly

    more efficient than the state-of-the-art adaptive finite difference methods,

    especially in dealing with spot prices near the barrier. Numerical results are also

    examined in order to provide new insight into the significant effects of the rebate on

    the option price, the hedging parameters, and the optimal exercise boundary.

    Keywords. American barrier options, decomposition, Fourier sine transform, rebate,

    optimal exercise boundary, heat equation, time-dependent spatial domain.

Authors


  •   Le, Nhat Tan (external author)
  •   Dang, Duy-Minh (external author)
  •   Khanh, Tran Vu

Publication Date


  • 2017

Citation


  • Le, N., Dang, D. & Khanh, T. (2017). A decomposition approach via Fourier sine transform for valuing American knock-out options with rebates. Journal of Computational and Applied Mathematics, 317 652-671.

Scopus Eid


  • 2-s2.0-85009074951

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6360

Number Of Pages


  • 19

Start Page


  • 652

End Page


  • 671

Volume


  • 317