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An integral equation approach for the valuation of American-style down-and-out calls with rebates

Journal Article


Abstract


  • In this paper, an integral equation approach is adopted to price American-style down-and-out calls. Instead of using the probability theory as used in the literature, we use the continuous Fourier sine transform to solve the partial differential equation system governing the option prices. As a way of validating our approach, we show that the "early exercise premium representation" for American-style down-and-out calls without rebate can be re-derived by using our approach. We then examine the case that time-dependent rebates are included in the contract of American-style down-and-out calls. As a result, a more general integral representation for the price of an American-style down-and-out call, with the presence of an extra term associated with the rebate, is obtained. Our numerical method based on the newly-derived integral representation appears to be efficient in computing the price and the hedging parameters for American-style down-and-out calls with rebates. In addition, significant effects of rebates on the option prices and the optimal exercise boundaries are illustrated through selected numerical results.

Publication Date


  • 2016

Citation


  • Le, N., Zhu , S. & Lu, X. (2016). An integral equation approach for the valuation of American-style down-and-out calls with rebates. Computers and Mathematics with Applications, 71 (2), 544-564.

Scopus Eid


  • 2-s2.0-84960801528

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5312

Has Global Citation Frequency


Number Of Pages


  • 20

Start Page


  • 544

End Page


  • 564

Volume


  • 71

Issue


  • 2

Place Of Publication


  • United Kingdom

Abstract


  • In this paper, an integral equation approach is adopted to price American-style down-and-out calls. Instead of using the probability theory as used in the literature, we use the continuous Fourier sine transform to solve the partial differential equation system governing the option prices. As a way of validating our approach, we show that the "early exercise premium representation" for American-style down-and-out calls without rebate can be re-derived by using our approach. We then examine the case that time-dependent rebates are included in the contract of American-style down-and-out calls. As a result, a more general integral representation for the price of an American-style down-and-out call, with the presence of an extra term associated with the rebate, is obtained. Our numerical method based on the newly-derived integral representation appears to be efficient in computing the price and the hedging parameters for American-style down-and-out calls with rebates. In addition, significant effects of rebates on the option prices and the optimal exercise boundaries are illustrated through selected numerical results.

Publication Date


  • 2016

Citation


  • Le, N., Zhu , S. & Lu, X. (2016). An integral equation approach for the valuation of American-style down-and-out calls with rebates. Computers and Mathematics with Applications, 71 (2), 544-564.

Scopus Eid


  • 2-s2.0-84960801528

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5312

Has Global Citation Frequency


Number Of Pages


  • 20

Start Page


  • 544

End Page


  • 564

Volume


  • 71

Issue


  • 2

Place Of Publication


  • United Kingdom