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A predictor-corrector approach for pricing American options under the finite moment log-stable model

Journal Article


Abstract


  • This paper investigates the pricing of American options under the finite moment log-stable (FMLS) model. Under the FMLS model, the price of American-style options is governed by a highly nonlinear fractional partial differential equation (FPDE) system, which is much more complicated to solve than the corresponding Black-Scholes (B-S) system, with difficulties arising from the semi-globalness of the fractional operator, in conjunction with the nonlinearity associated with the early exercise nature of American-style options. Albeit difficult, in this paper, we propose a new predictor-corrector scheme based on the spectral-collocation method to solve for the prices of American options under the FMLS model. In the current approach, the nonlinearity of the pricing system is successfully dealt with using the predictor-corrector framework, whereas the non-localness of the fractional operator is elegantly handled. We have also provided an elegant error analysis for the current approach. Various numerical experiments suggest that the current method is fast and efficient, and can be easily extended to price American-style options under other fractional diffusion models. Based on the numerical results, we have also examined quantitatively the influence of the tail index on American put options.

Authors


  •   Chen, Wenting (external author)
  •   Xu, Xiang (external author)
  •   Zhu , Song-Ping

Publication Date


  • 2015

Citation


  • Chen, W., Xu, X. & Zhu , S. (2015). A predictor-corrector approach for pricing American options under the finite moment log-stable model. Applied Numerical Mathematics, 97 15-29.

Scopus Eid


  • 2-s2.0-84937905377

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4564

Has Global Citation Frequency


Number Of Pages


  • 14

Start Page


  • 15

End Page


  • 29

Volume


  • 97

Place Of Publication


  • Netherlands

Abstract


  • This paper investigates the pricing of American options under the finite moment log-stable (FMLS) model. Under the FMLS model, the price of American-style options is governed by a highly nonlinear fractional partial differential equation (FPDE) system, which is much more complicated to solve than the corresponding Black-Scholes (B-S) system, with difficulties arising from the semi-globalness of the fractional operator, in conjunction with the nonlinearity associated with the early exercise nature of American-style options. Albeit difficult, in this paper, we propose a new predictor-corrector scheme based on the spectral-collocation method to solve for the prices of American options under the FMLS model. In the current approach, the nonlinearity of the pricing system is successfully dealt with using the predictor-corrector framework, whereas the non-localness of the fractional operator is elegantly handled. We have also provided an elegant error analysis for the current approach. Various numerical experiments suggest that the current method is fast and efficient, and can be easily extended to price American-style options under other fractional diffusion models. Based on the numerical results, we have also examined quantitatively the influence of the tail index on American put options.

Authors


  •   Chen, Wenting (external author)
  •   Xu, Xiang (external author)
  •   Zhu , Song-Ping

Publication Date


  • 2015

Citation


  • Chen, W., Xu, X. & Zhu , S. (2015). A predictor-corrector approach for pricing American options under the finite moment log-stable model. Applied Numerical Mathematics, 97 15-29.

Scopus Eid


  • 2-s2.0-84937905377

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4564

Has Global Citation Frequency


Number Of Pages


  • 14

Start Page


  • 15

End Page


  • 29

Volume


  • 97

Place Of Publication


  • Netherlands