Valuation of the American put option as a free boundary problem through a high-order difference scheme
Küçük Resim Yok
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
De Gruyter Open Ltd
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
Valuation of the American options encountered commonly in finance is quite difficult due to the possibility of early exercise alternatives. Since an exact solution for the American options does not exist, effective numerical methods are needed to understand the behavior of option pricing models. Therefore, in this paper, a new approach based on a high-order difference scheme is proposed to discuss the valuation of an American put option as a free boundary problem. Using a front-fixing approach that transforms the unknown free boundary (optimal stopping) into a fixed one, a sixth-order finite difference scheme (FD6) in space and a third-order strong-stability preserving Runge-Kutta (SSPRK3) in time are applied to the model converted to a nonlinear partial differential equation. The computed results revealed that the combined method is seen to attempt to pull up the capacity of the algorithm to achieve higher accuracy. It is seen that the quantitative and qualitative results produced by the method proposed with minimal computational effort are sufficiently accurate and meaningful. Therefore, this article provides some new insights about the physical characteristics of financial problems and such realistic phenomena. © 2021 Walter de Gruyter GmbH, Berlin/Boston.
Açıklama
Anahtar Kelimeler
American put option, free boundary, front-fixing method, high-order difference
Kaynak
International Journal of Nonlinear Sciences and Numerical Simulation
WoS Q Değeri
Q2
Scopus Q Değeri
Q2
