On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-05-28
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
This paper develops and analyses a Crank–Nicolson fitted finite volume method to price American options on a zero-coupon bond under the Cox–Ingersoll–Ross (CIR) model governed by a partial differential complementarity problem (PDCP).
Based on a penalty approach, the PDCP results in a nonlinear partial differential equation (PDE).
We then apply a fitted finite volume method for the spatial discretization along with a Crank–Nicolson time-stepping scheme for the PDE, which results in a nonlinear algebraic equation.
We show that this scheme is consistent, stable, and monotone, and hence, the convergence of the numerical solution to the viscosity solution of the continuous problem is guaranteed.
To solve the system of nonlinear equations effectively, an iterative algorithm is established and its convergence is proved.
Numerical experiments are presented to demonstrate the accuracy, efficiency, and robustness of the new numerical method.
American Psychological Association (APA)
Gan, Xiaoting& Xu, Dengguo. 2020. On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1193011
Modern Language Association (MLA)
Gan, Xiaoting& Xu, Dengguo. On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options. Mathematical Problems in Engineering No. 2020 (2020), pp.1-13.
https://search.emarefa.net/detail/BIM-1193011
American Medical Association (AMA)
Gan, Xiaoting& Xu, Dengguo. On the Convergence of a Crank–Nicolson Fitted Finite Volume Method for Pricing American Bond Options. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1193011
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1193011