A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model

Author:

Yu Xiwei1,Hu Qing1,Sun Yudong2ORCID

Affiliation:

1. College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China

2. Department of Finance, Guizhou Minzu University, Guiyang 550025, China

Abstract

In this paper, we construct a new numerical algorithm for the partial differential equation of up-and-out put barrier options under the CEV model. In this method, we use the Crank-Nicolson scheme to discrete temporal variables and the cubic B-spline collocation method to discrete spatial variables. The method is stable and has second-order convergence for both time and space variables. The convergence analysis of the proposed method is discussed in detail. Finally, numerical examples verify the stability and accuracy of the method.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Reference24 articles.

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2. Cox, J. (1975). Notes on Option Pricing I: Constant Elasticity of Variance Diffusions, Stanford University, Graduate School of Business. Unpublished Note.

3. Computing the constant elasticity of variance option pricing formula;Schroder;J. Financ.,1989

4. Friedman, A. (2008). Partial Differential Equations of Parabolic Type, Courier Dover Publications.

5. Efficient and high accuracy pricing of barrier options under the CEV diffusion;Thakoor;J. Comput. Appl. Math.,2014

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