Cubic Trigonometric B-spline Collocation Approach for Black-Scholes Method
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O241.8

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    A cubic trigonometric B-spline collocation approach is developed for the numerical solution of Black-Scholes equation governing European option pricing. The Black-Scholes equation is fully-discretized using the cubic trigonometric B-spline collocation for spatial discretization and the forward finite difference for the time discretization. A hybrid difference scheme is obtained by means of parameter θ. According to Von Neumann (Fourier) method, it is shown that the presented scheme is unconditionally stable for 1/2≤θ≤1. A numerical experiment is performed to illustrate the validity and accuracy of the proposed method. Moreover, the numerical results are given to show that it is superior to Crank-Nicolson finite difference method and cubic B-spline collocation approach.

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Cite this article as: WU Bei-Bei, YIN Jun-Feng, JIN Meng. Cubic Trigonometric B-spline Collocation Approach for Black-Scholes Method [J]. J Sichuan Univ: Nat Sci Ed, 2017, 54: 1153.

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History
  • Received:March 05,2017
  • Revised:May 18,2017
  • Adopted:June 22,2017
  • Online: November 13,2017
  • Published: