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

Author

Listed:
  • Xiwei Yu

    (College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China)

  • Qing Hu

    (College of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China)

  • Yudong Sun

    (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.

Suggested Citation

  • Xiwei Yu & Qing Hu & Yudong Sun, 2023. "A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3979-:d:1243005
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    References listed on IDEAS

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    1. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    2. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-219, March.
    3. Jia‐Hau Guo & Lung‐Fu Chang, 2020. "Repeated Richardson extrapolation and static hedging of barrier options under the CEV model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 974-988, June.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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