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A hybrid finite difference scheme for pricing Asian options

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  • Cen, Zhongdi
  • Xu, Aimin
  • Le, Anbo

Abstract

In this paper we apply a hybrid finite difference scheme to evaluate the prices of Asian call options with fixed strike price. We use the Crank–Nicolson method to discretize the time variable and a hybrid finite difference scheme to discretize the spatial variable. The hybrid difference scheme uses the central difference approximation whenever the mesh points are sufficiently away from the left-hand side of the domain to ensure the stability of the scheme; otherwise a midpoint upwind difference scheme is used. The matrix associated with the discrete operator is an M-matrix, which ensures that the spatial discretization scheme is maximum-norm stable. It is proved that the scheme is second-order convergent with respect to both time and spatial variables. Numerical experiments support these theoretical results.

Suggested Citation

  • Cen, Zhongdi & Xu, Aimin & Le, Anbo, 2015. "A hybrid finite difference scheme for pricing Asian options," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 229-239.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:229-239
    DOI: 10.1016/j.amc.2014.12.007
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    References listed on IDEAS

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    1. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    2. Jérôme Barraquand & Thierry Pudet, 1996. "Pricing Of American Path‐Dependent Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 17-51, January.
    3. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
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    Cited by:

    1. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    2. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de Opciones Call Asiáticas Promedio Aritmético bajo Movimiento Browniano Logístico," Working Papers 46, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.
    3. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de opciones call asiáticas Promedio Aritmético usando Taylor Estocástico 1.5," Working Papers 44, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.

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