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Exponential Time Integration and Second‐Order Difference Scheme for a Generalized Black‐Scholes Equation

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  • Zhongdi Cen
  • Anbo Le
  • Aimin Xu

Abstract

We apply an exponential time integration scheme combined with a central difference scheme on a piecewise uniform mesh with respect to the spatial variable to evaluate a generalized Black‐Scholes equation. We show that the scheme is second‐order convergent for both time and spatial variables. It is proved that the scheme is unconditionally stable. Numerical results support the theoretical results.

Suggested Citation

  • Zhongdi Cen & Anbo Le & Aimin Xu, 2012. "Exponential Time Integration and Second‐Order Difference Scheme for a Generalized Black‐Scholes Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:796814
    DOI: 10.1155/2012/796814
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    References listed on IDEAS

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    1. Courtadon, Georges, 1982. "A More Accurate Finite Difference Approximation for the Valuation of Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(5), pages 697-703, December.
    2. 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.
    3. Schwartz, Eduardo S., 1977. "The valuation of warrants: Implementing a new approach," Journal of Financial Economics, Elsevier, vol. 4(1), pages 79-93, January.
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