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Valuation of Two-Factor Interest Rate Contingent Claims Using Green's Theorem


  • Ghulam Sorwar
  • Giovanni Barone-Adesi


Over the years a number of two-factor interest rate models have been proposed that have formed the basis for the valuation of interest rate contingent claims. This valuation equation often takes the form of a partial differential equation that is solved using the finite difference approach. In the case of two-factor models this has resulted in solving two second-order partial derivatives leading to boundary errors, as well as numerous first-order derivatives. In this article we demonstrate that using Green's theorem, second-order derivatives can be reduced to first-order derivatives that can be easily discretized; consequently, two-factor partial differential equations are easier to discretize than one-factor partial differential equations. We illustrate our approach by applying it to value contingent claims based on the two-factor CIR model. We provide numerical examples that illustrate that our approach shows excellent agreement with analytical prices and the popular Crank-Nicolson method.

Suggested Citation

  • Ghulam Sorwar & Giovanni Barone-Adesi, 2011. "Valuation of Two-Factor Interest Rate Contingent Claims Using Green's Theorem," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(4), pages 277-289.
  • Handle: RePEc:taf:apmtfi:v:18:y:2011:i:4:p:277-289
    DOI: 10.1080/1350486X.2010.531588

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    Box method; derivatives; Green's theorem;


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