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

## Author

Listed:
• Ghulam Sorwar

## Abstract

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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File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.531588

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## References listed on IDEAS

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1. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
2. David B. Colwell & Robert J. Elliott, 1993. "Discontinuous Asset Prices And Non-Attainable Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 295-308.
3. Mark Broadie & Jérôme Detemple, 1997. "The Valuation of American Options on Multiple Assets," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 241-286.
4. Chandrasekhar Reddy Gukhal, 2001. "Analytical Valuation of American Options on Jump-Diffusion Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 97-115.
5. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
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### Keywords

Box method; derivatives; Green's theorem;

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