## Valuation of two-factor interest rate contingent claims using Green's theorem

### Sorwar, Ghulam ; Barone-Adesi, Giovanni

### In: Applied mathematical finance, 2011, vol. 18, no. 4, p. 277-289

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... Plus

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- 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 paper we demonstrate that using Green’s theorem second order derivatives can be reduced to first order derivatives, that can be easily discretised; consequently two factor partial differential equations are easier to discretise 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 which illustrates that our approach shows excellent agreement with analytical prices and the popular Crank Nicolson method.