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Numerical pricing of American put options on zero-coupon bonds. (English) Zbl 1057.91039

It is well-known that American options can only be evaluated numerically with few exceptions. While there has been a large literature dealing with numerical methods for American options on stocks, there are not many papers for American options on default-free bonds. In this paper the authors propose and analyse two types of numerical methods for pricing American put options on zero-coupon bonds under the Cox-Ingersoll-Ross model: Finite Volume Method (FVM) and Finite Element Method (FEM). The FVMs considered here are different from previous ones in two aspects: more general discretization schemes in time are considered, e.g., the Crank-Nicholson scheme and discrete linear complementary problems are written in symmetric forms and thus can be solved exactly and rapidly by using the Brennan-Schwartz algorithm instead of the projected iteration process. The FEMs are based on a new formulation of the originally free boundary problem by introducing transforms. The degenerate factor in the highest order derivative term is removed. Thus the FEMs are numerically stable in a stronger sense. Stability and convergence for both methods are established. Numerical examples show that the methods provide very accurate approximations of the options prices.

MSC:

91B28 Finance etc. (MSC2000)
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