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Zero-coupon bond prices in the Vasicek and CIR models: their computation as group-invariant solutions. (English) Zbl 1132.91438

Summary: We compute prices of zero-coupon bonds in the Vasicek and Cox-Ingersoll-Ross interest rate models [J. C. Cox, J. E. Ingersoll jun. and S. A. Ross, Econometrica 53, 363–384 (1985; Zbl 0576.90006)] as group-invariant solutions. Firstly, we determine the symmetries of the valuation partial differential equation that are compatible with the terminal condition and then seek the desired solution among the invariant solutions arising from these symmetries. We also point to other possible studies on these models using the symmetries admitted by the valuation partial differential equations.

MSC:

91G30 Interest rates, asset pricing, etc. (stochastic models)
22E70 Applications of Lie groups to the sciences; explicit representations
35C05 Solutions to PDEs in closed form
35K15 Initial value problems for second-order parabolic equations
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences

Citations:

Zbl 0576.90006
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References:

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