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Zbl 1132.91438
Sinkala, W.; Leach, P.G.L.; O'Hara, J.G.
Zero-coupon bond prices in the Vasicek and CIR models: Their computation as group-invariant solutions. (English)
[J] Math. Methods Appl. Sci. 31, No. 6, 665-678 (2008). ISSN 0170-4214; ISSN 1099-1476/e

Summary: We compute prices of zero-coupon bonds in the Vasicek and Cox-Ingersoll-Ross interest rate models [{\it J. C. Cox, J. E. Ingersoll jun.} and {\it 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 2000:: *91B24 Price theory and market structure
22E70 Appl. of Lie groups to physics
35C05 Solutions of PDE in closed form
35K15 Second order parabolic equations, initial value problems
35Q80 Appl. of PDE in areas other than physics

Keywords: Lie symmetry analysis; Vasicek model; Cox-Ingersoll-Ross model; zero-coupon bond; group-invariant solutions; interest rate models; partial differential equations

Citations: Zbl 0576.90006

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