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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 [{\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.

91B24Price theory and market structure
22E70Applications of Lie groups to physics; explicit representations
35C05Solutions of PDE in closed form
35K15Second order parabolic equations, initial value problems
35Q80Applications of PDE in areas other than physics (MSC2000)
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