Zero-coupon bond prices in the Vasicek and CIR models: Their computation as group-invariant solutions

We compute prices of zero-coupon bonds in the Vasicek and Cox-Ingersoll-Ross interest rate models 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.