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Zero‐coupon bond prices in the Vasicek and CIR models: Their computation as group‐invariant solutions |
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| Authors: | W. Sinkala P. G. L. Leach J. G. O'Hara |
| Affiliation: | 1. Department of Mathematics, Faculty of Science and Engineering, Walter Sisulu University, Private Bag X1, Mthatha 5117, Republic of South Africa;2. School of Mathematical Sciences, Howard College, University of KwaZulu‐Natal, Durban 4041, Republic of South Africa;3. School of Statistics and Actuarial Science, Howard College, University of KwaZulu‐Natal, Durban 4041, Republic of South Africa |
| Abstract: | 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. Copyright © 2007 John Wiley & Sons, Ltd. |
| Keywords: | Lie symmetry analysis Vasicek model Cox– Ingersoll– Ross model zero‐coupon bond group‐invariant solutions interest rate models partial differential equations |