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Embedding the Vasicek model into the Cox–Ingersoll–Ross model |
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| Authors: | W Sinkala P G L Leach J G O'Hara |
| Institution: | 1. Department of Applied Mathematics, Faculty of Science, Engineering and Technology, Walter Sisulu University, Private Bag X1, Mthatha 5117, Republic of South Africa;2. School of Mathematical Sciences, University of KwaZulu‐Natal, Private Bag X54001, Durban 4000, Republic of South Africa;3. Centre for Computational Finance and Economic Agents, University of Essex, Colchester CO4 3SQ, U.K. |
| Abstract: | The Cox–Ingersoll–Ross (CIR) model and the Vasicek model are two well‐known single factor models of the interest spot rate. In this paper, we construct a mapping by means of which the price of a zero‐coupon bond in the CIR model may be obtained from a corresponding price in the Vasicek model. We use symmetry analysis to construct this mapping and verify it by transforming three arbitrary solutions of the pricing equation in the Vasicek model into solutions of the corresponding equation in the CIR model. Copyright © 2010 John Wiley & Sons, Ltd. |
| Keywords: | lie symmetry analysis Vasicek model Cox– Ingersoll– Ross model zero‐coupon bond interest rate model partial differential equation financial mathematics |