| Short rate models commonly used are those that lead to affine term structures. We start with one such model, due to Hull and White, which is very popular in practice. We ask the question: what if the real situation is very close, but not exactly the same as the Hull-White model? We consider a slight perturbation of the Hull-White model and identify it by imposing the arbitrage free condition on the derived forward rate process. We apply this to the US bond data and identify the model parameters in that situation.
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