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Stochastic delay differential equations (SDDE's) have been used for financialmodeling. In this article, we study a SDDE obtained by the equation of a CIRprocess, with an additional fixed delay term in drift; in particular, we provethat there exists a unique strong solution (positive and integrable) which wecall fixed delay CIR process. Moreover, for the fixed delay CIR process, wederive a Feynman-Kac type formula, leading to a generalized exponential-affineformula, which is used to determine a bond pricing formula when the interestrate follows the delay's equation. It turns out that, for each maturity time T,the instantaneous forward rate is an affine function (with time dependentcoefficients) of the rate process and of an auxiliary process (also dependingon T). The coefficients satisfy a system of deterministic delay differentialequations.

A Feynman-Kac type formula for a fixed delay CIR model