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

Stochastic delay differential equations (SDDE’s) have been used for financial modeling. In this article, we study a CIR process with delay term in drift; in particular, we prove that there exists a unique strong solution and prove that it is positive and integrable. Moreover, we derive a generalization of Feynman-Kac type formula to determine a bond pricing formula when the interest rate follows the delay’s equation. It turns out that the forward rate is an affine function of the rate process with time dependent coefficients, satisfying a system of deterministic differential equations.