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This paper proposes a defaultable bonds pricing model extending the traditional spread process definition. The posited model is able to incorporate any potential cyclical, non-linear, or long-term process not fully captured by the stochastic behavior of the spot rate and the instantaneous default rate process. Under this framework, we analyze the empirical ability of our model to capture the spread dynamics of three different Investment-grade US Corporate bonds indexes. Our findings show that when compared to the Benchmark, our model improves the empirical performance reducing the yield spread mispricing by 35%, 37%, and 29% for the High grade, Upper medium grade, and Lower medium grade index, respectively. [ABSTRACT FROM AUTHOR]