I am new to quantitative finance.
We know that in the CIR model the short rate can't go negative. My question then concerns calibration of CIR to a ZCB yield curve. Is it (and why?) possible to calibrate the CIR model to a yield curve with negative yields in the short end? Why (or why not) is this possible, when the short rate can't go negative?
There is probably something conceptual I have missed about the relationship short rates and yields.