I don’t understand why the Black Scholes model is broken for negative interest rates. There is no such assumption about positivity of the interest rate in BS.

I don’t understand why the Black Scholes model is broken for negative interest rates. There is no such assumption about positivity of the interest rate in BS. The CIR model is broken yes because of the square root, and people started to use the old Vasicek model instead. Nothing in the HJM framework forbids negative interest rates neither. Edit: ah they meant model the IR directly with BS like SDE?