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With the Fed raising interest rates so fast and so drastically, classical interest rate models such as the Black Karasinski (BK), Hull-White (HW), etc., may have trouble calibrating to current rate levels and at the same time passing backtesting due to resent negative rates,

For example, you can shift BK to capture the past negative rates, but then you fail to capture high-interest rates (even when reasonably increasing the volatility terms)...

I wonder what is being done in practice under the current market environment in industry.

Any suggestions? I appreciate any available references.

Thank you.

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