I think both can happen and here is my reasoning. Please correct me if I am wrong.
During times of increased volatility in the equity market, investors adopt a more risk-averse approach and gravitate towards safer assets (bonds) to safeguard their investments. As a consequence, there is a tendency for interest rates to decrease since demand for bonds increases.
But can increased volatility can actually lead to higher interest rates? This is when investors demand higher risk premiums in order to compensate for the increased risk.
I am confused now. I don't know if I made any logical errors here.