If the basis-point volatility is zero, this means there is no uncertainty or variability in the change of the short rate, implying that the short rate is constant. Given the condition that the short rate is initially zero and the drift is positive, the short rate will always be non-negative. The reason for this is that the drift term represents the expected change in the short rate. If the short rate is zero and the drift is positive, this suggests that the short rate is expected to increase. But with zero volatility, there's no variability around this expectation, so the short rate will remain at zero or increase, but it will never go negative.

Things to Remember

• Interest Rate Models (IRMs) are used to model the evolution of interest rates over time.
• Short rate is the instantaneous interest rate at a specific point in time.
• Drift in interest rate models represents the expected change in the short rate over time.
• Volatility in interest rate models represents the uncertainty or variability in the change of the short rate.
• When volatility is zero, there is no randomness or variability in the short rate movement.
• Positive drift implies an expected increase in the short rate over time.
• Long rate is the average interest rate over a longer period of time.