Which variable in the CIR model represents the long-run value of the short-term rate?

In the Cox-Ingersoll-Ross (CIR) model, the parameter that represents the long-run value of the short-term interest rate is denoted as theta. This variable serves as the mean level that the short-term interest rate tends to revert to over time, capturing the idea that interest rates will return to a long-term average despite short-term fluctuations.

The CIR model incorporates a mean-reverting feature where the short-term rate, denoted as r, follows a stochastic process influenced by both the long-run mean (theta) and a volatility factor (sigma). The parameter k represents the speed at which the interest rate reverts to this mean level, emphasizing the relationship between short-term rates and their equilibrium level (theta).

Understanding this relationship is crucial in interest rate modeling, as it helps explain how rates behave over time and aids in pricing fixed-income securities and managing interest rate risk. In summary, theta signifies the theoretical long-run average that the short-term interest rate is expected to approach, highlighting its central role in the dynamics of the CIR model.