What is the difference between equilibrium model and no-arbitrage model for short-interest rate?

The equilibrium model and the no-arbitrage model are two different approaches to modeling short-term interest rates in financial mathematics.

1. Equilibrium Model: This model is based on economic theory and it assumes that the current state of the economy is in equilibrium. It tries to model the interest rate by considering various macroeconomic factors like inflation, GDP growth, unemployment rate, etc. The Vasicek and Cox-Ingersoll-Ross (CIR) models are examples of equilibrium models. The main advantage of this model is that it can provide an economic interpretation of the parameters. However, it may not fit the market data well.

2. No-Arbitrage Model: This model, on the other hand, does not rely on any economic theory. Instead, it is based on the principle of no-arbitrage,