What is an equilibrium interest-rate model?

What will be an ideal response?

An equilibrium interest-rate model is a model that seeks to describe the dynamics of the term structure using fundamental economic variables that are assumed to affect the interest-rate process. In the modeling process, restrictions are imposed allowing for the derivation of
closed-form solutions for equilibrium prices of bonds and interest rate derivatives. In these models (1) a functional form of the interest-rate volatility is assumed and (2) how the drift moves up and down over time is assumed. More details are given below.

In characterizing the difference between arbitrage-free and equilibrium models, one can think of the distinction being whether the model is designed to be consistent with any initial term structure, or whether the parameterization implies a particular family of term structure of interest rates. Arbitrage-free models have the deficiency that the initial term structure is an input rather than being explained by the model. Basically, equilibrium models and arbitrage models are seeking to do different things.

To implement an equilibrium model, estimates of the parameters of the assumed interest-rate process are needed, including the parameters of the volatility function for interest rates. These estimated parameters are typically obtained using econometric techniques using historical yield curves without regard to how the final model matches any market prices.