Cox–Ingersoll–Ross Model

The Cox–Ingersoll–Ross (CIR) model is a partial equilibrium term structure model that describes the evolution of interest rates. It assumes that interest rates are mean reverting and interest rate volatility is directly related to the level of interest rates.

The CIR model assumes that every individual has to make consumption and investment decisions with their limited capital. Investing in the productive process may lead to higher consumption in the following period, but it requires sacrificing today’s consumption. The individual must determine his or her optimal trade-off assuming that he or she can borrow and lend in the capital market. Ultimately, interest rates will reach a market equilibrium rate at which no one needs to borrow or lend. The CIR model can explain interest rate movements in terms of an individual’s preferences for investment and consumption as well as the risks and returns of the productive processes of the economy.

As a result of this analysis, the model shows how the short-term interest rate is related to the risks facing the productive processes of the economy. Assuming that an individual requires a term premium on the long-term rate, the model shows that the short-term rate can determine the entire term structure of interest rates and the valuation of interest rate–contingent claims.

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