Options, Futures, and Other Derivatives, 10th Edition

31.2 ONE-FACTOR MODELS

Equilibrium models usually start with assumptions about economic variables and derive a process for the short rate, r. They then explore what the process for r implies about bond prices and option prices.

In a one-factor equilibrium model, the process for r involves only one source of uncertainty. Usually the process for the short rate is assumed to be stationary in the sense that the parameters of the process are not functions of time. This means that the process we considered earlier can be written as

$$dr=m\left(r\right)dt+s\left(r\right)dz$$

The assumption of a single factor is not as restrictive as it might appear. A one-factor model implies that all rates move in the same direction over any short time interval, but not that they all ...