# LO 14.1: Describe the short-term rate process under a model with time-dependent

LO 14.1: Describe the short-term rate process under a model with time-dependent volatility.
This topic provides a natural extension to the prior topic on modeling term structure drift by incorporating the volatility of the term structure. Following the notation convention of the previous topic, the generic continuously compounded instantaneous rate is denoted r and will change (over time) according to the following relationship:
dr = \(t)dt + cr(t)dw
It is useful to note how this model augments Model 1 and the Ho-Lee model. The functional form of Model 1 (with no drift), dr = adw, now includes time-dependent drift and time-dependent volatility. The Flo-Lee model, dr = \(t)dt + crdw, now includes non- constant volatility. As in the earlier models, dw is normally distributed with mean 0 and standard deviation V d t.