Editing Hull–White model (section)

===Two-factor model===
The two-factor Hull–White model {{harvcol|Hull|2006|pp=657–658}} contains an additional disturbance term whose mean reverts to zero, and is of the form:

:<math>d\,f(r(t)) = \left [\theta(t) + u - \alpha(t)\,f(r(t))\right ]dt + \sigma_1(t)\, dW_1(t),</math>

where <math>\displaystyle f</math> is a deterministic function, typically the identity function (extension of the one-factor version, analytically tractable, and with potentially negative rates), the natural logarithm (extension of the [[Black–Karasinski model]], not analytically tractable, and with positive interest rates), or combinations (proportional to the natural logarithm on small rates and proportional to the identity function on large rates); and <math>\displaystyle u</math> has an initial value of 0 and follows the process:

:<math>du = -bu\,dt + \sigma_2\,dW_2(t)</math>