Ho-Lee and Hull-White Extended Vasicek/CIR: Derivation of the Drifts using HJM

Derives the drift function of Ho-Lee and Hull-White Extended Vasicek using HJM framework. Include the Hull White extended CIR as an exercise, which you should be able to derive easily once you understand the idea. Here is the outline of the content by timeline:

0:32/15:01: A quick recap of the Merton, Vasicek, and CIR dynamics
3:56/15:01: Explain the purpose of the extended versions
6:00/15:01: Derive the connection between the dynamics of the instantaneous forward and the short rate
07:54/15:01: Shows how to express the three short rate models in the HJM form
09:13/15:01: Use the HJM form of the Merton model to infer the drift of the Ho Lee model
11:13/15:01: Use the HJM form of the Vasicek model to infer the drift of the Hull White extended model
14:31/15:01: Outline the exercise to do the same for the CRR