# Discrete time Ho lee model

This is my first question in this forum. I am stuck with my current testing the Ho Lee model. I am having difficulty computing the perturbation factor $\Delta$.

The ho lee model should be completely determined by the initial term structure $B(0,1),B(0,2),...$ its risk neutral probability of an up jump $p$ (which is independent of time and should be the same at each node through out the tree), and the perturbation factor $\Delta=\frac{h(1;u)}{h(1;d)}$.

Now I am given the task of knowing the initial term structure $B(0,1),B(0,2),...$, $p$ and short rates $r(0)$ and $r(1;u)$, and have to compute the perturbation factor delta instead. Any help is much appreciated.

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There is a relationship: $\log \delta^{-1} = \frac{\sqrt{Var[r(t)]}}{\sqrt{p(1-p)}}$
To solve for $\delta$ you do need the vol of short rate given initially. What exactly are those $r(1;u)$ that you have? you have a populated interest rate tree?