Overview
The Ho and Lee short rate model is given by the following equation.
{% dr = \theta (t) dt + \sigma dW %}
Zero Coupon Bond Price
The Ho-Lee model admits a affine term structure solution to the price of a zero coupon bond.
{% p(t, T) = exp[A(t, T) - B(t, T)r] %}
where
{% B = T-t %}
{% \displaystyle A(t,T) = \int_t^T \theta(s)(s-T)ds + \frac{1}{6} \sigma^2 (T-t)^3 %}
see wilmott 16.6.3
Calibration
{% \theta (t) = \sigma^2 t + \frac{\partial f(t)}{\partial T} %}
where {% f(t) %} is the current instantaneous forward rate at time {% t %}.