Overview
Given a short rate model, specified by the following equation
{% dr(t) = \mu(t, r(t))dt + \sigma(t, r(t))dW(t) %}
An affine term structure model is a model where the prices of zero coupon bonds maturing at time
{% T %}, and valued at time {% t %} is given by
{% p(t, T) = exp[A(t, T) - B(t, T)r] %}
(see bjork pg 377)
Models with an Affine Term Structure
If the coefficients {% \mu %} and {% \sigma %} given above have the following forms,
{% \mu(t, r) = \alpha(t)r + \beta(t) %}
{% \sigma(t, r) = \sqrt{\gamma(t)r + \delta(t)} %}
then the model admits an affine term structure.