Affine term structure model

An affine term structure model is a specific type of financial model which relates zero coupon bond prices (i.e. the discount curve) to a spot rate model. It is particularly useful for inverting the yield curve - the process of determining spot rate model inputs from observable bond market data.

Background

Start with a stochastic short rate model $r(t)$ with dynamics

$dr(t)=\mu (t,r(t))dt+\sigma (t,r(t))dW(t)$

and a risk-free zero-coupon bond maturing at time $T$ with price $p(t,T)$ at time $t$. If

$p(t,T)=F^{T}(t,r(t))$

and F has the form

$F^{T}(t,r)=e^{A(t,T)-B(t,T)r}$

where $A$ and $B$ are deterministic functions, then the short rate model is said to have an affine term structure.