Discounted bond price martingale
= Discounted bond price martingale
{title2=$D_tP(t,T)=P(0,T)\mathcal E(-\int_0^\cdot b_s^T dW_s)_t$}
In the one-factor <Heath-Jarrow-Morton model>, put $b_t^T=\int_t^T\sigma(t,u)du$. The <Itô formula> gives $dP/P=r_tdt-b_t^TdW_t$. Thus multiplying by the <discount factor> yields the displayed <stochastic exponential>. Bounded forward volatility on a finite maturity horizon implies the <Novikov condition>, so the discounted bond is a true <martingale>.