Interest rate agreed today for borrowing/lending over a future period [T_1, T_2], implied by spot zero rates: F(0; T_1, T_2) = dfrac1T_2 - T_1left(dfracP(0,T_1)P(0,T_2) - 1right) (simple-compounded). The instantaneous forward rate f(0,T) = -dfracpartial ln P(0,T)partial T is the state variable of the HJM framework. Under the expectations hypothesis, F(0;T_1,T_2) = mathbbE^mathbbQ^T_2[L(T_1;T_1,T_2)] — forwards are martingales under the relevant forward measure (free of risk premium only there).