Suppose the current moment is t, the spot interest rate due at t is r, and the spot interest rate due at T * (T * > T) is r *, then T * at t? The forward interest rate rF during the T period shall satisfy the following equation:
rF(T *？ T) = r * (T *？ t)？ r(T？ t) ( 1)
If the equation (1) does not hold, there is arbitrage space.
Right rF(T *? T) = r * (T *？ t)？ r(T？ T) available deformation:
(2)
This is a common formula for calculating the forward interest rate, which can be further deformed.
(3)
If the term structure of spot interest rate is T *? T period inclines upward, that is, r * >；; R, then rF > r *；;
If the term structure of spot interest rate inclines downward during T *-T, that is, R * < R, then RF