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What determines the forward interest rate?
Forward interest rate is determined by a series of spot interest rates.

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