If we have determined the yield curve, then all forward interest rates can be obtained according to the spot interest rate on the yield curve. Therefore, the forward interest rate is not an independent set of interest rates, but closely linked to the yield curve. In mature markets, some forward interest rates can also be directly observed from the market, that is, calculated according to the market price of interest rate forward or futures contracts.
Determination of forward interest rate [1]
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
Forward interest rate formula
If stands for the forward interest rate from t- 1 to t, st stands for the spot interest rate of t, St? 1 stands for the spot interest rate of t- 1 year, and its general calculation formula is:
(4)
For example:
Assuming that the two-year spot interest rate is 5% and the three-year spot interest rate is 6%, what is the forward interest rate from the second year to the third year?
(5)
(6)
f2，3 = 8% (7)
Importance of forward interest rate
In modern financial analysis, forward interest rate is widely used. They can predict the market's expectation of future interest rate trends and have always been a reference tool for the central bank to formulate and implement monetary policy. More importantly, in mature markets, the pricing of almost all interest rate derivatives depends on forward interest rates. Although there are no interest rate derivatives in China at present, with the development of financial globalization, the further expansion of China's opening to the outside world and the comprehensive promotion of interest rate marketization reform, it is imperative to launch these financial instruments.
Forward to forward transaction
1. Long-term loan and short-term loan comprehensive forward transaction
If the actual fund demand period of a company is 6- 12 months in the future, then at 0: 00, the borrower can borrow funds with a term of 12 months and lend funds with a term of 6 months, so that the loan interest rate for the next 6- 12 months can be locked immediately.
For example, a customer borrows $6,543,800+from a bank with a term of 6 months.