ForwardForward Agreements
A forwardforward agreement is a contract that guarantees a certain interest rate on an investment or a loan for a specified time interval in the future, that begins on one forward date and ends later. It is called a forwardforward interest rate because it is for a time period that both begins and ends in the future. Hence, a forwardforward contract protects against market changes in the interest rates.
A forwardforward is different from other interestrate derivatives. Both forward rate agreements and shortterm interest rate futures can protect against market changes in the interestrate, but they do so by paying the difference between the contract rate and the reference market rate, such as the libor. There are also forwardforward currency swaps, involving the swapping of 1 currency for another at the beginning of the forward period, which is then reversed at maturity.
Forwardforwards have a special notation to designate the future term. For instance, a term that begins in 6 months and ends 1 year later, would be designated as 6 v 18 or 6 × 18. To designate years, a forwardforward term that starts in 2 years and ends 1 year later would be designated as 2 years v 3 years, or 2 years × 3 years.
The forwardforward interestrate is the forward rate for the term of the contract. How is the forward rate determined? Banks generally set forwardforward rates by checking the prices of shortterm interest rate futures, which will allow banks to hedge their interestrate risk. Or they can check the yields on zerocoupon bonds for the forward period.
The forwardforward rates for a range of maturities can be represented by the forwardforward yield curve. The actual spot rates for forward periods cannot be known in advance, but implied forwardforward rates can be constructed by bootstrapping, which starts with shortterm market yields of money market instruments and futures, then uses those values to calculate yields for later periods. From this implied forwardforward yield curve, formulas can be used to calculate forwardforward rates for those periods covered by the yield curve. Forwardforward interest rates covering full years can be calculated by the following formula:
ForwardForward Rate  =  (1 + ZeroCoupon Rate for k Years)^{k} (1 + ZeroCoupon Rate for k + 1 Years)^{(k+1)} 

A forwardforward rate can also be calculated with discount rates for zerocoupon bonds. The discount rate = 1 ÷ (1 + Yield) raised to a power equal to the number of years till maturity.
Discount Rate  =  1 (1+Yield)^{k} 
k = Term in Years 
Thus, the discount rate for a 2year zero with a 2% yield would be:
Discount Rate  =  1 (1+.02)^{2}  =  1/1.0404  ≈  0.961169 
ForwardForward Rate  =  Discount Rate for k Years Discount Rate for k +1 Years  –  1 
ZeroCoupon Yields  

Year 1  4.0%  
Year 2  4.3%  
Year 3  4.6%  
Year 4  5.0%  
ZeroCoupon Discount Rates  
Year 1  0.961538462  = 1/(1+Year 1 Yield) 
Year 2  0.919245226  = 1/(1+Year 2 Yield)^{2} 
Year 3  0.873785727  = 1/(1+Year 3 Yield)^{3} 
Year 4  0.822702475  = 1/(1+Year 4 Yield)^{4} 
ForwardForward Rates  
1 v 2  0.046008654  = 4.6% = (Year 1 Discount) / (Year 2 Discount) – 1 
2 v 3  0.052025912  = 5.2% = (Year 2 Discount) / (Year 3 Discount) – 1 
3 v 4  0.062092012  = 6.2% = (Year 3 Discount) / (Year 4 Discount) – 1 
If the forwardforward term is less than 1 year, as it often is, then the above rate can be modified by multiplying by the number of days in the period divided by the number of days in a year, according to the daycount convention that applies, which is 365 days for sterling and 360 days for all other currencies:
Calculate Using Interest Rates for the ForwardForward Term  Then Annualize the Interest Rates  
ForwardForward Rate  =  [  FF2 FF1  – 1  ]  x  Days in Year Days in ForwardForward Term 

Note that the interest rates in the above formula are annualized.
In this example, market interest rates are used, and since the term is less than 1 year, money market instruments, such as commercial paper, are appropriate. In this example, the interestrate for the 1^{st} date is determined by the market yield on commercial paper with the term equal to the number of days from the agreement date until the 1^{st} date. Likewise, for the 2^{nd} date, using the market yield for commercial paper with the term equal to the number of days from the agreement date until the 2^{nd} date.
Interest Rate till Start of Forward Term  3.0% 
Number of Days till Start of Forward Term  91 
Interest Rate till End of Forward Term  3.3% 
Number of Days till End of Forward Term  183 
Days in Year (DayCount Convention)  360 
Days in ForwardForward Term  92 
ForwardForward Interest Rate  3.57% 
ForwardForward Rate  =  [  (1 + (.033 × 183/360)) (1 + (.03 × 91/360))  – 1  ]  x  360 92 
=  3.57% 