Forward rate

The forward rate (also forward rate ) means an interest rate which applies to a future date. The opposite of the forward interest rate is the spot interest rate, which is effective immediately for a specified term.

In general, the forward rate is not the same as the spot interest rate in seconds for one borrowing or investment to t. In addition, the forward rate must not be a good estimator for this future spot rate.

Preliminary remarks

The listed here formulas for the calculation of interest using the following symbols:

• Spot interest rate ( interest rate for the period between now and the time t:
• Forward rate from s to t:
• Discount factor of time t:

Thus, the following interest rate: the interest rate that applies to a five-year investment that begins to run in two years. The spot interest rate as a special case of the forward interest rate quoted at.

Calculation of cash interest

The forward rate can be calculated from the spot interest rates at different maturities ( yield curve ) clearly. The forward rates are included in the current interest rate structure and implicit. They are called, therefore, implicit interest rates. Since the representation of a yield curve by their discount factors is also possible that forward rates can be calculated from the discount curves. Basis of the calculation is the principle of no arbitrage. The forward rate is synthetically produced ( duplication).

Note that the forward rate of course depends on the chosen interest rate method and the selected Day count.

Discrete return

For discrete interest rate ( given in Zero rates ) applies

Continuous compounding

For continuous compounding (specified in Zero rates ) applies

Example

It should be given the following zero- interest curve:

To prevent arbitrage, the forward rate for the period [1,2 ] must be the same size, that at the present time does not matter whether you invest for 2.0%, the second year forward rate for the first year, or whether one interest both years to 3.0%.

So true: thus, thus R (1,2) = 4.0% applies.

R (2,3) is calculated analogously: so, thus R (2,3) = 5.1% applies.

R ( 3,4 ), so therefore we have R (3,4) = 5.7%.

R ( 4.5 ), so therefore we have R (4,5) = 5.7%.

Overall, therefore, applies

Relationship between zero- yield curve and forward rates

The general formula can be to reshape. From this one sees: valid between s and t that (rising curve - normal case ), then, that the forward rate is greater than zero, both sets. If one has, however, a falling curve, ie, it is also true, the forward rate is therefore smaller than both Zero sets.

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