Forward Rate

# Forward rate

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Description:
The forward rate is the future yield on a bond. It is calculated using the yield curve.

For example, the yield on a three-month Treasury bill six months from now is a forward rate.

## Forward rate calculation

In order to extract the forward rate, one needs the term structure of interest rates. The general formula used to calculate the forward rate is:

[itex]r_ = left( left(frac right) -1right)left( frac right) [/itex]

Where we assume that all involved tenors are at most 1 year (short term rate or linear discount). Use actuarial form for long term rate(>1 year).

[itex]r_ [/itex] is the forward rate between term [itex] t_1 [/itex] and term [itex] t_2 [/itex],

[itex] d_1 [/itex] is the time length between time 0 and term [itex] t_1 [/itex] (in years),

[itex] d_2 [/itex] is the time length between time 0 and term [itex] t_2 [/itex] (in years),

[itex] r_1 [/itex] is the interest rate for the period time 0 to term [itex] t_1 [/itex] ,

[itex] r_2 [/itex] is the interest rate for the period time 0 to term [itex] t_2 [/itex] ,

## Related instruments

A forward discount is when the forward rate of one currency relative to another currency is higher than the spot rate.

A forward premium is when the forward rate of one currency relative to another currency is lower than...

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