Forward Rate

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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:

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).

<math>r_ </math> is the forward rate between term <math> t_1 </math> and term <math> t_2 </math>,

<math> d_1 </math> is the time length between time 0 and term <math> t_1 </math> (in years),

<math> d_2 </math> is the time length between time 0 and term <math> t_2 </math> (in years),

<math> r_1 </math> is the interest rate for the period time 0 to term <math> t_1 </math> ,

<math> r_2 </math> is the interest rate for the period time 0 to term <math> t_2 </math> ,

## 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...

Read More

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

- <math>r_ = left( left(frac right) -1right)left( frac right) </math>

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).

<math>r_ </math> is the forward rate between term <math> t_1 </math> and term <math> t_2 </math>,

<math> d_1 </math> is the time length between time 0 and term <math> t_1 </math> (in years),

<math> d_2 </math> is the time length between time 0 and term <math> t_2 </math> (in years),

<math> r_1 </math> is the interest rate for the period time 0 to term <math> t_1 </math> ,

<math> r_2 </math> is the interest rate for the period time 0 to term <math> t_2 </math> ,

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...

Read More

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