Forward interest rate formula
Description of the Forward interest rate formula
Formula for the calculation of a forward interest rate between dates \( t_{1} \) and \( t_{2} \).
Formula
\[ r_{t_{1,2}} = \left [ \frac{\left (1+ \left ( r_{t_{0,2}} \times \frac{n_{t_{0,2}}}{d_{base}} \right ) \right )}{\left (1+ \left ( r_{t_{0,1}} \times \frac{n_{t_{0,1}}}{d_{base}} \right ) \right )} -1 \right ] \times \left( \frac{d_{base}}{n_{t_{1,2}}}\right ) \ \]
Symbols
\(d_{base}\ \)
Number of days per year (360, 365 or 366 depending on day-count convention)
\(n_{t_{0,1}}\ \)
Number of days between the calculation date $t_{0}$ and date $t_{1}$
\(n_{t_{0,2}}\ \)
Number of days between the calculation date $t_{0}$ and date $t_{2}$
\(n_{t_{1,2}}\ \)
Number of days between date $t_{1}$ and date $t_{2}$
\(r_{t_{0,1}}\ \)
Interest rate for the period between the calculation date $t_{0}$ and date $t_{1}$
\(r_{t_{0,2}}\ \)
Interest rate for the period between the calculation date $t_{0}$ and date $t_{2}$