I need some help with the following question: If the forward rates at \(30/9/2015\) are as follows: Year Rate \(1\) \(-0.076\%\) (negative) \(2\) \(-0.053\%\) (negative) \(3\) \(\;0.020\%\) \(4\) \( \;0.125\%\) Then find the forward rate \(i\) for Year \(1\), but starting at \(1/01/2016\). I tried working over two years: from \(30/9/2015\) to \(30/9/2017\) \[ (1+(-0.076\%))^{1/4}(1+i)^{1}(1+(-0.0299947\%))^{3/4}=(1+(-0.053\%))^2\Rightarrow i=0.064536\%. \] I obtained the \(-0.0299947\%\) from the \(-0.076\%\) and \(-0.053\%\). Thanks a lot!
Unusual question. Assume we have to assume that rates are constant within each period - which seems to then contradict working out rates for overlapping periods. Are those interest rates really %s? ie 0.076% and not 7.6%? Anyway, if the rates given in the question are forward rates then I think you are using them incorrectly as spot rates. -0.053% is the 1-year forward rate from time 1?? So you could use \[ (1+(-0.076\%))^{3/4}(1+(-0.053\%))^{1/4}=(1+ i) \]
