Extrapolation

The system performs extrapolation on the completed yield curve if an interest rate or discount factor is requested for a term that is longer than the longest term of all the grid points on the yield curve.

In Customizing for the yield curve, you can choose between the following procedures:

1. Keep continuous compounding zero rate constant

   The system assumes that the continuous compounding zero rate for terms in the extrapolated part of the curve are exactly the same as the last continuous compounding zero rate that actually exists in the yield curve.

   The equation depicted in the figure below applies:

   
   
   

2. Keep par interest rate constant

   The system assumes that the last par interest rate available in the yield curve, converted into a continuous compounding rate, is exactly the same as the continuous compounding forward rate in the extrapolated part of the curve. This means that the par interest rates are practically constant for terms in the extrapolated part of the curve. However, it does not mean that the par interest rates in the extrapolated part of the curve are exactly the same as the par interest rate of the last grid point. The system carries out the following calculation steps:

   • Calculate the par interest rate on the basis of the yield curve conditions set for the last yield curve interest grid point (for more information, see Calculation of Interest Rates from the Yield Curve Created).

     Note

     If you have only selected the characteristic value One Interest Payment At The End of The Term for the key figure Zero Interest Rate in Customizing for the yield curve, the system assumes, in contrast to this setting, a payment frequency of one year for the par interest rate to be kept constant.

   • Convert the par interest rate P to a continuous compounding representation (m = number of interest payments per year) and calculate the factor F as depicted in the figure below:

     
     
     

   • Calculate the discount factor d(T), as illustrated in the figure below:

     
     
     

   • Calculate the continuous compounding zero interest rate, as illustrated in the figure below:

     
     
     

3. Keep continuous compounding forward rate constant

   The system assumes that the continuous compounding forward rate of the last grid point in the yield curve is exactly the same as the continuous compounding forward rate in the extrapolated part of the curve. The system carries out the following calculation steps:

   • Determine how the interpolation lines increase between the penultimate and last yield curve grid points, as illustrated in the figure below:

     
     
     

   • Calculate the continuous compounding forward rate at the last yield curve grid point, as illustrated in the figure below:

     
     
     

   • Calculate the continuous compounding zero interest rate, as illustrated in the figure below: