Hi all,
does anybody know what type of end conditions does the SAP-implementation for interpolating with cubic splines use?
There are different types of cubic splines such as "clamped spline", "natural spline", "not-a-knot", etc. And depending on what type of splie is chosen, one have to chose the apporpriate end conditions. The natural splines, for example, assume that the curvature beyond the first and last sampling points is equal to 0 and thus the second derivations at these two Points are equal to 0.
Reading the online SAP documentation I can only infer that SAP uses the "natural splines" function. ("If the term of a required interest rate is before the first or after the last grid point, the first or the last grid point is transferred (extrapolation).")
However, computing the example given at
http://help.sap.com/saphelp_46c/helpdata/en/42/a3dc17fed111d2b4880060941936e3/content.htm
with other existing implementations of natural cubic splines and interpolating at P_{731 }yields a different result for the interpolation at 731:
SAP: P_{731}= 0.062503419
Other implementations: P_{731}= 0.06218164394642542
My read is that SAP uses a quite different end conditions or type of cubic-splines.
I'll be glad of any help or suggestions.
Thank you in advance.
Kind Regards,
Ivaylo