[R-sig-finance] swap to forward rates
Thomas Steiner
finbref.2006 at gmail.com
Fri Feb 24 10:49:12 CET 2006
Thanks for your answers David and Kris. I keep on working out the best
solution for me.
> Good luck! This is a very gnarly topic.
Still I did not get the basic message: why should there be different
methods to calculate forward rates from spanning swap rates? I am just
so impressed by the follwoing quote of Rebonato (Interest rate option
models, 2nd ed., p. 15):
In general, n discrete discount factors can allways be found, for any
viable set of n spanning equilibrium swap rates, as the solution of a
linear [n x n] problem.
This result is improtant, not simply because it shows that equilibrium
swap rates are yet another set equivalent quantities that can be used
to describe the yield curve, but because it shows that the somewhat
privileged role enjoyed by forward rates in term structure modelling
might be more the result of historical accident then of some
fundamental finacial reason.
I'd say that this means, that there is ONE way to come from n swap
rates to n (discrete) forward rates. If I want to have more forward
rates or at some other points in time, I totally agree, that you will
need interpolation and that there are many ways to do so.
I think the best way would be to start with n swap rates, get n exact
forward rates and THEN try to interpolate; eg with Nelson-Siegel,
Splines, Vasicek's family or whatsoever.
Thomas
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