Hi all,

I am currently building a multicurve calibrator based in OIS discounting using a multi-dimensional Newton-Raphson (in the past I would have said that I am "building" my curves but in the new framework it seems more reasonable to say that I am "calibrating" my curves).

The functions that I am plugging into my solver are those that calculate the PV of the instruments I use to build my curve, e.g. OIS swaps, Libor-OIS basis swaps, tenor swaps, IRS, FRAs, Futures, etc etc. To introduce some simple notation and make the question a bit clearer, let F be the vector of functions that are passed to the solver, and x the vector of unknowns (roots) to be calculated by the solver (discount factors and forward rates essentially).

Many of my discount factors and forward rates are dependant on different interpolating procedures (splines, linear interpolation, tensor splines, etc). The question is: do I have to include these (interpolated) discount factors in x, and thus also all equations that form my interpolation in F? In other words, if I assume my discount curve is formed of splines, do I have to include my spline-constructor equations inside my root solver too and solve for everything simultaneously?

I would like to think that I don't have to and that I can somehow get that problem out of the solver, but then again my spline coefficients are dependant on how the values of x are being calculated in each iteration of Newton-Raphson...  Any ideas or tips are welcome.

I would expect that you'd have to do a global solve across everything: if you change a spline level at time T+X, it will affect levels at times earlier than T, and I can't see how else you would cater for this.