# Retrieve zero coupon curve from forwards

Let's suppose I am given a forward swap curve of a certain maturity (10Y). The curve is not very smooth and is decreasing but whatever. I have the curve : $$S(0,t,t+T) = \frac{P(0,t) - P(0,t+T)}{\sum_{k=1...10} P(0,t+k)}$$

My goal is to retrieve a sort of coherent zero coupon curve which replicates the forward curve. I am aware that there are not enough points to allow this. But I am just looking for something working.

I have already tried to calibrate a parametric function (Nelson-Siegel) but the problem is to also produce LIBOR3M forward curve at time 0. When I use this method the LIBOR forward curve is not relevent. I've also tried to add a fictive additionnal curve for LIBOR in the optimization $$L(0,t) = S(0,t,t+T) - (Swap10Y(0) - Libor3M(0)) = 4(\frac{P(0,t)}{P(0,t+3M)}-1)$$ but the optimization is not succesfull

Have you any ideas?

Thank you in advance