# Constructing NS-Svensson parameters with zero coupon AND coupon bonds

I am in the process of calculating sovereign zero coupon yield curves using the NS-Svensson parameter for a number of countries. Due to data constraints, I would like to use the information from price data of both zero coupon and coupon bonds for the construction of the curves.

I had a look into different statistical packages (notably termstrc in R and IRFunctionCurve.fitSvenssonin Matlab), where some appear to be able to cope with the optimization across the two asset classes and others restrict themselves to Coupon bonds.

Ignoring for now the question which packages dominates others in terms of implemention, is there any conceptual problem in optimizing the parameters of the model over both asset classes?

• From a conceptual point of view, there is really no distinguishing coupon bearing bonds from from non-coupon bearing bonds, as long as other characteristics surrounding the bonds are equal (most commonly optionality), since a zero-coupon bond is really just a special case of the coupon-bearing bond. Since you would typically derive your zero coupon curve by minimizing model dirty price to observed dirty price, I see no issues in terms of modelling either. – Physcs Envy Jul 31 '15 at 18:20

Nowadays, government yield curves are customarily built with only coupon bonds. Zero coupon bonds (i.e., STRIPS in the US) are much less liquid compared with coupon Treasuries, and tend to trade very differently. If you plot a zero curve implied by coupon Treasuries vs yields of STRIPS, you'll notice that they can differ quite a bit in certain parts of the curve. If you include both coupon bonds and zeros, you'd get an "in-between" curve between the two very segmented markets.

Mechanically, as @Physcs Envy mentioned, there's no point in differentiating the two though. The curve fitting process can proceed with both in exactly the same fashion. After all, zero coupon bonds are simply coupon bonds with coupon rate of 0%.