Fitting Yield Curves from Coupon Bond Prices or Yields

# Estimating a Yield Curve in a country without Bond Stripping


# Estimating a Yield Curve in a country without Bond Stripping












I am currently working under estimating a Yield Curve. From my understanding common procedures to construct a yield Curve like Nelson Siegel have the input of a series of different zero rates and maturity pairs and returns a well behaved curve behind it. The zero rates in the united states are obtained from t-bills (that are bullets) and longer t-bonds that pay coupons in the middle, this doesn't seem a problem as you have a stripping program that lets you value each coupon transforming it into a bullet and giving you a zero rate via bootstrapping. The problem is that in my country i only have a very short series of zero coupon bonds and have long term govt securities with coupons. A lack of a stripping program from the central bank makes that the only data i have is the Yield of the bond, but the yield (internal rate of return) has the underlying assumption that you can reinvest each coupon at the actual rate which is a big assumption. I can certainly build a yield curve with the Yields, but doing so grossly underestimates this reinvestment risk and may lead to problems when using the yield curve for interest risk. Is there a procedure for estimating the yield curve in countries without strips?

## Answer by Enrico Schumann (score 5)

https://quant.stackexchange.com/a/46107

You do not need zero rates to estimate a parametric model of the yield curve, such as Nelson-Siegel. Suppose for instance that you have a cross-section of bond prices. Then:

- For given parameters for your yield-curve model, compute yield curve;

- with this yield curve, calculate theoretical bond prices;

- compute discrepancy between theoretical bond prices and observed bond prices.

Or suppose you have a cross-section of yields-to-maturity of bonds. Then:

- For given parameters for your yield-curve model, compute yield curve;

- with this yield curve, calculate theoretical bond prices;

- compute theoretical yields-to-maturity for theoretical bond prices;

- compute discrepancy between theoretical yields-to-maturity and observed yields-to-maturity.

You now have a link between your yield-curve paramaters and goodness-of-fit. You only have to find parameters for the model (step 1) that result in a small discrepancy between model quantities (prices or yields) and observed quantities. So, you put this computation into an objective function and feed it to a numerical optimization procedure.

## Answer by Dimitri Vulis (score 0)

https://quant.stackexchange.com/a/49177

As a further complication, in some countries the taxation and other treatment of zero-coupon bonds differs slightly from coupon bonds - for example, in Brazil LTNs vs. NTN-F's; in Colombia TES Corto Plazo v TES serie B; to a lesser extent in Mexico Cetes v MBONOs, etc. Practically this means that, unlike the U.S., a yield of an old coupon bond with year or less left to maturity will not be consistent with the yields of the zero-coupon bonds. You may prefer to buld two curves, one for zc and the other for coupon bonds, with some spread allowed between them.