Robust Methods for Smoothing Outliers in Yield Curves

# Smoothing Term Curve


# Smoothing Term Curve












Assume that we have current month term curve and the curves from the two previous months. The current curve may be shifted from the average of the previous two curve by some value (a parallel shift). The task is to identify outliers on the current curve and if they exist than smooth (interpolate) the outlying points.

I've tackled the problem using first degree derivatives to identify the outliers. The method seem to work well to detect the outliers using the difference of the first derivatives as a sample.

My question relates to smoothing. Using, for instance, of the splines or quadratic interpolation would not work well as I may have two consequative points as outliers. The terms structure consits of only 12 maturities, thus probably using a polynom of a higher degree might do the trick. Do you have any other ideas?

Thanks guys!

## Answer by Helin (score 3)

https://quant.stackexchange.com/a/11512

There are quite a few strategies you could take.

- Use models that are more resistant to noises. As others have already mentioned, parametric models such as Nelson-Siegel or Svensson may do the trick. I have also used Merrill Lynch Exponential Spline Model successfully (http://www.bankofcanada.ca/wp-content/uploads/2010/02/wp04-48.pdf).

- Change your objective function. For example, if you're currently minimizing $$\sum(P_\text{market} - P_\text{model})^2, $$ try minimizing $$\sum |P_\text{market} - P_\text{model}|. $$

- Exclude the outlier altogether. This is actually done quite frequently in practice... For example, most US yield curve models exclude the on-the-run (most recently auctioned issues) and first-off-the-run issues. Some banks also exclude old seasoned bonds as well as "outliers", which are bonds whose prices deviate from the model by a certain amount.

- If you want to be precise, you can introduce hypothetical bonds into the estimation. For example, you can calculate the spreads to a benchmark curve (say swap curve) for the two neighboring bonds; linearly interpolate to get the appropriate spread for the outlier bond; price this bond based on that spread and insert it back into the estimation set.

## Answer by KAT (score 0)

https://quant.stackexchange.com/a/8649

Just off the top of my head I would say that after you identify the outliers you remove them and do spline interpolation on the remaining points.

## Answer by Aksakal almost surely binary (score 0)

https://quant.stackexchange.com/a/10788

use a smoothing spline, there's a ton of literature on the subject, such as this one