# 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!

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Avoid high order polynomials, they can be unstable and are quite likely to give you a lot of overshoot. Splines are piecewise to reduce this risk. –  Phil H Jan 3 at 15:06
You might look into interpolation techniques that incorporate liquidity (assuming you can get the data). This would effectively put less weight on bonds that aren't being actively traded. Liquidity is an important consideration in volatility surfaces so you should be able to find some research on it. Alternately you can try a parsimonious model, like Nelson-Siegel (which there should be some questions about), and take deviations from that to identify outliers. –  John Jan 31 at 22:33