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Let us assume we have a LIBOR 3M curve and that I would like to introduce a small shock up/down of 1bp at a certain point along the curve. I am trying to find out what the best and most efficient way is of doing this, but so far I haven't found a standard approach to be followed.

My yield curve is made of cubic splines, and so shifting a point up by 1bp might cause my curve to suffer from unrealistic/undesirable twists around the point in question, rendering the new curve useless.

A different approach I have thought of could be shifting up the point by 1bp and then perform linear interpolation in that local area. Thus, if we shift the point at t(i) and I have t(i-1) < t(i) < t(i+1), then I would do linear interpolation for the points between t(i-1) and t(i+1).

Has anyone had to solve this problem before? What would be the best approach without making the new curve look funny?

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The new curve will look a bit strange no matter how you do it, although 1bp is not such a big move that will render it "useless". Two ways of doing it, as you point out, are (a) use a spline method, which will do whatever it will do, including moving some points that are far away from the point in question, and (b) do some linear interpolation, as you specify. The practical effect of this choice is that your hedges look very different. For example, if you do a swap with maturity t(i-0.5), under the second method the hedge will be a mixture of t(i-1) swaps and t(i) swaps, whereas under the first method the hedge could contain swaps from all over the curve in various amounts. This is a matter of preference. Some poeple like the simplicity of (b), but I like (a) better myself.

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