Choosing Par, Zero, or Forward Curves for Key Rate Duration

Summary

The document explains that key rate duration or DV01 can be calculated by shocking different representations of the interest-rate curve. The appropriate choice depends on the purpose of the measure and on how the curve is constructed, so there is no single universally correct curve for every use.

For matching bond-index duration statistics, the response recommends par-curve shocks because major index providers have used that convention for option-adjusted duration reporting. It cautions that par-curve shocks can produce counterintuitive effects, while zero-curve shocks tend to be easier to interpret. For hedging, the response suggests considering forward-curve shocks or shocks to the individual instruments used to build the curve. These are practical conventions rather than an exhaustive prescription; the document does not provide formulas, numerical comparisons, or a specific portfolio example.

Key ideas

• Key rate risk can be measured by shocking par, zero, or forward curves.
• The curve choice should reflect the purpose of the risk measure and the curve-building method.
• Par-curve shocks are used to align with reported bond-index duration statistics.
• Zero-curve shocks often produce more intuitive results, though curve choice has consequences.
• Hedging analysis may be better matched to forward rates or the instruments used to build the curve.

Tags

# To compute key rate duration, shall I use par curve or zero curve?


# To compute key rate duration, shall I use par curve or zero curve?












To calculate Key rate duration/Key rate DV01 for bonds, do we move the zero/spot curve or we move the par curve? Or either one is OK? Just want to know the industry standard.

## Answer by Helin (score 3)

https://quant.stackexchange.com/a/33893

You can do either. It depends on what you're trying to do and how you build your curve. If you're trying to match bond index duration, then shocking par curve is the way to go, because index providers, such as Barclays (now Bloomberg Barclays), Citi, and BofAML, all shock the par yield curve when reporting their option-adjusted duration statistics. However, a lot of "weird things" can happen when you do that (see "Duration Anomaly" and "Effective Duration versus Nominal Duration" by Bob Kopprasch); shocking zero curve tends to produce more intuitive results.

For hedging purposes, it may also be advisable to shock the forward curve, or individual input instruments you use to build the curve.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.