Choosing Curves to Shift for Swap DV01
Summary
The document explains that swap DV01 depends on which market curve or input rates are shocked. In older single-curve practice, the floating forecast curve was commonly used because the fixed-leg par curve was treated as a quoting construct. With collateralized, post-crisis valuation, forecast and discount curves both affect value, so sensitivities are often reported separately for each relevant curve.
One practical approach is to bump the market instruments used to build a curve, rebuild it, and reprice the swap. This measures sensitivity to tradable inputs, though the resulting shock is not a perfectly parallel shift in zero or par rates. Traders may focus on forecast-curve exposure for short-term hedging while also monitoring discount-curve and cross-currency collateral effects. The document emphasizes that conventions vary, so a DV01 number is meaningful only when its curve and bump method are specified.
Key ideas
- DV01 measures sensitivity to a specified market yield or curve input, so the shocked curve must be identified.
- Single-curve conventions often focused on the floating forecast curve.
- Multi-curve valuation creates distinct forecast-curve and discount-curve sensitivities.
- Bumping curve-building instruments and rebuilding the curve ties risk measures to tradable market inputs.
- Instrument bumps do not necessarily create a parallel shift in zero rates or par rates.
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Full text
# What curve are you shifting when you calculate DV01 for a swap?
# What curve are you shifting when you calculate DV01 for a swap?
I understand that a general swap has 4 curves attached to it: the flat forecast curve associated with the fixed leg, the forecast curve associated with the floating leg, the fixed leg discount curve and the floating leg discount curve.
I also understand that $DV01 = \dfrac{\partial V_{swap}}{\partial y}$, where $y$ is the yield.
What I don't understand is which curve(s) is the $y$? Which curve are we shifting by $1bp$ to calculate the $DV01$?
## Answer by Fred (score 6, accepted)
https://quant.stackexchange.com/a/35282
Let's step back and look at the reason for making a DV01 calculation first before answering the question; The reason for making a DV01 calculation is to quantify what market movements has impact on the valuation of the trade.
Since the 'flat' forecast curve won't be affected by market movements the answer is (using pre-2008 methodology): The floating forecast curve.
After 2008 the discount curves became more important regarding the valuation as the previous standard to discount on the floating forecast curve (aka. IBOR-curve) was replaced by discounting on OIS (Overnight Index Swap)-curves or discount curves based on the collateral posted by the trade counter party.
In such a case DV01 would be calculated for the forecast curve, and for the discounting curve (which should be the same for both legs of the swap as long as both legs are in the same currency), resulting in two DV01 measurements.
## Answer by Helin (score 3)
https://quant.stackexchange.com/a/35266
The short answer is that there's no consensus. A popular method is to shock each input instrument by 1 bp (i.e., change the futures rate by 1bp, the swap rates by 1bp, OIS rates by 1bp, etc.), rebuild the curve, and then reprice the instrument of interest to obtain its curve sensitivity. This of course is not quite a "parallel" shift of any curve (e.g., a 1bp change in futures rate won't correspond to a 1bp change in either the zero curve or the par curve), but it's close enough and it does make hedging easier (after all, you're shocking tradable instruments).
## Answer by phlsmk (score 2)
https://quant.stackexchange.com/a/35274
Agree with Helin. For short term risk management a trader would be usually looking at delta to the forecast curve (i.e. swaps curve and government curve for a swaps/options trader), although he/she would also have delta risk to the OIS curve and also to curves of other currencies now that multi-currency collateralisation is quite common. Those other deltas tend to build up more slowly and over time (and therefore account for a smaller % of daily PnL), and so are managed/hedged on a slightly longer time scale.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.