Interpreting DV01 and PV01 for Interest Rate Swaps
Summary
The document clarifies the scaling and conventions behind a plain-vanilla interest rate swap’s sensitivity to its fixed rate. If the derivative of swap value is taken with respect to a rate expressed as a decimal, the value change for a one-basis-point move requires scaling that derivative by one basis point. This distinguishes a rate derivative from the dollar or present value of a basis point as commonly defined.
The answer cautions that sources do not use DV01 and PV01 formulas consistently: some omit the basis-point scale factor for convenience, leaving it to context or a note. Sign conventions also vary, since traders may describe the same rate exposure using different long/short conventions. Users should therefore check both units and direction before comparing reported sensitivities. The document does not give a worked swap valuation or settle a universal sign convention.
Key ideas
- A derivative with respect to a decimal fixed rate must be scaled by one basis point to represent a one-basis-point value change.
- DV01 and PV01 notation may omit that scale factor in some sources.
- The intended units should be checked when interpreting a quoted swap sensitivity.
- Long and short conventions can produce different signs for the same rate exposure.
Tags
Full text
# DV01 of Interest rate swap
# DV01 of Interest rate swap
I am a beginner in financial risk management and recently I have been studying the plain vanilla interest rate swap.
I came across several articles talking about DV01 of interest rate swap as follow.
\begin{equation} DV01(t) = \frac{\partial V_{swap}(t)}{\partial R_{fix}} = \sum_{j=1}^N \alpha_j Z_t(t_j) \end{equation}
My question is: In the equation, $R_{fix}$ should be in decimals. Then for a 1 basis point (i.e. $1/10000$) change in $R_{fix}$, shouldn't it lead to a $(1/10000) \sum_{j=1}^N \alpha_j Z_t(t_j)$ change in the price of the interest rate swap?
Thank you.
## Answer by Attack68 (score 3)
https://quant.stackexchange.com/a/35895
Since DV01 and PV01 are short for 'dollar value of a basis point' and 'present value of a basis point' (for currencies not in USD) respectively then you are right that the value should be scaled to give the right value inline with the definition.
As a commenter highlighted definitions are not necessarily consistent across sources. I have written a number of articles myself and am guilty of this inconsistency, unfortunately. Since it generally obfuscates delta and gamma formulae to have $10^{-4}$ and $10^{-8}$ scalars I tend to leave them out with a footnote. The results and terminology often follow from context.
One other important item you should be aware that is not consistent is direction. Traders of interest rates can reference long/short differently and have plus/minus sign conventions for the risk of the same interest rate move.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.