Skip to content
All library documents

Converting Spot Curve PV01 into Forward-Period PV01

Article Quant Q&A · Author: Kiann
Read the original

Summary

The document presents a simple way to allocate spot curve PV01 exposures across successive forward periods. It treats each spot maturity’s PV01 as evenly distributed over the annual segments from the present to that maturity. For example, the three-year spot exposure is divided equally among the three one-year intervals, while the two-year exposure is split between its two intervals.

The resulting forward-period risks are found by adding the contributions from each spot maturity that spans that interval. In the stated example, the first interval receives contributions from all three maturities, the second from the two- and three-year maturities, and the final interval from the three-year maturity alone. The approach is explicitly simplified: it ignores discounting and provides no treatment of curve construction, instrument-specific sensitivities, or nonannual periods, so it should not be taken as a general PV01 transformation method.

Key ideas

  • A spot PV01 can be approximated as evenly distributed across the annual periods up to its maturity.
  • Each forward-period PV01 is the sum of contributions from spot maturities that extend through that period.
  • Longer spot maturities contribute to more forward intervals than shorter maturities.
  • The example ignores discounting, limiting its accuracy for practical curve-risk conversion.

Tags

Fixed incomeRisk managementStatistics
Full text
# project curve spot risk (PV01) into forward risk (PV01)


# project curve spot risk (PV01) into forward risk (PV01)












is there a (simplistic?) formula to convert spot risk PV01 into the forward risk PV01?

For example, if I have a

a) PV01 spot risk : 1yr = 100k/bp, 2yr = 50k/bp, 3yr = 25k/bp

b) how can I project this into the forward risk seen from 0 to 1yr (? k/bp), 1yr to 2yr (? k/bp) and 2y to 3yr (? k/bp)

Kind regards

## Answer by dm63 (score 0)

https://quant.stackexchange.com/a/50838

Yes. Ignoring discounting, you can say the following:

25k 3yr spot = 8.3k (0y to 1y)+ 8.3k (1yto2y) +8.3k (2y to 3y)

50k 2yr spot = 25k (0y to 1y )+ 25k (1y to 2y)

100k 1yr spot = 100k (0yto 1y)

Adding, we have 133.3k (0y to 1y)+ 33.3k (1yto2y) + 8.3k (2y to 3y)

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.