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Using a Bond Curve to Model Government Bond Maturity in PRIIPs Risk Estimates

Article Quant Q&A · Author: iugrina
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Summary

The document raises a modeling concern about applying historical-return bootstrapping to a government bond product under the PRIIPs Category 3 market-risk measure. A bootstrap based on past returns may project prices that do not reflect the bond’s convergence toward face value as it approaches maturity, potentially distorting simulated price quantiles and VaR. The concern is especially salient when the historical sample comes from a period in which the bond price was generally rising or stable.

The response suggests using the government bond curve as the basis for simulation. As the simulated horizon advances, the bond can be repriced from curve points with progressively shorter maturities, which makes convergence toward nominal value part of the valuation process. This is a brief conceptual answer, not a detailed implementation guide. It does not specify curve dynamics, treatment of changing rates or credit risk, or demonstrate whether the suggested approach satisfies every PRIIPs requirement.

Key ideas

  • Historical-return bootstrapping may fail to represent a bond’s convergence to face value near maturity.
  • A price path that ignores maturity convergence could affect simulated quantiles and VaR estimates.
  • The response proposes valuing the bond against a government curve as simulated time advances.
  • Using shorter-tenor curve points can build maturity convergence into the projected price.
  • The note does not provide a full curve simulation method or regulatory analysis.

Tags

Fixed incomeBacktestingRisk management
Full text
# PRIIPs bootstrap for Category 3 MRM - bonds - future values to maturity


# PRIIPs bootstrap for Category 3 MRM - bonds - future values to maturity












PRIIPs regulation Annex 2 states in Point 20 that bootstrapping is to be used to infer the expected distribution of prices or price levels for the PRIIP’s underlying contracts from the observed distribution of returns.

For a product based on a government bond this approach seems to be inefficient/wrong since there is some knowledge about the way the value of the bond will behave in the future. Namely, it should be expected that the bond will drop to its face (nominal) value. However, if I am correct in understanding what bootstrapping based on historical values will do, this will not be accounted for in the bootstrapping approach?

Especially if the historical data is collected where the value of the bond has been (in average) rising (e.g. mid or early term of a long term bond) or (in average) stable. In this case, bootstrapping will produce an average curve (among others) that is not falling down to the face value. Thus, for government bonds we would see something quite extraordinary at maturity :)

This is quite problematic since all of the quantiles will be overestimated leading to an overestimate in VaR!

Since there is no mention of "domain knowledge" in PRIIPs (Annexes), how would you approach this problem? If you do not find this to be a problem could you please explain why you think so?

## Answer by Antoine Conze (score 1)

https://quant.stackexchange.com/a/37046

In the case of a govt bond, shouldn't the simulation be based on a (govt bond) curve (point 23 in the annex) in which case as time passes in your simulation you will recompute the bond price from shorter and shorter tenor points on the curve, thus ensuring that the bond price converges to its nominal value at maturity ?

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.