Solvency II SCR Ratios Near a Duration Match

Summary

The document simplifies the Solvency II interest-rate capital requirement for a single asset and liability as a parallel rate shock multiplied by the difference between their DV01s. It then expresses the SCR ratio as own funds divided by that capital amount. Under this simplified setup, matching asset and liability DV01s makes the denominator zero, raising the possibility of an unbounded ratio. The author also suggests the ratio could form a bell-shaped profile around the matching point as rates move.

These are posed as questions rather than resolved findings. The document offers no regulatory treatment, empirical insurer data, or evidence that actual SCR ratios follow the proposed shape. Its scope is deliberately narrow: other risk modules may contribute to total capital and reduce the effect of a zero rate-risk component. Readers should treat the infinite-ratio concern as a consequence of the simplified formula, not as a demonstrated behavior of the full Solvency II framework.

Key ideas

• In a single-asset, single-liability simplification, interest-rate SCR depends on the difference in their DV01s.
• If those DV01s match exactly, the simplified SCR denominator becomes zero.
• The author hypothesizes a bell-shaped SCR ratio around the duration-matching point.
• The document asks whether regulation or other risk modules prevent this outcome but supplies no answers or empirical evidence.

Tags

# Is SCR Ratio ill defined ? Is there risk of infinite Ratio?


# Is SCR Ratio ill defined ? Is there risk of infinite Ratio?












In the rate risk module of Solvency II, the SCR can be simplified in the scenario of single asset vs single liability as the impact of a parallel shock in interest rate.

Approximately by :

SCR = Shock x ( asset_DV01 - liability_DV01)

Besides that, the SCR ratio can be conceptualized in this case as :

SCR Ratio = Own Funds / SCR = (Asset - Liability) / {Shock x ( asset_DV01 - liability_DV01)}

This can lead to:

- A risk of an infinite SCR ratio when the DV01s perfectly match, as the denominator becomes zero.

=> How should the rate risk module handle these scenarios to avoid unrealistic results, and are there practical solutions or regulatory adjustments to address this "infinite SCR" risk? Are regulators aware of it ?

Also it Leads to :

- A bell-shaped SCR profile, where the SCR is infinite at the point of perfect duration match and decreases symmetrically with rate moves around that point.

=> Practically, do we observe the Bell shape of SCR Ratio of insurers with regards to rates moves ? Even if I believe the risk of infinite SCR ratio for rate risk should be diluted with the addition of the other risk modules.

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.