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Bond Risk Factor CQS3 Simplification

Market

Calculate the Effective Risk Factor instantly.

%

Effective Risk Factor

1.8%

Credit Quality Step 3 Risk Factor

1.8%

1Step 1

Credit Quality Step 3 Risk Factor

Credit Quality Step 3 Risk Factor=1.8\textit{Credit Quality Step 3 Risk Factor} = 1.8
2Step 2

80% ECAI Coverage Test Passed

80% ECAI Coverage Test Passed=gte⁡(Portfolio Value Covered by Nominated ECAI Assessments,80)\textit{80\% ECAI Coverage Test Passed} = \operatorname{gte}\left(\textit{Portfolio Value Covered by Nominated ECAI Assessments}, 80\right)
3Step 3

article_105a_not_structured_security_flag

article_105a_not_structured_security_flag=1−Bond Is a Structured Note or Collateralised Security (0/1)\textit{article\_105a\_not\_structured\_security\_flag} = 1 - \textit{Bond Is a Structured Note or Collateralised Security (0/1)}
4Step 4

article_105a_not_excluded_liability_cover_flag

article_105a_not_excluded_liability_cover_flag=1−Bond Covers Profit-Participation, Unit-Linked, Index-Linked, or Matching-Adjustment Liabilities (0/1)\textit{article\_105a\_not\_excluded\_liability\_cover\_flag} = 1 - \textit{Bond Covers Profit-Participation, Unit-Linked, Index-Linked, or Matching-Adjustment Liabilities (0/1)}
5Step 5

Article 105a Conditions Met

Article 105a Conditions Met=min⁡(80% ECAI Coverage Test Passed,Bond Has No Nominated ECAI Assessment (0/1),Bond Has Fixed Redemption and Regular Coupon Structure (0/1),article_105a_not_structured_security_flag,article_105a_not_excluded_liability_cover_flag)\textit{Article 105a Conditions Met} = \min(\textit{80\% ECAI Coverage Test Passed}, \textit{Bond Has No Nominated ECAI Assessment (0/1)}, \textit{Bond Has Fixed Redemption and Regular Coupon Structure (0/1)}, \textit{article\_105a\_not\_structured\_security\_flag}, \textit{article\_105a\_not\_excluded\_liability\_cover\_flag})
6Step 6

Assigned Credit Quality Step

Assigned Credit Quality Step=3×Article 105a Conditions Met\textit{Assigned Credit Quality Step} = 3 \times \textit{Article 105a Conditions Met}
7Step 7

Effective Risk Factor

Effective Risk Factor=Credit Quality Step 3 Risk Factor×Article 105a Conditions Met\textit{Effective Risk Factor} = \textit{Credit Quality Step 3 Risk Factor} \times \textit{Article 105a Conditions Met}

Understand the Bond Risk Factor CQS3 Simplification

Overview

This calculator implements the simplified bond risk factor (`b_i`) used within the Spread Risk sub-module of the Solvency II standard formula.[1] It computes the per-instrument spread-risk factor as a function of modified duration and credit quality step, providing the factor input needed by the Spread Risk Bonds Simplification to derive the standalone capital charge. This engine does not itself output a standalone capital requirement.

Input Terms

  • Market Value (MV_i): The current market value of the bond or loan.[1]
  • Modified Duration (dur_i): The modified duration of the bond used as a proxy for price sensitivity.
  • Credit Quality Step (CQS): The regulatory rating step used to determine the applicable risk factor.

Technical Rationale

The Bond Risk Factor Simplification derives the `b_i` spread-risk factor for each bond by expressing it as a linear function of the instrument's modified duration and its credit quality step, as defined in Article 104.[1] This factor measures the percentage loss in value of a bond for a given unit change in credit spreads scaled to the instrument's duration profile. The resulting `b_i` value feeds directly into the Spread Risk Bonds Simplification to produce the per-instrument capital charge.

This method is governed by the principle of proportionality (Article 109), ensuring that smaller or captive undertakings can calculate their solvency capital requirements without the operational burden of a full-scale valuation engine. The resulting factor is used as an intermediate input, not as a final capital requirement.

Important Notes

  • Proportionality Bound: This factor is only valid where the nature, scale, and complexity of the risks justify use of the Article 104 simplification. If the bond portfolio contains complex embedded derivatives or non-standard trigger events, a fuller build is required.
  • Factor Output Only: This engine outputs the `b_i` factor per instrument. The full simplified standalone Spread Risk SCR is produced by the Spread Risk Bonds Simplification engine, which applies this factor to the instrument market values.
  • Regulatory deviation: Material deviation from the standard-formula assumptions or from the conditions supporting this simplification may support a capital add-on or a move toward a fuller or internal-model approach where justified.[2]
  • Reporting: The simplified result is intended to support the corresponding standard-formula component feeding the S.25.01 standard-formula reporting view, not to replace the connected article-chain result where the simplification is not justified.[3]

Sources

  1. Delegated Regulation (EU) 2015/35 - Art. 104 (Spread risk on bonds simplification) - EUR-Lex
  2. Directive 2009/138/EC - Art. 37 (Capital add-on) - EIOPA
  3. Commission Implementing Regulation (EU) 2015/2450 - QRT S.25.01 - EUR-Lex

Default values are illustrative sample inputs for navigation, training, and QA. Replace them with controlled data before using the result in capital analysis, governance, or reporting decisions.