Counterparty Default Risk (Type 1) | Actuably

#	Counterparty Name	CQS	PD	Exposure at Default	Collateral
1	Counterparty Name	Credit Quality Step	0.01%	Exposure at Default€	Collateral€
2	Counterparty Name	Credit Quality Step	0.01%	Exposure at Default€	Collateral€
3	Counterparty Name	Credit Quality Step	0.05%	Exposure at Default€	Collateral€
4	Counterparty Name	Credit Quality Step	0.24%	Exposure at Default€	Collateral€

Total LGD

€35 655 000

After 85% collateral recognition

Sigma

€448 336

Square root of Vinter + Vintra

SCR Def,1

€1 345 009

3 × sigma

Included Rows

4

Rows with positive exposure or collateral

Grouped Names

3

Single-name exposures after grouping

Total EAD

€40 500 000

Before collateral recognition

Recognized Collateral

€4 845 000

85% recognition factor applied

V inter

€54 287 718 847

Cross-bucket variance term

V intra

€146 717 734 063

Within-bucket variance term

Variance

€201 005 452 910

V inter + V intra

Sigma / Total LGD

1.26%

3 × sigma

Standalone Name Concentration

Counterparty	Share	Amount
Cedar Re	45.7%	€1.1M
North Harbor Re	35.7%	€871K
Main Street Bank	18.6%	€453K

Single-Name Loss-Given-Default and Capital Build

NameSingle NameEADPDRec. Coll.Rec. CollateralLGDSigmaCharge

Cedar Re

1 row3 (BBB)

€8.0M€8 000 000

0.24%

€425 000

€7.6M€7 575 000

€370 652

€1.1M€1 111 956

North Harbor Re

1 row2 (A)

€14M€14 000 000

0.05%

€1.0M€1 020 000

€13M€12 980 000

€290 169

€870 507

Main Street Bank

2 rows1 (AA)

€19M€18 500 000

0.01%

€3.4M€3 400 000

€15M€15 100 000

€150 992

€452 977

Probability of Default Lookup

CQSRating BucketPD Factor

CQS 0

AAA

0.002%

CQS 1

AA

0.01%

CQS 2

A

0.05%

CQS 3

BBB

0.24%

CQS 4

BB

1.2%

CQS 5

B

4.2%

CQS 6

CCC / Unrated

4.2%

1Step 1

Haircut collateral by 85% and floor each row-level LGD at zero

LGD_r = \max\left(EAD_r - 0.85 \times Collateral_r,\ 0\right)

2Step 2

Group repeated names into a single-name exposure

LGD_i = \sum_{r \in i} LGD_r, \qquad EAD_i = \sum_{r \in i} EAD_r

3Step 3

Compute the single-name PD as the LGD-weighted average of row PDs

PD_i = \frac{\sum_{r \in i} PD_r \times LGD_r}{\sum_{r \in i} LGD_r}

4Step 4

Bucket grouped exposures by common PD and sum total LGD inside each bucket

TLGD_j = \sum_{i: PD_i = PD_j} LGD_i

5Step 5

Calculate the inter-bucket Article 201 variance term

V_{inter} = \sum_{(j,k)} \frac{PD_k(1-PD_k)PD_j(1-PD_j)}{1.25(PD_k + PD_j) - PD_kPD_j} \times TLGD_j \times TLGD_k

6Step 6

Calculate the intra-bucket Article 201 variance term

V_{intra} = \sum_j \frac{1.5 \times PD_j(1-PD_j)}{2.5 - PD_j} \times \sum_{i: PD_i = PD_j} LGD_i^2

7Step 7

Take the square root of total variance

\sigma = \sqrt{V_{inter} + V_{intra}}

8Step 8

Apply the Article 200 threshold logic

SCR_{def,1} = \begin{cases} 3\sigma, & \sigma \le 7\% \times TLGD \\ 5\sigma, & 7\% \times TLGD < \sigma \le 20\% \times TLGD \\ TLGD, & \sigma > 20\% \times TLGD \end{cases}

Understand the Counterparty Default Risk (Type 1)

Overview

This calculator implements the gross capital requirement for the Counterparty Default Risk (Type 1) sub-module within the Solvency II standard formula. The Type 1 requirement is defined as the economic capital necessary to cover the loss in basic own funds resulting from a 1-in-200 year stress event affecting rated and concentrated financial exposures.^[1]^[2]

Input Terms

Counterparty Name: The legal entity or group name used to aggregate exposures into a single-name exposure set.^[3]
Credit Quality Step (CQS): The regulatory rating classification used to map the counterparty's probability of default (PD).^[4]
Exposure at Default (EAD): The gross exposure amount before any risk-mitigation or collateral adjustments.
Collateral: The value of eligible risk-mitigation assets, subject to a standard 85% haircut within this engine path.
Type 1 Loss Variance (V): The total variance of the loss distribution for Type 1 exposures, used in the proxy calculation path.^[3]

Technical Rationale

The Type 1 capital requirement is calibrated to a 99.5% confidence level over a one-year horizon. Unlike simpler factor-based modules, Type 1 uses a probability-weighted loss distribution (Vasicek model) to capture the credit quality and concentration of the counterparty portfolio.^[1]

The calculation centers on the Portfolio Variance (V), which aggregates individual counterparty variances (V-intra) and cross-counterparty correlations (V-inter).^[3] The final capital requirement reflects the standard formula's non-linear sensitivity to the "single-name exposure" structure, where lower-rated or highly concentrated exposures generate disproportionately higher capital needs.

Important Notes

Rulebook build: The Standard Formula sheet groups repeated names into a single-name exposure, applies `LGD = max(EAD - 85% x Collateral, 0)`, and follows the Article 200 / 201 sigma-and-LGD presentation.
Single-Name Grouping: To ensure regulatory compliance, multiple exposures to the same legal group must be aggregated. This regrouping is performed automatically in the standard formula path to avoid understating concentration risk.
Collateral Haircut: A standard 85% haircut is applied to visible collateral values. Exposures requiring more complex Article 192 risk-mitigation treatments should be modeled using the Proxy path with pre-adjusted LGD values.
Gross vs. Net SCR: This calculator determines the standalone Counterparty Default Risk (Type 1) SCR. Solvency II risk is only finalized as a net impact on Basic Own Funds after diversification in Counterparty Risk, then within BSCR, and after the top-level LAC TP and LACDT adjustments.
Regulatory deviation: Material deviation from standard-formula assumptions at this layer may support a capital add-on or a move toward an internal model where justified.^[5]
Reporting: The displayed result is intended to support the corresponding standard-formula component feeding the S.25.01 standard-formula reporting view.^[6]

Sources