# Capital Adequacy Requirements (CAR) Chapter 8 – Credit Valuation Adjustment (CVA) Risk

## Document Properties

• Type of Publication: Guideline
• Effective Date: February 2023 / April 2023Footnote 1
• Audiences: Banks / BHC / T&L

The Capital Adequacy Requirements (CAR) for banks (including federal credit unions), bank holding companies, federally regulated trust companies, federally regulated loan companies and cooperative retail associations, collectively referred to as 'institutions', are set out in nine chapters, each of which has been issued as a separate document. This document, Chapter 8 – Credit Valuation Adjustment (CVA) Risk, should be read in conjunction with the other CAR chapters which include:

• Chapter 1 - Overview
• Chapter 2 - Definition of Capital
• Chapter 3 - Operational Risk
• Chapter 4 - Credit Risk - Standardized Approach
• Chapter 5 - Credit Risk - Internal Ratings Based Approach
• Chapter 6 - Securitization
• Chapter 7 - Settlement and Counterparty Risk
• Chapter 8 - Credit Valuation Adjustment (CVA) Risk
• Chapter 9 - Market Risk

Please refer to OSFI's Corporate Governance Guideline for OSFI's expectations of institution Boards of Directors in regards to the management of capital and liquidity.

## Chapter 8 – Credit Valuation Adjustment (CVA) Risk

1. This chapter is drawn from the Basel Committee on Banking Supervision (BCBS) Basel framework, published on the BIS websiteFootnote 2, effective December 15, 2019. For reference, the Basel paragraph numbers that are associated with the text appearing in this chapter are indicated in square brackets at the end of each paragraphFootnote 3.

### 8.1. CVA Risk Capital Charge

1. The risk weighted assets (RWA) for CVA risk are determined by multiplying the capital requirements calculated as set out in this chapter by 12.5. [Basel Framework, MAR 50.1]

2. In addition to the default risk capital requirements for counterparty credit risk determined based on the standardised or internal ratings-based (IRB) approaches for credit risk, an institution must add a capital charge to cover the risk of mark-to-market losses on the expected counterparty risk (such losses being known as credit value adjustments, CVA) to OTC derivatives. The CVA capital charge will be calculated in the manner set forth below depending on the institution's approved method of calculating capital charges for counterparty credit risk and specific interest rate risk. An institution is not required to include in this capital charge (i) transactions with a qualifying central counterparty (QCCP); and (ii) securities financing transactions (SFT), unless OSFI determines that the institution's CVA loss exposures arising from SFT transactions are material. [Basel Framework, MAR 50.2]

3. The introduction of the Standardized Approach for Measuring Counterparty Credit Risk (SACCR) to calculate derivatives exposure also impacts the CVA capital charge. Further, OSFI intends to implement the revised CVA framework in 2023Footnote 4. Introducing multiple changes to a framework can introduce volatility in capital requirements in a short period of time. As such, from the beginning of the first fiscal quarter of 2019 until the end of the fourth fiscal quarter of 2023, banks may apply a scalar of 0.7 to the SACCR exposure amounts that enter into the formulas described in paragraphs 5 and 17.

#### 8.1.1 Institutions with IMM approval and Specific Interest Rate Risk VaR modelFootnote 5 approval for bonds: Advanced CVA risk capital charge

1. Institutions with IMM approval for counterparty credit risk and approval to use the market risk internal models approach for the specific interest-rate risk of bonds must calculate this additional capital charge by modelling the impact of changes in the counterparties' credit spreads on the CVAs of all OTC derivative counterparties, together with eligible CVA hedges according to paragraphs 12 and 14, using the institution's VaR model for bonds. This VaR model is restricted to changes in the counterparties' credit spreads and does not model the sensitivity of CVA to changes in other market factors, such as changes in the value of the reference asset, commodity, currency or interest rate of a derivative. Regardless of the accounting valuation method a institution uses for determining CVA, the CVA capital charge calculation must be based on the following formula for the CVA of each counterparty:

$\mathrm{CVA}=\left({\mathrm{LGD}}_{\mathrm{MKT}}\right)×\sum _{i=1}^{T}\mathrm{MAX}\left[0;\mathrm{exp}\left(-\frac{{s}_{i-1}×{t}_{i-1}}{{\mathrm{LGD}}_{\mathrm{MKT}}}\right)-\mathrm{exp}\left(-\frac{{s}_{i}×{t}_{i}}{{\mathrm{LGD}}_{\mathrm{MKT}}}\right)\right]×\left(\frac{{\mathrm{EE}}_{i-1}×{D}_{i-1}+{\mathrm{EE}}_{i}×{D}_{i}}{2}\right)$

Where

• ti is the time of the i-th revaluation time bucket, starting from t0=0;
• tT is the longest contractual maturity across the netting sets with the counterparty;
• si is the credit spread of the counterparty at tenor ti, used to calculate the CVA of the counterparty. Whenever the credit default swap (CDS) spread of the counterparty is available, this must be used. Whenever such a CDS spread is not available, the institution must use a proxy spread that is appropriate based on the rating, industry and region of the counterparty;
• LGDMKT is the loss given default of the counterparty and should be based on the spread of a market instrument of the counterparty (or where a counterparty instrument is not available, based on the proxy spread that is appropriate based on the rating, industry and region of the counterparty). It should be noted that this LGDMKT, which inputs into the calculation of the CVA risk capital charge, is different from the LGD that is determined for the IRB and CCR default risk charge, as this LGDMKT is a market assessment rather than an internal estimate;
• the first factor within the sum represents an approximation of the market implied marginal probability of a default occurring between times ti-1 and ti. Market implied default probability (also known as risk neutral probability) represents the market price of buying protection against a default and is in general different from the real-world likelihood of a default;
• EEi is the expected exposure to the counterparty at revaluation time ti, as defined in Chapter 7 (regulatory expected exposure), where exposures of different netting sets for such counterparty are added, and where the longest maturity of each netting set is given by the longest contractual maturity inside the netting set;
• Di is the default risk-free discount factor at time ti, where D0 = 1.

[Basel Framework, MAR 50.3]

2. The formula in paragraph 5 must be the basis for all inputs into the institution's approved VaR model for bonds when calculating the CVA risk capital charge for a counterparty. For example, if this approved VaR model is based on full repricing, then the formula must be used directly. If the institution's approved VaR model is based on credit spread sensitivities for specific tenors, the institution must base each credit spread sensitivity on the following formula Footnote 6:

${\mathrm{Regulatory CS01}}_{i}=0.0001×{t}_{i}×\mathrm{exp}\left(-\frac{{s}_{i}×{t}_{i}}{{\mathrm{LGD}}_{\mathrm{MKT}}}\right)×\left(\frac{{\mathrm{EE}}_{i-1}×{D}_{i-1}-{\mathrm{EE}}_{i+1}×{D}_{i+1}}{2}\right)$

If the institution's approved VaR model uses credit spread sensitivities to parallel shifts in credit spreads (Regulatory CS01), then the institution must use the following formulaFootnote 7:

$\mathrm{Regulatory CS01}=0.0001×\sum _{i}^{T}\left({t}_{i}×\mathrm{exp}\left(-\frac{{s}_{i}×{t}_{i}}{{\mathrm{LGD}}_{\mathrm{MKT}}}\right)-{t}_{i-1}×\mathrm{exp}\left(-\frac{{s}_{i-1}×{t}_{i-1}}{{\mathrm{LGD}}_{\mathrm{MKT}}}\right)\right)×\left(\frac{{\mathrm{EE}}_{i-1}×{D}_{i-1}+{\mathrm{EE}}_{i}×{D}_{i}}{2}\right)$

[Basel Framework, MAR 50.4 to MAR 50.6]

3. If the bank's approved VaR model uses second-order sensitivities to shifts in credit spreads (spread gamma), the gammas must be calculated based on the formula in paragraph 5. [Basel Framework, MAR 50.7]

4. Institutions with IMM approval for the majority of their businesses, but which use SACCR for certain smaller portfolios, and which have approval to use the market risk internal models approach for the specific interest rate risk of bonds, will include these non-IMM netting sets into the CVA risk capital charge, according to paragraph 5, unless OSFI decides that paragraph 17 should apply for these portfolios. Non-IMM netting sets are included into the advanced CVA risk capital charge by assuming a constant EE profile, where EE is set equal to the EAD as computed under SACCR for a maturity equal to the maximum of (i) half of the longest maturity occurring in the netting set and (ii) the notional weighted average maturity of all transactions inside the netting set. The same approach applies where the IMM model does not produce an EE profile. [Basel Framework, MAR 50.8]

5. For exposures to certain counterparties, the institution's approved market risk VaR model may not reflect the risk of credit spread changes appropriately, because the institution's market risk VaR model does not appropriately reflect the specific risk of debt instruments issued by the counterparty. For such exposures, the institution is not allowed to use the advanced CVA risk charge. Instead, for these exposures the institution must determine the CVA risk charge by application of the standardised method in paragraph 17. Only exposures to counterparties for which the institution has supervisory approval for modelling the specific risk of debt instruments are to be included into the advanced CVA risk charge. [Basel Framework, MAR 50.9]

6. The CVA risk capital charge consists of both general and specific credit spread risks, including Stressed VaR but excluding IRC (incremental risk charge). The VaR figure should be determined in accordance with the quantitative standards described in chapter 9. It is thus determined as the sum of (i) the non-stressed VaR component and (ii) the stressed VaR component.

• when calculating the non-stressed VaR, current parameter calibrations for expected exposure must be used;
• when calculating the stressed VaR future counterparty EE profiles (according to the stressed exposure parameter calibrations as defined in Chapter 7) must be used. The period of stress for the credit spread parameters should be the most severe one-year stress period contained within the three year stress period used for the exposure parameters.Footnote 8

[Basel Framework, MAR 50.10]

7. This additional CVA risk capital charge is the stand alone market risk charge, calculated on the set of CVAs (as specified in paragraph 5) for all OTC derivatives counterparties, collateralised and uncollateralised, together with eligible CVA hedges. Within this standalone CVA risk capital charge, no offset against other instruments on the institution's balance sheet will be permitted (except as otherwise expressly provided herein). [Basel Framework, MAR 50.11]

8. Only hedges used for the purpose of mitigating CVA risk, and managed as such, are eligible to be included in the VaR model used to calculate the above CVA capital charge or in the standardised CVA risk capital charge set forth in paragraph 17. For example, if a CDS referencing an issuer is in the institution's inventory and that issuer also happens to be an OTC counterparty but the CDS is not managed as a hedge of CVA, then such a CDS is not eligible to offset the CVA within the standalone VaR calculation of the CVA risk capital charge. [Basel Framework, MAR 50.12]

9. Only hedges that are with external counterparties are eligible to reduce CVA. A hedge that is only with an internal desk cannot be used to reduce CVA. [Basel Framework, MAR 50.12, FAQ #1]

10. The only eligible hedges that can be included in the calculation of the CVA risk capital charge under paragraphs 5 or 17 are single-name CDSs, single-name contingent CDSs, other equivalent hedging instruments referencing the counterparty directly, and index CDSs. In case of index CDSs, the following restrictions apply:

• the basis between any individual counterparty spread and the spreads of index CDS hedges must be reflected in the VaR. This requirement also applies to cases where a proxy is used for the spread of a counterparty, since idiosyncratic basis still needs to be reflected in such situations. For all counterparties with no available spread, the institution must use reasonable basis time series out of a representative bucket of similar names for which a spread is available;
• if the basis is not reflected to OSFI's satisfaction, then the institution must reflect only 50% of the notional amount of index hedges in the VaR.

[Basel Framework, MAR 50.13]

11. Other types of counterparty risk hedges must not be reflected within the calculation of the CVA capital charge, and these other hedges must be treated as any other instrument in the institution's inventory for regulatory capital purposes. Tranched or nth to- default CDSs are not eligible CVA hedges. Eligible hedges that are included in the CVA capital charge must be removed from the institution's market risk capital charge calculation. [Basel Framework, MAR 50.14]

12. Although market risk hedges of CVA are not recognized in the CVA capital charge, market risk hedges used for the purposes of mitigating CVA risk and managed as such, are exempt from market risk capital requirements.

#### 8.1.2 All Other Institutions: Standardized CVA Risk Capital Charge

1. When an institution does not have the required approvals to use paragraph 5 to calculate a CVA capital charge for its counterparties, the institution must calculate a portfolio capital charge using the following formula:

$K=2.33×\sqrt{h}×\sqrt{{\left(\sum _{i}0.5×{w}_{i}×\left({M}_{i}×{\mathrm{EAD}}_{i}^{\mathrm{total}}-{M}_{i}^{\mathrm{hedge}}×{B}_{i}\right)-\sum _{i⁣n⁣d}{w}_{i⁣n⁣d}×{M}_{i⁣n⁣d}×{B}_{i⁣n⁣d}\right)}^{2}+\sum _{i}0.75×{w}_{i}^{2}×{\left({M}_{i}×{\mathrm{EAD}}_{i}^{\mathrm{total}}-{M}_{i}^{\mathrm{hedge}}×{B}_{i}\right)}^{2}}$

Where

• h is the one-year risk horizon (in units of a year), h = 1;
• wi is the weight applicable to counterparty 'i'. Counterparty 'i' must be mapped to one of the seven weights wi based on its external rating, as shown in the table of this paragraph below. When a counterparty does not have an external rating, the institution must, subject to OSFI approval, map the internal rating of the counterparty to one of the external ratings. If the institution does not have an approved rating system, then any unrated counterparty will receive a weight of 2.0%;
• EADitotal is the exposure at default of counterparty 'i' (summed across its netting sets), including the effect of collateral as per the existing IMM or SACCR rules as applicable to the calculation of counterparty risk capital charges for such counterparty by the institution. For non-IMM institutions the exposure should be discounted by applying the factor (1‑exp (-0.05×Mi))/(0.05×Mi). For IMM institutions, no such discount should be applied as the discount factor is already included in Mi;
• Bi is the notional of purchased single name CDS hedges (summed if more than one position) referencing counterparty 'i', and used to hedge CVA risk. This notional amount should be discounted by applying the factor (1‑exp(- 0.05×Mihedge))/(0.05×Mihedge);
• Bind is the full notional of one or more index CDS of purchased protection, used to hedge CVA risk. This notional amount should be discounted by applying the factor (1-exp(-0.05×Mind))/(0.05× Mind);
• wind is the weight applicable to index hedges. The institution must map indices to one of the seven weights wi based on the average spread of index 'ind'; Footnote 9
• Mi is the effective maturity of the transactions with counterparty 'i'. For IMM institutions, Mi is to be calculated as per Chapter 7. For non-IMM institutions, Mi is the notional weighted average maturityFootnote 10 as referred to in Chapter 5. However, for this purpose, Mi should not be capped at 5 years;
• Mihedge is the maturity of the hedge instrument with notional Bi (the quantities Mihedge x Bi are to be summed if these are several positions);
• Mind is the maturity of the index hedge 'ind'. In case of more than one index hedge position, it is the notional weighted average maturityFootnote 11.

For any counterparty that is also a constituent of an index on which a CDS is used for hedging counterparty credit risk, the notional amount attributable to that single name (as per its reference entity weight) may, with OSFI approval, be subtracted from the index CDS notional amount and treated as a single name hedge (Bi) of the individual counterparty with maturity based on the maturity of the index.

The weights are given in this table, and are based on the external rating of the counterpartyFootnote 12:

Rating Weight Wi
AAA 0.7%
AA 0.7%
A 0.8%
BBB 1.0%
BB 2.0%
B 3.0%
CCC 10.0%

Similarly to institutions using the advanced CVA capital charge, market risk hedges used for the purposes of mitigating CVA risk and managed as such, are exempt from market risk capital requirements.

[Basel Framework, MAR 50.15 and 50.16]

## Footnotes

Footnote 1

For institutions with a fiscal year ending October 31 or December 31, respectively.

Footnote 2
Footnote 3

Following the format: [Basel Framework, XXX yy.zz].

Footnote 4

See the section on minimum capital requirements for CVA risk at https://www.bis.org/bcbs/publ/d424.htm.

Footnote 5

"VaR model" refers to the internal model approach to market risk.

Footnote 6

This derivation assumes positive marginal default probabilities before and after time bucket ti and is valid for i<T. For the final time bucket i=T, the corresponding formula is:

${\mathrm{Regulatory CS01}}_{T}=0.0001×{t}_{T}×\mathrm{exp}\left(-\frac{{s}_{T}×{t}_{T}}{{\mathrm{LGD}}_{\mathrm{MKT}}}\right)×\left(\frac{{\mathrm{EE}}_{T-1}×{D}_{T-1}+{\mathrm{EE}}_{T}×{D}_{T}}{2}\right)$

Footnote 7

This derivation assumes positive marginal default probabilities.

Footnote 8

Note that the three-times multiplier inherent in the calculation of a bond VaR and a stressed VaR will apply to these calculations.

Footnote 9

Institutions should first look through index constituents' ratings so as to determine the corresponding weight for each constitutent, which then should be weighted-averaged for determining the weight of the index.

Footnote 10

The one year floor for Mi applies at the netting set level. That is, if there is more than one netting set to the same counterparty, the effective maturity should be determined separately for each netting set, the EAD of each netting set should be discounted according to its individual maturity and the quantities M x EAD should be summed.

Footnote 11

If there are more than one index CDS position on the same index, each index contract is discounted using its individual maturity and the quantities M x B are to be summed.

Footnote 12

The notations follow the methodology used by one institution, Standard & Poor's. The use of Standard & Poor's credit ratings is an example only; those of some other approved external credit assessment institutions could be used on an equivalent basis. The ratings used throughout this document, therefore, do not express any preferences or determinations on external assessment institutions by OSFI.