The Capital Adequacy Requirements (CAR) for banks, banks holding companies, and trust and loan companies, 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. The complete list of CAR chapters is as follows:

Institutions that are required to determine market risk capital requirements for trading book positions (see Chapter 9) must meet the requirements of this chapter. The riskweighted assets for credit value adjustment risk are determined by multiplying the capital requirements calculated as set out in this chapter by 12.5. [Basel Framework, MAR 50.1]

In the context of this document, CVA stands for credit valuation adjustment specified at a counterparty level. CVA reflects the adjustment of default riskfree prices of derivatives and securities financing transactions (SFTs) due to a potential default of the counterparty. [Basel Framework, MAR 50.2]

Unless explicitly specified otherwise, the term CVA in this document means regulatory CVA. Regulatory CVA may differ from CVA used for accounting purposes as follows:

regulatory CVA excludes the effect of the institution's own default; and

several constraints reflecting best practice in accounting CVA are imposed on calculations of regulatory CVA. [Basel Framework, MAR 50.3]

CVA risk is defined as the risk of losses arising from changing CVA values in response to changes in counterparty credit spreads and market risk factors that drive prices of derivative transactions and SFTs. [Basel Framework, MAR 50.4]

The capital requirements for CVA risk must be calculated by all institutions involved in covered transactions in both banking book and trading book. Covered transactions include:

all derivatives except those transacted directly with a qualified central counterparty and except those transactions meeting the conditions of paragraph 181 to paragraph 183 of Chapter 7; and

SFTs that are fairvalued by an institution for accounting purposes, if OSFI determines that the institution's CVA loss exposures arising from SFT transactions are material. In case the institution deems the exposures immaterial, the institution must justify its assessment to OSFI by providing relevant supporting documentation.
For the purpose of CVA capital requirement, SFTs that are fairvalued for accounting purposes and for which an institution records zero for CVA reserves for accounting purposes are included in the scope of covered transactions if the CVA risk of those SFTs is deemed material as described in the above subparagraph (2).
[Basel Framework, MAR 50.5]

The CVA risk capital requirements are calculated for an institution's "CVA portfolio" on a standalone basis. The CVA portfolio includes CVA for an institution's entire portfolio of covered transactions and eligible CVA hedges. [Basel Framework, MAR 50.6]

Two approaches are available for calculating CVA capital requirements: the standardized approach (SACVA) and the basic approach (BACVA). Institutions must use the BACVA unless they receive approval from OSFI to use the SACVA.^{Footnote 2} [Basel Framework, MAR 50.7]

Institutions that have received approval of OSFI to use the SACVA may carve out from the SACVA calculations any number of netting sets. CVA capital requirements for all carvedout netting sets must be calculated using the BACVA. When applying the carveout, a legal netting set may also be split into two synthetic netting sets, one containing the carvedout transactions subject to the BACVA and the other subject to the SACVA, subject to one or both of the following conditions:

the split is consistent with the treatment of the legal netting set used by the institution for calculating accounting CVA (e.g. where certain transactions are not processed by the front office/accounting exposure model); or

OSFI approval to use the SACVA is limited and does not cover all transactions within a legal netting set.
[Basel Framework, MAR 50.8]

Institutions that are below the materiality threshold specified in subsection (1) may opt not to calculate its CVA capital requirements using the SACVA or BACVA and instead choose an alternative treatment.

Any institution whose aggregate notional amount of noncentrally cleared derivatives is less than or equal to 100 billion euro is deemed as being below the materiality threshold.

Any institution below the materiality threshold may choose to set its CVA capital requirement equal to 100% of the institution's capital requirement for counterparty credit risk (CCR).

CVA hedges are not recognized under this treatment.

If chosen, this treatment must be applied to the institution's entire portfolio instead of the BACVA or the SACVA.

OSFI, however, can remove this option if it determines that CVA risk resulting from the institution's derivative positions materially contributes to the institution's overall risk.
[Basel Framework, MAR 50.9]

Eligibility criteria for CVA hedges are specified in paragraph 17 to paragraph 19 for the BACVA and in paragraph 37 to paragraph 39 for the SACVA. [Basel Framework, MAR 50.10]

CVA hedging instruments can be external (i.e. with an external counterparty) or internal (i.e. with one of the institution's trading desks).

All external CVA hedges (including both eligible and ineligible external CVA hedges) that are covered transactions must be included in the CVA calculation of the counterparty providing to the hedge.

All eligible external CVA hedges must be excluded from an institution's market risk capital requirement calculations under Chapter 9.

Ineligible external CVA hedges are treated as trading book instruments and are capitalized under Chapter 9.

An internal CVA hedge involves two perfectly offsetting positions: one of the CVA desk and the opposite position of the trading desk:

If an internal CVA hedge is ineligible, both positions belong to the trading book where they cancel each other, so there is no impact on either the CVA portfolio or the trading book.

If an internal CVA hedge is eligible, the CVA desk's position is part of the CVA portfolio where it is capitalized as set out in this chapter, while the trading desk's position is part of the trading book where it is capitalized as set out in Chapter 9.

If an internal CVA hedge involves an instrument that is subject to curvature risk, default risk charge or the residual risk addon under the standardized approach as set out in Chapter 9, it can be eligible only if the trading desk that is the CVA desk's internal counterparty executes a transaction with an external counterparty that exactly offsets the trading desk's position with the CVA desk.
[Basel Framework, MAR 50.11]

Institutions that use the BACVA or the SACVA for calculating CVA capital requirements may cap the maturity adjustment factor at 1 for all netting sets contributing to CVA capital requirements when they calculate CCR capital requirements under the Internal Ratings Based (IRB) approach. [Basel Framework, MAR 50.12]

The capital requirements for CVA risk under the reduced version of the BACVA (DS_{BACVA }× K_{reduced}, where the discount scalar DS_{BACVA} = 0.65) are calculated as follows (where the summations are taken over all counterparties that are within scope of the CVA charge), where:

SCVA_{c} is the CVA capital requirement that counterparty c would receive if considered on a standalone basis (referred to as "standalone CVA capital" – see the paragraph below for its calculation);

The supervisory correlation parameter is ρ = 50%. Its square, ρ^{2}=25%, represents the correlation between credit spreads of any two counterparties.^{Footnote 3} In the formula below, the effect of ρ is to recognize the fact that the CVA risk to which an institution is exposed is less than the sum of the CVA risk for each counterparty, given that the credit spreads of counterparties are typically not perfectly correlated; and

The first term under the square root in the formula below aggregates the systematic components of CVA risk, and the second term under the square root aggregates the idiosyncratic components of CVA risk.
${\mathrm{K}}_{\mathrm{reduced}}=\sqrt{{\left(\mathrm{\rho}\cdot \sum _{c}{\mathrm{SCVA}}_{\mathrm{C}}\right)}^{2}+\left(1{\mathrm{\rho}}^{2}\right)\cdot \sum _{c}{\mathrm{SCVA}}_{\mathrm{C}}^{2}}$
[Basel Framework, MAR 50.14]

The standalone CVA capital requirements for counterparty c that are used in the formula in the paragraph above (SCVAc) are calculated as follows (where the summation is across all netting sets with the counterparty), where:

RW_{c} is the risk weight for counterparty c that reflects the volatility of its credit spread. These risk weights are based on a combination of sector and credit quality of the counterparty as prescribed in the paragraph below.

M_{NS} is the effective maturity for the netting set NS. For institutions that have OSFI's approval to use the IMM, M_{NS} is calculated as per paragraphs 35 and 36 of Chapter 7, with the exception that the fiveyear cap in paragraph 35 is not applied. For institutions that do not have OSFI approval to use the IMM, M_{NS} is calculated according to paragraph 132 to paragraph 140 of Chapter 5, with the exception that the fiveyear cap in paragraph 132 of Chapter 5 is not applied.

EAD_{NS} is the exposure at default (EAD) of the netting set NS, calculated in the same way as the institution calculates it for minimum capital requirements for CCR.

DF_{NS} is a supervisory discount factor. It is 1 for institutions using the IMM to calculate EAD, and is
$\frac{1{e}^{{0.05\cdot M}_{NS}}}{{0.05\cdot M}_{NS}}$
for institutions not using the IMM.^{Footnote 4}

α = 1.4.^{Footnote 5}
${\mathrm{SCVA}}_{C}=\frac{1}{\alpha}\cdot {\mathrm{RW}}_{C}\cdot \sum _{\mathrm{NS}}{M}_{\mathrm{NS}}\cdot {\mathrm{EAD}}_{\mathrm{NS}}\cdot {\mathrm{DF}}_{\mathrm{NS}}$
[Basel Framework, MAR 50.15]

The supervisory risk weights (RW_{c}) are given in Table 1. Credit quality is specified as either investment grade (IG), high yield (HY), or not rated (NR). Where there are no external ratings or where external ratings are not recognized within a jurisdiction, institutions may, subject to OSFI's approval, map the internal rating to an external rating and assign a risk weight corresponding to either IG or HY.^{Footnote 6} Otherwise, the risk weights corresponding to NR is to be applied.
Table 1 Supervisory risk weights, RW_{C}
Sector of counterparty 
Credit quality of counterparty 
IG 
HY and NR 
Sovereigns including central banks and multilateral development banks 
0.5% 
2.0% 
Local government, governmentbacked nonfinancials, education and public administration 
1.0% 
4.0% 
Financials including governmentbacked financials 
5.0% 
12.0% 
Basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying 
3.0% 
7.0% 
Consumer goods and services, transportation and storage, administrative and support service activities 
3.0% 
8.5% 
Technology, telecommunications 
2.0% 
5.5% 
Health care, utilities, professional and technical activities 
1.5% 
5.0% 
Other sector 
5.0% 
12.0% 
[Basel Framework, MAR 50.16]

As set out in paragraph 13 the full version of the BACVA recognizes the effect of counterparty credit spread hedges. Only transactions used for the purpose of mitigating the counterparty credit spread component of CVA risk, and managed as such, can be eligible hedges. [Basel Framework, MAR 50.17]

Only singlename credit default swaps (CDS), singlename contingent CDS, risk participation agreements and index CDS can be eligible CVA hedges. [Basel Framework, MAR 50.18]

Eligible singlename credit instruments must:

reference the counterparty directly; or

reference an entity legally related to the counterparty, where legally related refers to cases where the reference name and the counterparty are either a parent and its subsidiary or two subsidiaries of a common parent; or

reference an entity that belongs to the same sector and region as the counterparty. [Basel Framework, MAR 50.19]

Institutions that intend to use the full version of BACVA must calculate the reduced version (K_{reduced}) as well. Under the full version, capital requirements for CVA risk DS_{BACVA} × K_{full} is calculated as follows, where DS_{BACVA} = 0.65, and β=0.25 is the supervisory parameter that is used to provide a floor that limits the extent to which hedging can reduce the capital requirements for CVA risk:
${\mathrm{K}}_{\mathrm{full}}=\mathrm{\beta}\cdot {\mathrm{K}}_{\mathrm{reduced}}+\left(1\mathrm{\beta}\right)\cdot {\mathrm{K}}_{\mathrm{hedged}}$
[Basel Framework, MAR 50.20]

The part of capital requirements that recognizes eligible hedges (K_{hedged}) is calculated as follows (where the summations are taken over all counterparties c that are within scope of the CVA charge), where:

Both the standalone CVA capital (SCVA_{C}) and the correlation parameter (ρ) are defined in exactly the same way as for the reduced version calculation of the BACVA.

SNHC is a quantity that gives recognition to the reduction in CVA risk of the counterparty c arising from the institution's use of singlename hedges of credit spread risk. See paragraph 23 for its calculation.

IH is a quantity that gives recognition to the reduction in CVA risk across all counterparties arising from the institution's use of index hedges. See paragraph 24 for its calculation.

HMAC is a quantity characterizing hedging misalignment, which is designed to limit the extent to which indirect hedges can reduce capital requirements given that they will not fully offset movements in a counterparty's credit spread. That is, with indirect hedges present, K_{hedged} cannot reach zero. See paragraph 25 for its calculation.
${\mathrm{K}}_{\mathrm{hedged}}=\sqrt{{\left(\mathrm{\rho}\cdot \sum _{\mathrm{C}}\left({\mathrm{SCVA}}_{\mathrm{C}}{\mathrm{SNH}}_{\mathrm{C}}\right)\mathrm{IH}\right)}^{2}+{\left(1{\mathrm{\rho}}^{2}\right)\cdot \sum _{\mathrm{C}}\left({\mathrm{SCVA}}_{\mathrm{C}}{\mathrm{SNH}}_{\mathrm{C}}\right)}^{2}+\sum _{\mathrm{C}}{\mathrm{HMA}}_{\mathrm{C}}}$
[Basel Framework, MAR 50.21]

The formula for K_{hedged} in the paragraph above comprises three main terms as below:

The first term
${\left(\mathrm{\rho}\cdot \sum _{\mathrm{C}}\left({\mathrm{SCVA}}_{\mathrm{C}}{\mathrm{SNH}}_{\mathrm{C}}\right)\mathrm{IH}\right)}^{2}$
aggregates the systematic components of CVA risk arising from the institution's counterparties, the singlename hedges and the index hedges.

The second term
${\left(1{\mathrm{\rho}}^{2}\right)\cdot \sum _{\mathrm{C}}\left({\mathrm{SCVA}}_{\mathrm{C}}{\mathrm{SNH}}_{\mathrm{C}}\right)}^{2}$
aggregates the idiosyncratic components of CVA risk arising from the institution's counterparties and the singlename hedges.

The third term
$\sum _{\mathrm{C}}{\mathrm{HMA}}_{\mathrm{C}}$
aggregates the components of indirect hedges that are not aligned with counterparties' credit spreads.
[Basel Framework, MAR 50.22]

The quantity SNH_{c} is calculated as follows (where the summation is across all single name hedges h that the institution has taken out to hedge the CVA risk of counterparty c), where:

r_{hc} is the supervisory prescribed correlation between the credit spread of counterparty c and the credit spread of a singlename hedge h of counterparty c. The value of r_{hc} is set out in the Table 2 of paragraph 26. It is set at 100% if the hedge directly references the counterparty c, and set at lower values if it does not.

${\mathrm{M}}_{\mathrm{h}}^{\mathrm{S}\mathrm{N}}$
is the remaining maturity of singlename hedge h.

${\mathrm{B}}_{\mathrm{h}}^{\mathrm{S}\mathrm{N}}$
is the notional of singlename hedge h. For singlename contingent CDS, the notional is determined by the current market value of the reference portfolio or instrument.

${\mathrm{D}\mathrm{F}}_{\mathrm{h}}^{\mathrm{S}\mathrm{N}}$
is the supervisory discount factor calculated as
$\mathrm{}\frac{1{\mathrm{e}}^{{0.05\cdot \mathrm{M}}_{\mathrm{h}}^{\mathrm{S}\mathrm{N}}}}{{0.05\cdot \mathrm{M}}_{\mathrm{h}}^{\mathrm{S}\mathrm{N}}}$

RW_{h} is the supervisory risk weight of singlename hedge h that reflects the volatility of the credit spread of the reference name of the hedging instrument. These risk weights are based on a combination of the sector and the credit quality of the reference name of the hedging instrument as prescribed in Table 1 of paragraph 16.
${\mathrm{SNH}}_{\mathrm{c}}=\sum _{\mathrm{h}\in \mathrm{c}}{\mathrm{r}}_{\mathrm{h}\mathrm{c}}\cdot {\mathrm{R}\mathrm{W}}_{\mathrm{h}}\cdot {\mathrm{M}}_{\mathrm{h}}^{\mathrm{S}\mathrm{N}}\cdot {\mathrm{B}}_{\mathrm{h}}^{\mathrm{S}\mathrm{N}}\cdot {\mathrm{D}\mathrm{F}}_{\mathrm{h}}^{\mathrm{S}\mathrm{N}}$
[Basel Framework, MAR 50.23]

The quantity IH is calculated as follows (where the summation is across all index hedges i that the institution has taken out to hedge CVA risk), where:

${\mathrm{M}}_{\mathrm{i}}^{\mathrm{ind}}$
is the remaining maturity of index hedge i.

${\mathrm{B}}_{\mathrm{i}}^{\mathrm{ind}}$
is the notional of the index hedge i.

${\mathrm{DF}}_{\mathrm{i}}^{\mathrm{ind}}$
is the supervisory discount factor calculated as
$\frac{1{\mathrm{e}}^{{0.05\cdot \mathrm{M}}_{\mathrm{i}}^{\mathrm{i}\mathrm{n}\mathrm{d}}}}{{0.05\cdot \mathrm{M}}_{\mathrm{i}}^{\mathrm{i}\mathrm{n}\mathrm{d}}}$

${\mathrm{RW}}_{\mathrm{i}}$
is the supervisory risk weight of the index hedge i.
${\mathrm{RW}}_{\mathrm{i}}$
is taken from the Table 1 of paragraph 16 based on the sector and the credit quality of the index constituents and adjusted as follows:

For an index where all index constituents belong to the same sector and are of the same credit quality, the relevant value in the Table 1 of paragraph 16 is multiplied by 0.7 to account for diversification of idiosyncratic risk within the index.

For an index spanning multiple sectors or with a mixture of investment grade constituents and other grade constituents, the nameweighted average of the risk weights from the Table 1 of paragraph 16 should be calculated and then multiplied by 0.7.
$\mathrm{IH}=\sum _{\mathrm{i}}{\mathrm{RW}}_{\mathrm{i}}\cdot {\mathrm{M}}_{\mathrm{i}}^{\mathrm{ind}}\cdot {\mathrm{B}}_{\mathrm{i}}^{\mathrm{ind}}\cdot {\mathrm{DF}}_{\mathrm{i}}^{\mathrm{ind}}$
[Basel Framework, MAR 50.24]

The quantity HMA_{C} is calculated as follows (where the summation is across all single name hedges h that have been taken out to hedge the CVA risk of counterparty c), where
${\mathrm{r}}_{\mathrm{h}\mathrm{c}},{\mathrm{M}}_{\mathrm{h}}^{\mathrm{SN}},{\mathrm{B}}_{\mathrm{h}}^{\mathrm{SN}},{\mathrm{DF}}_{\mathrm{h}}^{\mathrm{SN}}$
and RW_{h} have the same definitions as set out in [MAR50.23].
${\mathrm{HMA}}_{\mathrm{c}}=\sum _{\mathrm{h}\in \mathrm{c}}\left(1{\mathrm{r}}_{\mathrm{h}\mathrm{c}}^{2}\right)\cdot {\left({\mathrm{RW}}_{\mathrm{h}}\cdot {\mathrm{M}}_{\mathrm{h}}^{\mathrm{SN}}\cdot {\mathrm{B}}_{\mathrm{h}}^{\mathrm{SN}}\cdot {\mathrm{DF}}_{\mathrm{h}}^{\mathrm{SN}}\right)}^{2}$
[Basel Framework, MAR 50.25]

The supervisory prescribed correlations rhc between the credit spread of counterparty c and the credit spread of its singlename hedge h are set in Table 2 as follows:
Table 2 Correlations between credit spread of counterparty and singlename hedge
Singlename hedge h of counterparty c 
Value of r_{hc} 
References counterparty c directly 
100% 
Has legal relation with counterparty c 
80% 
Shares sector and region with counterparty c 
50% 
[Basel Framework, MAR 50.26]

An institution must calculate regulatory CVA for each counterparty with which it has at least one covered position for the purpose of the CVA risk capital requirements. [Basel Framework, MAR 50.31]

Regulatory CVA at a counterparty level must be calculated according to the following principles. An institution must demonstrate its compliance to the principles to OSFI.

Regulatory CVA must be calculated as the expectation of future losses resulting from default of the counterparty under the assumption that the institution itself is free from the default risk. In expressing the regulatory CVA, nonzero losses must have a positive sign. This is reflected in paragraph 52 where
${\mathrm{W}\mathrm{S}}_{\mathrm{k}}^{\mathrm{h}\mathrm{d}\mathrm{g}}$
must be subtracted from
${\mathrm{WS}}_{\mathrm{k}}^{\mathrm{CVA}}$
.

The calculation must be based on at least the following three sets of inputs:

term structure of marketimplied probability of default (PD);

marketconsensus expected lossgivendefault (ELGD);

simulated paths of discounted future exposure.

The term structure of marketimplied PD must be estimated from credit spreads observed in the markets. For counterparties whose credit is not actively traded (ie illiquid counterparties), the marketimplied PD must be estimated from proxy credit spreads estimated for these counterparties according to the following requirements:

An institution must estimate the credit spread curves of illiquid counterparties from credit spreads observed in the markets of the counterparty's liquid peers via an algorithm that discriminates on at least the following three variables: a measure of credit quality (e.g. rating), industry, and region.

In certain cases, mapping an illiquid counterparty to a single liquid reference name can be allowed. A typical example would be mapping a municipality to its home country (i.e. setting the municipality credit spread equal to the sovereign credit spread plus a premium). An institution must justify to OSFI each case of mapping an illiquid counterparty to a single liquid reference name.

When no credit spreads of any of the counterparty's peers is available due to the counterparty's specific type (e.g. project finance, funds), an institution is allowed to use a more fundamental analysis of credit risk to proxy the spread of an illiquid counterparty. However, where historical PDs are used as part of this assessment, the resulting spread cannot be based on historical PD only – it must relate to credit markets.

The marketconsensus ELGD value must be the same as the one used to calculate the riskneutral PD from credit spreads unless the institution can demonstrate that the seniority of the exposure resulting from covered positions differs from the seniority of senior unsecured bonds.^{Footnote 7} Collateral provided by the counterparty does not change the seniority of the exposure.

The simulated paths of discounted future exposure are produced by pricing all derivative transactions with the counterparty along simulated paths of relevant market risk factors and discounting the prices to today using riskfree interest rates along the path.

All market risk factors material for the transactions with a counterparty must be simulated as stochastic processes for an appropriate number of paths defined on an appropriate set of future time points extending to the maturity of the longest transaction.

For transactions with a significant level of dependence between exposure and the counterparty's credit quality, this dependence should be taken into account.

For margined counterparties, collateral is permitted to be recognized as a risk mitigant under the following conditions:

Collateral management requirements outlined in paragraph 56 and 57 of Chapter 7 are satisfied.

All documentation used in collateralized transactions must be binding on all parties and legally enforceable in all relevant jurisdictions. Institutions must have conducted sufficient legal review to verify this and have a well founded legal basis to reach this conclusion, and undertake such further review as necessary to ensure continuing enforceability.

For margined counterparties, the simulated paths of discounted future exposure must capture the effects of margining collateral that is recognized as a risk mitigant along each exposure path. All the relevant contractual features such as the nature of the margin agreement (unilateral vs bilateral), the frequency of margin calls, the type of collateral, thresholds, independent amounts, initial margins and minimum transfer amounts must be appropriately captured by the exposure model. To determine collateral available to an institution at a given exposure measurement time point, the exposure model must assume that the counterparty will not post or return any collateral within a certain time period immediately prior to that time point. The assumed value of this time period, known as the margin period of risk (MPoR), cannot be less than a supervisory floor. For SFTs and client cleared transactions as specified in paragraph 179 of Chapter 7 the supervisory floor for the MPoR is equal to 4+N business days, where N is the remargining period specified in the margin agreement (in particular, for margin agreements with daily or intradaily exchange of margin, the minimum MPoR is 5 business days). For all other transactions, the supervisory floor for the MPoR is equal to 9+N business days.
[Basel Framework, MAR 50.32]

The simulated paths of discounted future exposure are obtained via the exposure models used by an institution for calculating front office/accounting CVA, adjusted (if needed) to meet the requirements imposed for regulatory CVA calculation. Model calibration process (with the exception of the MPoR), market and transaction data used for regulatory CVA calculation must be the same as the ones used for accounting CVA calculation. [Basel Framework, MAR 50.33]

The generation of market risk factor paths underlying the exposure models must satisfy and an institution must demonstrate to OSFI its compliance to the following requirements:

Drifts of risk factors must be consistent with a riskneutral probability measure. Historical calibration of drifts is not allowed.

The volatilities and correlations of market risk factors must be calibrated to market data whenever sufficient data exist in a given market. Otherwise, historical calibration is permissible.

The distribution of modelled risk factors must account for the possible nonnormality of the distribution of exposures, including the existence of leptokurtosis ("fat tails"), where appropriate.
[Basel Framework, MAR 50.34]

Netting recognition is the same as in the accounting CVA calculations used by the institution. In particular, netting uncertainty can be modelled. [Basel Framework, MAR 50.35]

An institution must satisfy and demonstrate to OSFI its compliance to the following requirements:

Exposure models used for calculating regulatory CVA must be part of a CVA risk management framework that includes the identification, measurement, management, approval and internal reporting of CVA risk. An institution must have a credible track record in using these exposure models for calculating CVA and CVA sensitivities to market risk factors.

Senior management should be actively involved in the risk control process and must regard CVA risk control as an essential aspect of the business to which significant resources need to be devoted.

An institution must have a process in place for ensuring compliance with a documented set of internal policies, controls and procedures concerning the operation of the exposure system used for accounting CVA calculations.

An institution must have an independent control unit that is responsible for the effective initial and ongoing validation of the exposure models. This unit must be independent from business credit and trading units (including the CVA desk), must be adequately staffed and must report directly to senior management of the institution.

An institution must document the process for initial and ongoing validation of its exposure models to a level of detail that would enable a third party to understand how the models operate, their limitations, and their key assumptions; and recreate the analysis. This documentation must set out the minimum frequency with which ongoing validation will be conducted as well as other circumstances (such as a sudden change in market behaviour) under which additional validation should be conducted. In addition, the documentation must describe how the validation is conducted with respect to data flows and portfolios, what analyses are used and how representative counterparty portfolios are constructed.

The pricing models used to calculate exposure for a given path of market risk factors must be tested against appropriate independent benchmarks for a wide range of market states as part of the initial and ongoing model validation process. Pricing models for options must account for the nonlinearity of option value with respect to market risk factors.

An independent review of the overall CVA risk management process should be carried out regularly in the institution's own internal auditing process. This review should include both the activities of the CVA desk and of the independent risk control unit.

An institution must define criteria on which to assess the exposure models and their inputs and have a written policy in place to describe the process to assess the performance of exposure models and remedy unacceptable performance.

Exposure models must capture transactionspecific information in order to aggregate exposures at the level of the netting set. An institution must verify that transactions are assigned to the appropriate netting set within the model.

Exposure models must reflect transaction terms and specifications in a timely, complete, and conservative fashion. The terms and specifications must reside in a secure database that is subject to formal and periodic audit. The transmission of transaction terms and specifications data to the exposure model must also be subject to internal audit, and formal reconciliation processes must be in place between the internal model and source data systems to verify on an ongoing basis that transaction terms and specifications are being reflected in the exposure system correctly or at least conservatively.

The current and historical market data must be acquired independently of the lines of business and be compliant with accounting. They must be fed into the exposure models in a timely and complete fashion, and maintained in a secure database subject to formal and periodic audit. An institution must also have a welldeveloped data integrity process to handle the data of erroneous and/or anomalous observations. In the case where an exposure model relies on proxy market data, an institution must set internal policies to identify suitable proxies and the institution must demonstrate empirically on an ongoing basis that the proxy provides a conservative representation of the underlying risk under adverse market conditions.
[Basel Framework, MAR 50.36]

The SACVA capital requirements are calculated as the sum of the capital requirements for delta and vega risks calculated for the entire CVA portfolio (including eligible hedges).
[Basel Framework, MAR 50.42]

The capital requirements for delta risk are calculated as the simple sum of delta capital requirements calculated independently for the following six risk classes:

interest rate risk;

foreign exchange (FX) risk;

counterparty credit spread risk;

reference credit spread risk (i.e. credit spreads that drive the CVA exposure component);

equity risk; and

commodity risk.
[Basel Framework, MAR 50.43]

If an instrument is deemed as an eligible hedge for credit spread delta risk, it must be assigned in its entirety (see paragraph 37) either to the counterparty credit spread or to the reference credit spread risk class. Instruments must not be split between the two risk classes. [Basel Framework, MAR 50.44]

The capital requirements for vega risk are calculated as the simple sum of vega capital requirements calculated independently for the following five risk classes. Note there here are no vega capital requirements for counterparty credit spread risk.

interest rate risk;

FX risk;

reference credit spread risk;

equity risk; and

commodity risk.
[Basel Framework, MAR 50.45]

Delta and vega capital requirements are calculated in the same manner using the same procedures set out in paragraph 47 to paragraph 53. [Basel Framework, MAR 50.46]

For each risk class, (i) the sensitivity of the aggregate CVA,
${\mathrm{s}}_{\mathrm{k}}^{\mathrm{C}\mathrm{V}\mathrm{A}}$
, and (ii) the sensitivity of the market value of all eligible hedging instruments in the CVA portfolio,
${\mathrm{s}}_{\mathrm{k}}^{\mathrm{H}\mathrm{d}\mathrm{g}}$
, to each risk factor k in the risk class are calculated. The sensitivities are defined as the ratio of the change of the value in question (i.e. (i) aggregate CVA or (ii) market value of all CVA hedges) caused by a small change of the risk factor's current value to the size of the change. Specific definitions for each risk class are set out in paragraph 54 to paragraph 77. These definitions include specific values of changes or shifts in risk factors. However, an institution may use smaller or larger values of risk factor shifts if doing so is consistent with internal risk management calculations.
An institution may use algorithmic techniques, such as adjoint algorithmic differentiation to calculate CVA sensitivities under the SACVA if doing so is consistent with the institution's internal risk management calculations and the relevant validation standards described in the SACVA framework. [Basel Framework, MAR 50.47]

CVA sensitivities for vega risk are always material and must be calculated regardless of whether or not the portfolio includes options. When CVA sensitivities for vega risk are calculated, the volatility shift must apply to both types of volatilities that appear in exposure models:

volatilities used for generating risk factor paths; and

volatilities used for pricing options.
[Basel Framework, MAR 50.48]

If a hedging instrument is an index, its sensitivities to all risk factors upon which the value of the index depends must be calculated. The index sensitivity to risk factor k must be calculated by applying the shift of risk factor k to all index constituents that depend on this risk factor and recalculating the changed value of the index. For example, to calculate delta sensitivity of S&P500 to large financial companies, an institution must apply the relevant shift to equity prices of all large financial companies that are constituents of S&P500 and recompute the index. [Basel Framework, MAR 50.49]

For the following risk classes, an institution may choose to introduce a set of additional risk factors that directly correspond to qualified credit and equity indices. For delta risks, a credit or equity index is qualified if it satisfies liquidity and diversification conditions specified in paragraph 143 of Chapter 9; for vega risks, any credit or equity index is qualified. Under this option, an institution must calculate sensitivities of CVA and the eligible CVA hedges to the qualified index risk factors in addition to sensitivities to the nonindex risk factors. Under this option, for a covered transaction or an eligible hedging instrument whose underlying is a qualified index, its contribution to sensitivities to the index constituents is replaced with its contribution to a single sensitivity to the underlying index. For example, for a portfolio consisting only of equity derivatives referencing only qualified equity indices, no calculation of CVA sensitivities to nonindex equity risk factors is necessary. If more than 75% of constituents of a qualified index (taking into account the weightings of the constituents) are mapped to the same sector, the entire index must be mapped to that sector and treated as a singlename sensitivity in that bucket. In all other cases, the sensitivity must be mapped to the applicable index bucket.

counterparty credit spread risk;

reference credit spread risk; and

equity risk.
[Basel Framework, MAR 50.50]

The weighted sensitivities
${\mathrm{W}\mathrm{S}}_{\mathrm{k}}^{\mathrm{C}\mathrm{V}\mathrm{A}}$
and
${\mathrm{W}\mathrm{S}}_{\mathrm{k}}^{\mathrm{H}\mathrm{d}\mathrm{g}}$
for each risk factor k are calculated by multiplying the net sensitivities
${\mathrm{s}}_{\mathrm{k}}^{\mathrm{C}\mathrm{V}\mathrm{A}}$
and
${\mathrm{s}}_{\mathrm{k}}^{\mathrm{H}\mathrm{d}\mathrm{g}}$
, respectively, by the corresponding risk weight RW_{k} (the risk weights applicable to each risk class are specified in paragraph 54 to paragraph 77). [Basel Framework, MAR 50.51]
${\mathrm{WS}}_{\mathrm{k}}^{\mathrm{CVA}}={\mathrm{RW}}_{\mathrm{k}}{\mathrm{s}}_{\mathrm{k}}^{\mathrm{CVA}}$
${\mathrm{WS}}_{\mathrm{k}}^{\mathrm{Hdg}}={\mathrm{RW}}_{\mathrm{k}}{\mathrm{s}}_{\mathrm{k}}^{\mathrm{Hdg}}$

The net weighted sensitivity of the CVA portfolio s_{k} to risk factor k is obtained by:
${\mathrm{WS}}_{\mathrm{k}}={\mathrm{WS}}_{\mathrm{K}}^{\mathrm{CVA}}{\mathrm{WS}}_{\mathrm{k}}^{\mathrm{Hdg}}$
Note that the formula in paragraph 52 is set out under the convention that the CVA is positive as specified in paragraph 32. It intends to recognize the risk reducing effect of hedging. For example, when hedging the counterparty credit spread component of CVA risk for a specific counterparty by buying credit protection on the counterparty: if the counterparty's credit spread widens, the CVA (expressed as a positive value) increases resulting in the positive CVA sensitivity to the counterparty credit spread. At the same time, as the value of the hedge from the institution's perspective increases as well (as credit protection becomes more valuable), the sensitivity of the hedge is also positive. The positive weighted sensitivities of the CVA and its hedge offset each other using the formula with the minus sign. If CVA loss had been expressed as a negative value, the minus sign in paragraph 52 would have been replaced by a plus sign. [Basel Framework, MAR 50.52]

For each risk class, the net sensitivities are aggregated as follows:

The weighted sensitivities must be aggregated into a capital requirement K_{b} within each bucket b (the buckets and correlation parameters ρ_{kl} applicable to each risk class are specified in paragraph 54 to paragraph 77), where R is the hedging disallowance parameter, set at 0.01, that prevents the possibility of recognizing perfect hedging of CVA risk.
${K}_{b}=\sqrt{\left(\sum _{k\in b}{\mathrm{WS}}_{k}^{2}+\sum _{k\in b}\sum _{l\in b,l\ne k}{\rho}_{\mathrm{kl}}{\mathrm{WS}}_{k}{\mathrm{WS}}_{l}\right)+R\times \sum _{k\in b}\left({\left({\mathrm{WS}}_{k}^{\mathrm{Hdg}}\right)}^{2}\right)}$

Bucketlevel capital requirements must then be aggregated across buckets within each risk class (the correlation parameters γ_{bc} applicable to each risk class are specified in paragraph 54 to paragraph 77). Note that this equation differs from the corresponding aggregation equation for market risk capital requirements in paragraph 116 of Chapter 9, including the multiplier m_{CVA}.
$\mathrm{K}={\mathrm{m}}_{\mathrm{CVA}}\sqrt{\sum _{b}{\mathrm{K}}_{\mathrm{b}}^{2}+\sum _{b}\sum _{\mathrm{b\ne c}}{\mathrm{\gamma}}_{\mathrm{bc}}{\mathrm{S}}_{\mathrm{b}}{\mathrm{S}}_{\mathrm{c}}}$

In calculating K in above (2), S_{b} is defined as the sum of the weighted sensitivities WS_{k} for all risk factors k within bucket b, floored by K_{b} and capped by K_{b}, and the S_{c} is defined in the same way for all risk factors k in bucket c:
${S}_{b}=max\left\{{K}_{b};min\left(\sum _{k\u03f5b}{\mathrm{WS}}_{k};{K}_{b}\right)\right\}$
${S}_{c}=max\left\{{K}_{c};min\left(\sum _{k\u03f5c}{\mathrm{WS}}_{k};{K}_{c}\right)\right\}$
[Basel Framework, MAR 50.53]

For interest rate delta and vega risks, buckets must be set per individual currencies. [Basel Framework, MAR 50.54]

For interest rate delta and vega risks, crossbucket correlation γ_{bc} is set at 0.5 for all currency pairs. [Basel Framework, MAR 50.55]

The interest rate delta risk factors for an institution's reporting currency and for the following currencies USD, EUR, GBP, AUD, CAD, SEK or JPY:

The interest rate delta risk factors are the absolute changes of the inflation rate and of the riskfree yields for the following five tenors: 1 year, 2 years, 5 years, 10 years and 30 years.

The sensitivities to the abovementioned riskfree yields are measured by changing the riskfree yield for a given tenor for all curves in a given currency by 1 basis point (0.0001 in absolute terms) and dividing the resulting change in the aggregate CVA (or the value of CVA hedges) by 0.0001. The sensitivity to the inflation rate is obtained by changing the inflation rate by 1 basis point (0.0001 in absolute terms) and dividing the resulting change in the aggregate CVA (or the value of CVA hedges) by 0.0001.

The risk weights RW_{k} are set as follows:
Table 3 Risk weight for interest rate risk factors
(specified currencies)
blank 
1 year 
2 years 
5 years 
10 years 
30 years 
Inflation 
Risk weight 
1.11% 
0.93% 
0.74% 
0.74% 
0.74% 
1.11% 

The correlations between pairs of risk factors ρ_{kl} are set as follows:
Table 4 Correlations for interest rate risk factors (specified currencies)
Tenor 
Tenor 
1 year 
2 years 
5 years 
10 years 
30 years 
Inflation 
1 year 
100% 
91% 
72% 
55% 
31% 
40% 
2 years 
n/a 
100% 
87% 
72% 
45% 
40% 
5 years 
n/a 
n/a 
100% 
91% 
68% 
40% 
10 years 
n/a 
n/a 
n/a 
100% 
83% 
40% 
30 years 
n/a 
n/a 
n/a 
n/a 
100% 
40% 
Inflation 
n/a 
n/a 
n/a 
n/a 
n/a 
100% 
[Basel Framework, MAR 50.56]

The interest rate delta risk factors for other currencies not specified in paragraph above:

The interest rate risk factors are the absolute change of the inflation rate and the parallel shift of the entire riskfree yield curve for a given currency.

The sensitivity to the yield curve is measured by applying a parallel shift to all riskfree yield curves in a given currency by 1 basis point (0.0001 in absolute terms) and dividing the resulting change in the aggregate CVA (or the value of CVA hedges) by 0.0001. The sensitivity to the inflation rate is obtained by changing the inflation rate by 1 basis point (0.0001 in absolute terms) and dividing the resulting change in the aggregate CVA (or the value of CVA hedges) by 0.0001.

The risk weights for both the riskfree yield curve and the inflation rate RW_{k} are set at 1.58%.

The correlations between the riskfree yield curve and the inflation rate ρ_{kl} are set at 40%.
[Basel Framework, MAR 50.57]

The interest rate vega risk factors for all currencies:

The interest rate vega risk factors are a simultaneous relative change of all volatilities for the inflation rate and a simultaneous relative change of all interest rate volatilities for a given currency.

The sensitivity to (i) the interest rate volatilities or (ii) inflation rate volatilities is measured by respectively applying a simultaneous shift to (i) all interest rate volatilities or (ii) inflation rate volatilities by 1% relative to their current values and dividing the resulting change in the aggregate CVA (or the value of CVA hedges) by 0.01.

The risk weights for both the interest rate volatilities and the inflation rate volatilities RW_{k} are set to 100%.

Correlations between the interest rate volatilities and the inflation rate volatilities ρ_{kl} are set at 40%.
[Basel Framework, MAR 50.58]