New to banking regulation? Start with the basics glossary ↓. Underlined terms throughout this guide open a plain-language explanation and example.
Why the framework kept changing
A bank lends, trades and processes payments. Each activity can generate losses. The Basel Committee on Banking Supervision sets international prudential standards; national and regional authorities implement them through their own rules. The Committee was established in 1974 following disturbances in international banking, including the failure of Bankhaus Herstatt. [BCBS history]
Basel I
A common 8% total-capital benchmark, primarily for credit risk.
Market risk
The market-risk amendment extends capital coverage to trading exposures.
Basel II
More risk-sensitive calculations, three pillars and explicit operational-risk capital.
Basel 2.5
Stronger trading-book treatment following the financial crisis.
Final reforms
Revised RWA approaches, output floor and amended FRTB standards.
Publication dates describe international standards; domestic effective dates differ. History · Final Basel III reforms · Revised market-risk standard
1974: settlement risk and the Basel Committee
The failure of Bankhaus Herstatt exposed the danger of paying one currency before receiving the other in an FX transaction. Banking disturbances in 1974 prompted the formation of the Basel Committee. The Committee develops international standards; domestic authorities give them legal effect. BCBS history
Why a private bank needs a public capital standard
Deposit insurance protects depositors, but can weaken their incentive to monitor a bank. Expectations of government support can encourage risk-taking. A bank failure can disrupt other institutions and payments, while outsiders find loan books difficult to value. Capital standards help banks bear more of the losses associated with their decisions.
Average credit losses inform pricing and provisions. On ₹100 crore EAD, 1% PD and 45% LGD imply ₹0.45 crore expected loss.
Actual losses can exceed that average. Regulatory capital supports resilience against adverse outcomes.
A confidence level is a model calibration, not a guarantee. Stress testing and supervision examine vulnerabilities beyond one formula.
Under IRB, the comparison of regulatory expected loss with eligible provisions can itself create capital adjustments. Provisioning and capital therefore interact. IRB expected losses and provisions
Capital absorbs losses; RWA measures regulatory risk
Imagine Mountain Bank with ₹1,000 crore of assets funded by ₹920 crore of liabilities and ₹80 crore of equity. A ₹30 crore asset loss reduces equity to ₹50 crore, assuming liabilities stay unchanged.
Capital is a funding and loss-absorption layer, not a separate cash reserve. Liquidity concerns meeting payments when due. Regulatory capital also differs from accounting equity because eligibility criteria and deductions apply. [Basel III]
Simple credit example: RWA = Exposure amount × Applicable risk weight
| Qualifying exposure | Amount | Historical weight | RWA |
|---|---|---|---|
| Qualifying sovereign | ₹100 cr | 0% | ₹0 cr |
| Qualifying bank | ₹100 cr | 20% | ₹20 cr |
| Qualifying residential mortgage | ₹100 cr | 50% | ₹50 cr |
| Ordinary corporate loan | ₹100 cr | 100% | ₹100 cr |
| Total | ₹400 cr | — | ₹170 cr |
At 8%, illustrated capital is ₹170 crore × 8% = ₹13.6 crore. Historical eligibility conditions mattered; these weights are not current universal classifications. Broad categories could assign similar charges to borrowers with different risk profiles. [1988 Accord]
How netting reduces derivative exposure
Netting combines covered positive and negative derivative values into one enforceable obligation. Assume three trades with the same counterparty, all covered by one qualifying bilateral agreement, with values to the bank of +₹10 crore, −₹5 crore and +₹3 crore. Positive values are amounts receivable; a negative value is an amount payable by the bank.
₹13 crore
Current exposure = max(10, 0) + max(−5, 0) + max(3, 0). The payable ₹5 cannot offset separate positive claims.
₹8 crore
Current exposure = max(10 − 5 + 3, 0). The covered payable offsets the receivables.
Keep an add-on
Trade values can move after today. The historical Current Exposure Method (CEM) adds a prescribed allowance for PFE.
The 1995 netted add-on formula
NGR = Net replacement cost / Gross replacement cost
Credit equivalent = Current replacement cost + Applicable add-on
Assume the sum of the individual trade add-ons, Agross, is ₹5 crore. NGR = 8 / 13 = 0.6153846. It measures the extent of offsetting in current values. The formula keeps 40% of the gross add-on and scales the remaining 60% by NGR.
| Step | Without netting | With qualifying netting | Reason |
|---|---|---|---|
| 1. Current replacement cost | 10 + 3 = 13 | max(10 − 5 + 3, 0) = 8 | Covered negative values offset positive values only when the agreement qualifies. |
| 2. Net-to-gross ratio | Not used | 8 / 13 = 0.6153846 | Net current exposure divided by gross positive current exposure. |
| 3. Future-exposure add-on | Agross = 5.00 | 0.4 × 5 + 0.6 × (8 / 13) × 5 = 3.8461538 | ₹2.00 is retained; ₹1.8461538 comes from the NGR-weighted portion. |
| 4. Credit equivalent | 13 + 5 = 18.00 | 8 + 3.8461538 = 11.8461538 | Current exposure plus the allowance for potential future exposure. |
Reduction = (18 − 11.8461538) / 18 × 100 = 34.19%, or about 34%.
Use the unrounded 8 / 13 in calculations, then round the result. Displaying NGR as 0.62 is convenient for reading but gives ₹3.86 if used as the calculation input, rather than ₹3.85.
Why the agreement matters
Historical recognition required a single enforceable net obligation on default or insolvency, supported by legal review in the relevant jurisdictions. A liquidator must not be able to demand payment on favourable trades while rejecting unfavourable trades. Ordinary payment netting alone does not establish this protection. Do not offset trades with unrelated counterparties.
The 1995 amendment extended netting recognition to the add-on calculation and took effect from end-1995. This is the historical CEM treatment within Basel I as amended. The applicable counterparty risk weight converts the credit equivalent into RWA; the add-on itself is not a capital charge. BCBS 1995 amendment
Netting remains important under modern counterparty rules, but the old 0.4 / 0.6 formula does not calculate SA-CCR PFE. Compare the SA-CCR example →
Three pillars supporting one bank
Pillar 1 calculates prescribed requirements; Pillar 2 assesses whether they are sufficient for the institution; Pillar 3 makes the risk and capital position visible. [Basel II]
Pillar 1: connecting the three risks
12.5 = 1 ÷ 8%. This converts a capital charge into an RWA equivalent.
| Mountain Bank component | Input | RWA equivalent |
|---|---|---|
| Credit risk | Calculated RWA | ₹500 cr |
| Market risk | ₹8 cr capital × 12.5 | ₹100 cr |
| Operational risk | ₹4 cr capital × 12.5 | ₹50 cr |
| Total | 8% × ₹650 cr | ₹52 cr capital |
Simplified teaching calculation, before buffers and add-ons. Basel II capital calculation
Pillar 2: when a formula is not enough
Suppose most loans go to property developers in one city. A local downturn could harm many borrowers together. Mountain Bank's ICAAP should assess its risks, capital needs and capital strategy; supervisors review it and can require corrective action.
- Banks assess capital adequacy against their risk profile.
- Supervisors review the assessment and capital strategy.
- Banks are expected to operate above minimum ratios.
- Supervisors intervene early when capital becomes inadequate.
Concentration, interest-rate risk in the banking book, control weaknesses and stress scenarios belong in the broader review. [Supervisory review]
Pillar 3: understanding the number behind the number
Two banks can report the same capital ratio with different concentrations or calculation methods. Disclosures on exposures, RWA, capital and approaches help readers understand the difference. Common templates support comparison; disclosure does not replace supervision. [Disclosure framework]
Who estimates the risk inputs?
Credit risk arises when a borrower or counterparty fails to meet obligations. Three main routes illustrate the balance between prescribed rules and internal estimates.
IRB means Internal Ratings-Based. Both IRB routes use regulatory risk-weight functions and require supervisory approval. This foundation/advanced distinction applies to eligible non-retail exposures; retail IRB has its own treatment. Final reforms restrict A-IRB for certain classes and impose parameter floors. [IRB overview] [Revised credit risk]
| Input | Meaning | Example |
|---|---|---|
| PD | Probability of default | 1% over one year |
| LGD | Proportion lost conditional on default | 40% |
| EAD | Exposure at default | ₹100 cr |
| M | Effective maturity where applicable | 2.5 years |
Expected loss is an average-loss estimate, not the complete IRB capital requirement. Capital calculations use prescribed functions and further adjustments. Off-balance-sheet commitments also create exposures; conversion factors, collateral and guarantees affect the prescribed treatment. [Credit-risk framework]
Same loan amount, different RWA
A hypothetical ₹100 crore loan at a 100% weight produces ₹100 crore RWA and ₹8 crore capital at 8%. A hypothetical 50% weight produces ₹50 crore RWA and ₹4 crore capital. Classification and eligibility determine the actual weight.
Off-balance-sheet promises also create exposure
RWA = Credit equivalent × Applicable risk weight
In a historical Basel II illustration, a ₹100 crore transaction-related performance guarantee at 50% CCF becomes ₹50 crore credit exposure. With an assumed 100% borrower risk weight, RWA is ₹50 crore and capital at 8% is ₹4 crore. A financial standby letter of credit acting as a direct credit substitute attracts a different CCF, historically 100%. Classification matters. Historical conversion rules
Collateral: allow for a fall in its value
A haircut reduces the recognised value of collateral. For a simplified comprehensive-approach illustration, assume ₹100 crore exposure, ₹80 crore eligible collateral, a 4% collateral haircut, and zero exposure and currency-mismatch haircuts.
E* = ₹100 − ₹80 × 96% = ₹23.2 crore
At an assumed 100% risk weight: RWA ₹23.2 crore; capital at 8% ₹1.856 crore.
The 4% haircut is an assumed input. Eligibility, holding period, revaluation, legal enforceability and maturity mismatch affect actual recognition. Basel II credit-risk mitigation
From PD to a corporate-loan risk weight
Use a performing corporate exposure with EAD ₹100 crore, PD 1%, LGD 45% and effective maturity M = 2.5 years. This illustration uses the corporate function without an SME adjustment, a financial-institution correlation multiplier, buffers or the aggregate output floor. LGD 45% is an assumed permitted input, not a universal current foundation-IRB value.
ρ = 0.12w + 0.24(1 − w)
WCDR = N[(N−1(PD) + √ρ × N−1(0.999)) / √(1 − ρ)]
b = (0.11852 − 0.05478 × ln(PD))²
MA = [1 + (M − 2.5)b] / (1 − 1.5b)
K = LGD × (WCDR − PD) × MA
RWA = 12.5 × K × EAD
N is the standard normal cumulative distribution function; N−1 is its inverse. Enter PD and LGD as decimals. WCDR is the conditional default rate at the 99.9% model calibration; K is a capital fraction of exposure.
| Step | Calculated value |
|---|---|
| Correlation ρ | 0.192784 |
| WCDR | 14.0273% |
| Maturity adjustment MA | 1.25981 |
| K | 7.3853% |
| Risk weight = 12.5 × K | 92.3168% |
| RWA / capital at 8% | ₹92.3168 crore / ₹7.3853 crore |
With PD raised to 2% and other inputs unchanged, the risk weight becomes 114.8542%. The example shows risk sensitivity; IRB need not produce a lower weight than an assumed 100% standardised weight. Historical Basel II also used a 1.06 scaling factor on credit IRB RWA; the displayed calculation follows the revised function without that historical scaler. BCBS risk-weight functions
Continue from IRB to portfolio models: explore Credit VaR, the granularity adjustment and CreditMetrics in the Advanced Credit VaR guide →. Regulatory IRB capital and a portfolio’s modelled loss quantile answer related but different questions.
Counterparty risk: whose default changes the value?
A derivative can be an asset today and a liability later. Counterparty credit risk concerns default before final settlement. Netting and collateral can reduce exposure when the applicable legal and regulatory conditions are met.
What could the bank lose if the other party defaults?
How does the other party's credit risk reduce today's value?
How does the bank's own default risk affect valuation of its obligations?
1. Zero-coupon bond: one promise, one possible loss
You buy a one-year zero-coupon bond promising ₹100 at maturity. There are no interim coupons. Assume a 5% risk-free discount rate, a 2% risk-neutral probability of default before payment, and recovery of ₹40 at maturity if default occurs.
Credit-risky value = (98% × ₹100 + 2% × ₹40) ÷ 1.05 = ₹94.10
Credit deduction = 2% × (₹100 − ₹40) ÷ 1.05 = ₹1.14
CVA intuition: a promise is worth less when the payer might fail. The bond's ₹1.14 credit deduction illustrates the same expected discounted loss idea. An ordinary cash bond is usually priced with issuer credit risk embedded in its price or yield; this is an analogy, not a separate Basel derivative CVA capital charge on the bond.
2. Coupon bond: several promises over time
Now hold a two-year coupon bond with ₹100 face value and a 5% annual coupon. It pays ₹5 at year 1 and ₹105 at year 2 if the issuer survives. Keep the 5% risk-free discount rate. Assume a 2% conditional risk-neutral default probability in each year and ₹40 principal recovery at the end of the year of default; no coupon is paid in that default year and no further payments follow.
| When | Default-free cash flow | Probability-weighted cash flow with credit risk |
|---|---|---|
| Year 1 | ₹5 | 98% × ₹5 + 2% × ₹40 = ₹5.70 |
| Year 2 | ₹105 | 98%² × ₹105 + (98% × 2%) × ₹40 = ₹101.626 |
Credit-risky value = ₹5.70 / 1.05 + ₹101.626 / 1.05² = ₹97.61
Credit deduction = ₹2.39
The year-1 expected cash flow exceeds the ₹5 coupon because some scenarios repay ₹40 recovery early; those scenarios lose all year-2 payments. Each payment date, survival probability and recovery assumption matters. This is why a multi-period credit adjustment needs a timeline rather than simply multiplying all promised coupons by one default probability.
3. DVA: turn the promise around
For the zero-coupon bond, the investor holds an asset and the issuer owes a liability. Under the same fair-value assumptions, the issuer's liability magnitude is ₹94.10 instead of the default-free ₹95.24. The ₹1.14 reduction illustrates DVA: the issuer's own possible non-payment reduces the fair value of what it owes. It does not change the contractual ₹100 due, produce cash, or reduce a liability carried at amortised cost automatically. The investor sees credit risk; the issuer sees own-credit risk.
4. Interest-rate swap: the promise can change direction
Bank A pays a fixed 5% and receives a floating rate from Company B on a ₹1 crore notional. In this plain interest-rate swap, the notional is used to calculate interest; it is not exchanged. For a one-year period with no day-count adjustment, a 7% floating fixing means A receives a net ₹2 lakh; a 3% fixing means A pays a net ₹2 lakh.
₹1 crore × (7% − 5%) = ₹2 lakh.
B's failure to pay hurts A: CVA.
₹1 crore × (5% − 3%) = ₹2 lakh.
A's own failure to pay affects its liability value: DVA.
Use the amount at risk on replacement or settlement, not the ₹1 crore notional automatically.
For a final-settlement teaching example, use a 5% discount rate and 60% LGD. In the receive case, assume B has a 2% risk-neutral default probability. In the pay case, assume A has a 1% own risk-neutral default probability. Treat these as separate scenarios, with no collateral or netting.
| A's perspective | Adjustment | Adjusted signed value |
|---|---|---|
| Receive ₹2 lakh: clean value +₹190,476.19 | CVA = ₹200,000 × 2% × 60% / 1.05 = ₹2,285.71 | +₹190,476.19 − ₹2,285.71 = +₹188,190.48 |
| Pay ₹2 lakh: clean value −₹190,476.19 | DVA = ₹200,000 × 1% × 60% / 1.05 = ₹1,142.86 | −₹190,476.19 + ₹1,142.86 = −₹189,333.33 |
A newly agreed market-rate swap can have zero clean value today and still have future positive and negative exposure as rates move. A full swap valuation therefore uses future exposure profiles; the two settlement scenarios above explain the signs, not a complete swap pricing model. All default probabilities here are pricing assumptions, not historical default forecasts. BCBS CVA definition and regulatory scope
A one-period example in ₹ crore
Assume separate expected positive and negative exposure measures, discount factor 1, and market-consistent (risk-neutral) default probabilities. Ignore collateral, netting and first-to-default effects for this teaching example.
| Adjustment | Assumptions | Result |
|---|---|---|
| CVA: counterparty default | Positive exposure ₹10 × counterparty PD 2% × LGD 60% | ₹0.12 crore (₹12 lakh) |
| DVA: own default | Negative-exposure magnitude ₹8 × own PD 1% × LGD 60% | ₹0.048 crore (₹4.8 lakh) |
If clean value is ₹2 crore: ₹2 − ₹0.12 + ₹0.048 = ₹1.928 crore.
The positive and negative exposure measures describe possible future states; they are not both today's signed market value. Real pricing uses discounted exposure profiles, default timing, dependence, close-out terms, collateral and netting. Bilateral valuation research
CVA loss can occur before any default
If the illustrative counterparty PD rises from 2% to 4% with exposure and LGD unchanged, CVA rises from ₹0.12 crore to ₹0.24 crore in this fixed-exposure, one-period example. Over multiple periods it approximately doubles: survival weighting generally makes the increase slightly less than twofold. The one-period value falls by ₹0.12 crore even though the counterparty has not defaulted.
Basel CVA risk capital addresses losses from changing CVA as counterparty spreads and relevant market factors move. It is distinct from the CVA valuation amount and from counterparty default capital. Regulatory CVA excludes the bank's own default effect. Official CVA framework
A five-year swap: add the loss at each date
A flat 200 bp CDS spread and 40% recovery give the teaching approximation λ ≈ 0.02 / 0.60 = 3.3333% per year. Survival S(t) = exp(−λt); the marginal default probability in year t is S(t−1) − S(t). Actual pricing calibrates a default curve to market quotes.
| Year | Expected exposure ($mn) | Marginal PD | Assumed discount factor | CVA contribution ($000) |
|---|---|---|---|---|
| 1 | 1.20 | 3.2784% | 0.961 | 22.68 |
| 2 | 1.60 | 3.1709% | 0.923 | 28.10 |
| 3 | 1.70 | 3.0670% | 0.887 | 27.75 |
| 4 | 1.40 | 2.9664% | 0.852 | 21.23 |
| 5 | 0.80 | 2.8691% | 0.819 | 11.28 |
Total CVA is approximately $111,038 using the stated discount factors and unrounded probabilities. This assumes independence between exposure and default, time-bucket approximations and no collateral. Converting it to a swap-rate spread additionally requires notional and the swap annuity. Default-curve calibration research
SA-CCR and BA-CVA answer separate questions
SA-CCR determines exposure at default for counterparty default capital. With assumed replacement cost RC ₹2 crore and calculated PFE ₹0.5 crore, EAD = 1.4 × (RC + PFE) = ₹3.5 crore. PFE follows the prescribed add-on and multiplier rules. SA-CCR rules
Reduced BA-CVA calculates CVA risk capital without recognising hedges. For one non-IMM netting set per counterparty:
DF = [1 − exp(−0.05M)] / (0.05M)
K = 0.65 × √[(0.5 × ΣSCVA)² + 0.75 × Σ(SCVA²)]
Read the parameters: ρ = 50% is the supervisory correlation parameter; 1 − ρ² = 0.75. The 0.65 is the BA-CVA discount scalar, DSBA-CVA, applied after aggregation. RW is a supervisory spread-risk weight; M is effective maturity in years; DF is the supervisory discount factor; SCVA is stand-alone CVA capital before portfolio aggregation.
| Counterparty | RW | EAD ($mn) | M | DF | SCVA ($mn) |
|---|---|---|---|---|---|
| Bank C · Investment-grade financial | 5% | 100 | 5 years | 0.884797 | 15.79994 |
| Firm T · Investment-grade technology | 2% | 50 | 3 years | 0.928613 | 1.98989 |
≈ $16.41091 million before scaling
DSBA-CVA × Kreduced = 0.65 × 16.41091
CVA risk capital ≈ $10.6671 million
CVA RWA = 12.5 × capital ≈ $133.3386 million
Where do the 5% and 2% come from?
These weights measure supervisory credit-spread risk for BA-CVA; they are not ordinary credit-default risk weights. IG means investment grade; HY means high yield; NR means not rated.
| Counterparty sector | IG | HY and NR |
|---|---|---|
| Sovereigns, central banks, multilateral development banks | 0.5% | 2.0% |
| Local government, government-backed non-financials, education, public administration | 1.0% | 4.0% |
| Financials, including government-backed financials | 5.0% | 12.0% |
| Basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying | 3.0% | 7.0% |
| Consumer goods/services, transportation/storage, administrative/support services | 3.0% | 8.5% |
| Technology, telecommunications | 2.0% | 5.5% |
| Health care, utilities, professional/technical activities | 1.5% | 5.0% |
| Other sector | 5.0% | 12.0% |
MAR50.16 · complete supervisory table. Internal-to-external rating mapping needs supervisory permission where applicable; otherwise use NR treatment.
A single-name CDS on Bank C
Keep the same two counterparties. Buy an eligible five-year CDS directly referencing Bank C, managed as a CVA credit-spread hedge. Assume notional $71.42857 million, matching currency and maturity, no index hedge, and no indirect hedge. This is an intentionally matched teaching hedge, not a hedge-cost or trading recommendation.
= 1 × 5% × 5 × 71.42857 × 0.884797 = 15.79994 ($mn)
The direct-reference correlation rhC = 100%. Hedge notional is $100mn / 1.4, so this construction offsets Bank C’s SCVA. Hedge recognition uses notional, not the CDS market value, and has no extra division by 1.4. Firm T has SNH = 0. Define residual Xc = SCVAc − SNHc; then XC = 0 and XT = 1.98989. IH (index hedge recognition) = 0; HMA (indirect-hedge misalignment) = 0.
= √[(0.5 × 1.98989)² + 0.75 × 1.98989²] = 1.98989 ($mn)
β = 0.25
Kfull = β × Kreduced + (1 − β) × Khedged
= 0.25 × 16.41091 + 0.75 × 1.98989 = 5.59514 ($mn)
Full BA-CVA capital = 0.65 × Kfull = $3.63684 million
CVA RWA = 12.5 × 3.63684 = $45.4605 million
Capital falls about 65.9%. It stays positive: Firm T remains unhedged and the 25% reduced-component floor limits hedge recognition. Direct, legally related and sector/region proxy hedges receive different correlations; imperfect hedges need the misalignment term. CVA desks manage these spread exposures as well as pricing and market sensitivities. MAR50.17–50.26 · eligibility and full formula
Scope, proportionality and SA-CVA
What is covered?
Covered derivatives attract CVA risk capital. Transactions directly with qualifying central counterparties are excluded. Securities financing transactions enter only when their fair-value CVA is material, as assessed by the supervisor.
MAR50.5–50.9, 50.27–50.30 and sensitivities rules · 2020 targeted revisions. These are global Basel provisions; confirm domestic adoption before applying them to an Indian bank.
Accounting CVA versus CVA risk capital
| Accounting / pricing CVA | BA-CVA capital | |
|---|---|---|
| Question | What expected counterparty loss adjusts today’s value? | What capital covers adverse changes in CVA? |
| Inputs | Market-implied default probabilities from CDS spreads, expected exposure, recovery and discounting | Supervisory sector/credit-quality weights, EAD, maturity and aggregation; eligible hedges for full BA-CVA |
| Page illustration | Five-year swap: about $111,038 (rounded PD inputs) | Two-counterparty portfolio: $10.6671 million before hedging |
Different quantities and different portfolios: these examples explain two methods; their roughly 96-fold numerical difference is not a same-portfolio capital-to-CVA ratio. Capital is a loss-absorption requirement, not an additional valuation deduction of that amount.
Revisit bond and swap valuation examples → · See capital after the CDS hedge →
When prices move against the trading desk
Interest rates, credit spreads, exchange rates, equity prices and commodity prices can change portfolio values.
₹100 crore portfolio · Modified duration 5
Approximate price change = −Modified duration × Yield change. This ignores convexity and other effects. It is a sensitivity illustration, not a full capital calculation.
| Stage | Standardised route | Internal-model route |
|---|---|---|
| Basel II / pre-crisis | Prescribed market-risk charges | Primarily VaR-based requirements |
| Basel 2.5 | Strengthened treatment of certain trading exposures | Stressed VaR and incremental risk requirements |
| FRTB / Basel III | SBM + DRC + RRAO | Expected Shortfall, non-modellable risks and default risk |
Historical standardised rules · Historical internal models · Revised market risk
Historical VaR capital and the stress-period addition
In a simplified 1996-style example, yesterday's 10-day 99% VaR is ₹12 crore, the preceding 60-business-day average is ₹10 crore, the multiplier is 3 and the applicable separate specific-risk charge is ₹5 crore.
Assume the later Basel 2.5 stressed-VaR calculation produces an additional ₹75 crore charge. The same simplified total rises to ₹110 crore before any further applicable requirements. Stressed VaR used a relevant continuous 12-month stress period; incremental default/migration risk and securitisation treatment also mattered. These are historical illustrations, not the FRTB formula. Historical internal-model rules
FRTB: the Basel III market-risk redesign
FRTB addresses shortcomings exposed by the crisis: losses beyond a VaR threshold, liquidity under stress, model weaknesses and movement of positions between regulatory books. The standard was published in 2016 and amended in 2019. Banking-book/trading-book designation follows prescribed criteria; it is not a choice based on which treatment is cheaper. [FRTB standard]
The standardised route: three distinct components
| Component | What it captures | Example |
|---|---|---|
| SBM | Delta, vega and curvature exposures | Rate sensitivity of a bond; volatility sensitivity of an option |
| DRC | Jump-to-default risk | A trading-book bond issuer defaults |
| RRAO | Specified residual risks | Certain exotic underlyings and complex payoff risks |
Weighted sensitivities are aggregated under prescribed correlation scenarios. The three main charges are added without diversification benefits between them. [FRTB standardised structure]
How does value change with a small movement in the underlying risk factor?
How does value change when implied volatility moves?
What extra loss appears under large shocks because value changes nonlinearly?
Curvature uses prescribed upward and downward shocks; it is not simply gamma multiplied by a risk weight. The SBM covers interest rates, credit spreads, equities, FX and commodities, including specified securitisation risk classes. [SBM rules]
Market RWA equivalent = ₹8.5 cr × 12.5 = ₹106.25 cr
Assumed charge outputs, not a full trade-level calculation.
Internal models: looking into the loss tail
VaR identifies a loss threshold at a chosen confidence level. Expected Shortfall averages losses in the tail beyond that threshold.
97.5% ES = (10 + 12 + 15 + 20 + 43) ÷ 5 = ₹20 crore
VaR sits at the boundary of this tail; its exact empirical value depends on the quantile convention.
FRTB uses 97.5% ES calibrated to stress, with prescribed liquidity horizons from 10 to 120 days. Separate default-risk and non-modellable-risk requirements also matter. ES alone is not the total capital charge. [Internal-model capital calculation]
Models must earn their place
| Control | Question |
|---|---|
| Trading-desk approval | Is model use justified for this desk? |
| Backtesting | How do predicted risk measures compare with observed P&L? |
| P&L attribution | Does risk-theoretical P&L adequately track hypothetical P&L? |
| Risk-factor modellability | Are sufficient qualifying price observations available? |
Eligibility failures can require standardised treatment under the prescribed rules. Non-modellable factors require separate capital treatment rather than disappearing from the calculation. [Model testing] [FRTB overview]
From income proxies to a revised standardised method
Failed processes, people, systems and external events can cause operational losses. Legal risk is included; strategic and reputational risk are excluded from this regulatory definition. [Operational risk]
Payment errors, fraud and control failures
Cyber incidents and infrastructure outages
Disruption and other operational loss events
Historical Basel II approaches
| Approach | Basis | Illustration |
|---|---|---|
| BIA · Basic Indicator | 15% of average positive annual gross income over three years | ₹100 cr average → ₹15 cr capital |
| TSA · Standardised | Business-line income × prescribed beta | Retail banking 12%; commercial banking 15% |
| AMA · Advanced Measurement | Approved internal measurement system | Loss data, scenarios and control factors |
BIA example: gross income of ₹80, ₹100 and ₹120 crore averages ₹100 crore. Capital = 15% × ₹100 crore = ₹15 crore. RWA equivalent = ₹187.5 crore. Non-positive years are excluded; gross income is a regulatory measure, not net profit. [Historical BIA]
| 18% | 15% | 12% |
|---|---|---|
| Corporate finance Trading and sales Payment and settlement | Commercial banking Agency services | Retail banking Asset management Retail brokerage |
Assuming identical positive income in all three years and no other activities: retail ₹100 cr × 12% + commercial ₹50 cr × 15% = ₹19.5 cr capital. Actual TSA applies annual calculations and negative-income rules. AMA used internal and external losses, scenarios, and business-environment and internal-control factors. [Basel II operational approaches]
Final Basel III: a single standardised methodology
Assumed BIC ₹20 cr × ILM 1.2 = ₹24 cr capital
RWA equivalent = ₹24 cr × 12.5 = ₹300 cr
The financial-statement-based Business Indicator is converted to BIC using marginal coefficients. Historical losses inform ILM, subject to rules and national discretion; authorities can set ILM to one. The revised approach replaces BIA, TSA and AMA where implemented. It is distinct from the historical TSA despite the shared term “standardised”. [Revised operational risk]
Calculate BIC and ILM rather than assuming them
Assume a Business Indicator of €20 billion and eligible average annual operational losses of €0.25 billion over ten years. Use the Basel methodology with loss experience included.
Loss component LC = 15 × €0.25bn = €3.75bn
ILM = ln[e − 1 + (LC / BIC)0.8] = 1.072738
Operational-risk capital = €2.97bn × 1.072738 = €3.1860bn
The coefficients are marginal: 12% up to €1bn, 15% for the portion above €1bn up to €30bn, and 18% above €30bn. Applying 15% to the whole €20bn would be incorrect. If the authority sets ILM to one, this example gives €2.97bn capital. BCBS operational-risk calculation
Capital quality, buffers and funding resilience
Tier 1 = CET1 + AT1; Total capital = Tier 1 + Tier 2. Goodwill and other regulatory adjustments can reduce eligible capital. [Capital eligibility]
| Ratio | Baseline minimum | With conservation buffer alone |
|---|---|---|
| CET1 / RWA | 4.5% | 7% |
| Tier 1 / RWA | 6% | 8.5% |
| Total capital / RWA | 8% | 10.5% |
The 2.5% conservation buffer is CET1. Additional countercyclical, systemic-bank and supervisory requirements can apply. Entering the buffer brings distribution restrictions; it differs from breaching a minimum. These nested ratios are not added together. [Minimums and buffers]
Tier 1 ÷ Exposure
Baseline 3%. Exposure includes prescribed asset, derivative, financing and off-balance-sheet treatment.
Leverage rules →HQLA ÷ Net outflows
30-day prescribed stress window. Baseline 100% in normal conditions; buffers are usable in stress.
LCR rules →ASF ÷ RSF
Available versus required stable funding over a one-year horizon. Baseline 100%.
NSFR rules →Illustrations: ₹72 cr Tier 1 / ₹2,400 cr exposure = 3%; ₹150 cr HQLA / ₹120 cr net outflows = 125% LCR; ₹850 cr ASF / ₹800 cr RSF = 106.25% NSFR. Each ratio answers a different resilience question.
Meeting the minimum while entering the buffer
Bank X has RWA ₹1,000 crore, CET1 ₹60 crore, AT1 ₹15 crore and Tier 2 ₹25 crore. Its ratios are CET1 6%, Tier 1 7.5% and total capital 10%. It meets the global 4.5%, 6% and 8% minimums but falls below the corresponding levels with the conservation buffer alone.
| CET1 ratio | Minimum earnings retained |
|---|---|
| 4.5% to 5.125% | 100% |
| Above 5.125% to 5.75% | 80% |
| Above 5.75% to 6.375% | 60% |
| Above 6.375% to 7% | 40% |
| Above 7% | 0% under this schedule |
With no other requirements, Bank X's 6% CET1 ratio places it in the 60% retention band. Higher buffers or other constraints can tighten distributions. Only CET1 available after meeting minimum capital requirements counts toward the buffer. BCBS conservation rules
LCR and NSFR: different clocks, different questions
| Measure | Teaching example | Interpretation |
|---|---|---|
| LCR: 30-day stress | ₹150 cr HQLA ÷ ₹120 cr prescribed net outflows = 125% | Eligible liquid assets exceed the assumed stress outflows. |
| LCR: larger outflow estimate | ₹150 cr ÷ ₹180 cr = 83.33% | Below the normal-condition 100% minimum; buffers may be used during actual stress under supervisory assessment. |
| NSFR: one-year structure | ₹850 cr available stable funding ÷ ₹800 cr required stable funding = 106.25% | Weighted stable funding exceeds the required amount. |
| NSFR: more illiquid assets | ₹850 cr ÷ ₹900 cr = 94.44% | Stable funding is insufficient under the assumed weighted requirements. |
These amounts are assumed outputs of prescribed calculations. LCR is not simply cash divided by deposits; NSFR is not simply long-term borrowing divided by long-term loans. Eligibility, haircuts, weights and cash-flow assumptions matter. LCR rules · NSFR rules
Build the LCR numerator and denominator
Assume all assets qualify and are available, with no short-term financing unwinds affecting the caps.
| HQLA | Amount (₹cr) | Haircut | Recognised value (₹cr) |
|---|---|---|---|
| Eligible Level 1 | 150 | 0% | 150 |
| Eligible Level 2A | 60 | 15% | 51 |
| Eligible Level 2B equities / corporate debt subject to 50% haircut | 20 | 50% | 10 |
| Total | 230 | — | 211 |
Level 2 contributes 61 / 211 = 28.91%, below the 40% cap; Level 2B contributes 10 / 211 = 4.74%, below 15%. Some other Level 2B categories have different haircuts. HQLA eligibility and caps
Recognised inflows = min(₹120cr, 75% × ₹260cr) = ₹120cr
Net outflows = ₹260cr − ₹120cr = ₹140cr
LCR = ₹211cr / ₹140cr = 150.71%
The 5%, 10% and 40% rates assume qualifying stable retail, less-stable retail and qualifying non-financial wholesale funding respectively. Different deposit classifications can change them. Cash-flow rules
Build NSFR using funding and asset weights
| Funding / ASF | Amount (₹cr) | Factor | Weighted amount |
|---|---|---|---|
| Qualifying regulatory capital with required maturity | 100 | 100% | 100 |
| Qualifying stable retail deposits <1 year | 600 | 95% | 570 |
| Qualifying less-stable retail deposits <1 year | 400 | 90% | 360 |
| Other qualifying funding, 6 to <12 months | 900 | 50% | 450 |
| Total ASF | 2,000 | — | 1,480 |
| Assets / RSF | Amount (₹cr) | Factor | Weighted amount |
|---|---|---|---|
| Cash | 100 | 0% | 0 |
| Eligible unencumbered Level 1 securities | 300 | 5% | 15 |
| Performing non-financial corporate loans <1 year | 500 | 50% | 250 |
| Eligible unencumbered mortgages ≥1 year, qualifying ≤35% risk weight | 600 | 65% | 390 |
| Other qualifying unencumbered performing loans ≥1 year to non-financial borrowers | 500 | 85% | 425 |
| Total RSF | 2,000 | — | 1,080 |
“Wholesale funding under one year” alone is insufficient to assign 50% ASF. Provider type and remaining maturity matter. This example excludes derivatives, encumbrance and off-balance-sheet funding needs. ASF and RSF rules
Liquidity is a payment-timing problem
Can we meet stressed payments?
Compare usable HQLA with prescribed net cash outflows. A solvent bank may still need cash today.
| Illustrative bank | LCR | NSFR | What needs attention? |
|---|---|---|---|
| A · temporary cash buffer | ₹160 / ₹120 = 133.33% | ₹700 / ₹800 = 87.50% | Passes the short stress metric, but stable funding is insufficient. |
| B · stable but cash-poor | ₹90 / ₹120 = 75% | ₹900 / ₹800 = 112.50% | Stable structure does not cover the prescribed 30-day outflows. |
| C · stronger on both | ₹150 / ₹120 = 125% | ₹900 / ₹800 = 112.50% | Both ratios exceed the global baseline; concentrations and currency mismatches still matter. |
Three details that change the answer
The inflow cap: with outflows ₹260 crore and otherwise eligible inflows ₹240 crore, recognition is capped at 75% × ₹260 = ₹195 crore. Net outflows remain ₹65 crore, rather than ₹20 crore. With ₹211 crore eligible HQLA, LCR is 324.62%. The cap retains a buffer instead of relying entirely on incoming payments.
Haircuts and composition: ₹100 crore qualifying Level 2A securities contribute ₹85 crore before composition limits. Level 2 assets collectively face a 40% limit and Level 2B a 15% sublimit. Actual cap calculations adjust for specified short-term financing unwinds; the lab below assumes none.
Encumbrance: an asset pledged to another lender may be unavailable to meet other outflows. Saleability alone does not establish HQLA eligibility; legal, operational and category conditions matter.
HQLA rules · LCR cash-flow rules · NSFR funding and asset factors
From a market shock to a liquidity spiral
Collateral falls
Cash payments rise
Price pressure rises
A swap portfolio can require variation margin before any counterparty defaults. A borrower can draw an unused credit line while deposits leave. Funding liquidity and market liquidity can therefore reinforce credit and market losses.
Simple liquidity stress: start with ₹150 crore usable liquid assets and ₹120 crore assumed net outflows (125%). Add a ₹30 crore margin payment and ₹20 crore commitment drawdown, holding the numerator fixed for illustration: outflows become ₹170 and coverage falls to 88.24%. This is an internal cash-flow scenario, not a substitute for the regulatory LCR’s prescribed classifications.
A maturity ladder places contractual and behavioural inflows and outflows in time buckets. With usable opening cash ₹80 crore, day-1–7 payments ₹50 and receipts ₹10, cash falls to ₹40. With day-8–30 payments ₹70 and receipts ₹20, cash becomes −₹10: funding must be arranged before those payments fall due. A thirty-day total can hide an earlier cash shortage.
A contingency funding plan identifies collateral mobilisation, dependable funding options, escalation triggers and communication responsibilities. Test currency-specific cash needs and deposit concentration; do not assume a high consolidated ratio means cash can move freely between entities or currencies.
Mountain Bank’s liquidity simulator
Move one input at a time. This simplified lab starts with the worked example above. Amounts are ₹ crore. It assumes qualifying assets and funding, no encumbrance, and no short-term financing unwinds.
Read the assumptions and limits
LCR sliders use already-classified cash flows. Level 2B means only the assumed category with a 50% haircut. Composition adjustments use the simplified no-unwind setting. For NSFR, qualifying stable retail funding has 95% ASF; the replacement is financial-institution funding with maturity under six months, assumed 0% ASF. Cash has 0% RSF; replacement loans are qualifying unencumbered performing long-term non-financial loans at 85% RSF. Base ASF = ₹1,480 and RSF = ₹1,080. NSFR changes hold total assets and funding constant. These NSFR changes are isolated structural experiments: the lab does not simultaneously reclassify deposits in the LCR or deduct the cash-to-loan switch from the separate HQLA sliders.
100% is the global normal-condition baseline. Falling below LCR during actual stress can reflect intended buffer use and requires supervisory assessment. This lab is not a jurisdiction-specific compliance calculation.
Where the eleven advanced concepts fit in Basel
Basel sets minimum standards and supervisory requirements. An internal portfolio model supports decisions but does not automatically become a permitted Pillar 1 calculation. Use the distinctions below to connect portfolio risk with the regulatory framework.
| Concept | Basel connection | Worked model detail |
|---|---|---|
| Random / downturn LGD | Recovery estimates and permitted IRB inputs; Pillar 2 severity stress | Example & calculations → |
| Student-t copula | Dependence sensitivity and model risk under Pillar 2 | Example & calculations → |
| Euler allocation | Internal risk budgeting and ICAAP; not a replacement for prescribed RWA | Example & calculations → |
| Analytic credit ES | Validation benchmark; distinct from FRTB market-risk ES | Example & calculations → |
| Simulation confidence intervals | Numerical precision and model validation | Example & calculations → |
| CreditRisk+ | Internal loan-book model and concentration analysis | Example & calculations → |
| CreditPortfolioView | Macroeconomic PD and migration stress; capital planning | Example & calculations → |
| FRTB DRC and earlier IRC | Trading-book capital: default versus default-plus-migration | Example & calculations → |
| IFRS 9 / Ind AS 109 ECL | Provisions, earnings, eligible capital and IRB EL comparison | Example & calculations → |
| Counterparty loss and CVA risk | Exposure dynamics, SA-CCR and separate CVA capital | Example & calculations → |
| Climate / transition overlays | Scenario-based credit and liquidity assessment | Example & calculations → |
Pillar 2 · translate model risk into management action
For the constructed ₹100 crore loan book, matched simulations give 99.9% loss VaR of ₹7.965 crore with fixed LGD under Gaussian dependence, ₹12.2955 with adverse common LGD shocks, and ₹19.665 with a Student-t copula (five degrees of freedom, fixed LGD). The models preserve stated marginal inputs, but the dependent-LGD model also increases mean loss. These are internal-model sensitivity results, not three alternative Basel risk weights.
ICAAP asks whether capital and risk controls remain appropriate when the assumptions are challenged. Document PD/LGD calibration, concentration, tail dependence and simulation error. The original simulation’s VaR ₹8.01 has a sampling bracket [₹7.965, ₹8.145]; this says nothing about whether the model’s assumptions represent the bank.
Two granular sectors sharing one factor contribute ₹4.7609 and ₹9.7484 crore to an internal loss VaR of ₹14.5093. Those Euler contributions can guide sector limits and pricing. Regulatory RWA allocation follows the applicable rules and is not automatically identical to internal tail-risk allocation.
CreditRisk+ groups exposure losses and models uncertain default intensities; CreditPortfolioView links probabilities to macro conditions. Neither name, by itself, denotes an approved IRB approach. See the linked worked examples for their numerical distributions and assumptions.
FRTB · keep spread ES and default risk separate
For five equally likely worst-tail losses of ₹10, ₹12, ₹15, ₹20 and ₹43 crore, ES is ₹20 crore. This explains averaging tail severity; it is not a complete FRTB charge, which also requires stress calibration, liquidity-horizon treatment and risk-factor eligibility.
The Gaussian credit-book analytic 99.9% ES ₹9.4232 is a different calculation from FRTB’s 97.5% market-risk ES. FRTB internal-model DRC uses one-tail 99.9% VaR over one year; earlier IRC included default and migration. The standardised DRC instead uses prescribed jump-to-default treatment.
A ₹10 crore face-value bond worth ₹9.5 before default and recovering ₹4 has a ₹5.5 jump loss. Spread losses while it survives are separate. A default hedge can leave liquidity risk if margin cash is required immediately or hedge maturities differ.
Provisions, expected loss and capital
A provision recognises expected cash shortfalls; capital absorbs losses and supports solvency. An accounting expense can reduce retained earnings and therefore CET1, subject to the applicable regulatory adjustments. It does not necessarily remove the same amount of usable cash immediately.
Illustration: starting CET1 ₹80 crore and an additional ₹2 crore provision give ₹78 crore before tax effects, relief or other prudential adjustments. With unchanged RWA ₹1,000 crore, the ratio falls from 8% to 7.8%. This is an accounting-to-capital bridge, not a full regulatory calculation.
Under IRB, compare regulatory expected loss with eligible provisions under prescribed rules; shortfall and excess treatment differ. Accounting lifetime ECL is not automatically identical to regulatory EL, because horizons, scope and parameters can differ. Avoid deducting expected loss twice.
Stage 1 generally measures 12-month ECL; Stage 2 and credit-impaired Stage 3 generally use lifetime ECL. The related worked accounting example gives ₹0.4286 versus ₹2.3682 for its constructed three-year loan. RBI’s 27 April 2026 press release states a 1 April 2027 commencement for its new Commercial Banks directions; this remains prospective as of 10 October 2026.
Accounting example and source details · IRB EL and provision treatment
Counterparty risk · three different numbers
| Object | Question | Simple swap illustration |
|---|---|---|
| Future exposure / EAD | What can the counterparty owe when default occurs? | Exposure ₹10 or ₹30 with equal probability; mean positive exposure ₹20. Regulatory EAD requires the applicable method. |
| Counterparty default-loss VaR | How severe can realised credit loss become? | PD 2%, LGD 60%, independent exposure: EL ₹0.24; 99.9% loss VaR ₹18. |
| CVA and CVA risk | What is today’s pricing adjustment, and how can it change? | DF 0.97 × pricing LGD 60% × expected exposure ₹20 × pricing PD 3% = ₹0.3492 CVA. |
EE is exposure averaged at one date; EPE averages EE over a period. An average cannot reproduce an exposure tail. Wrong-way risk can raise losses even when marginal PD and average exposure stay unchanged. A margin call affects cash now, while counterparty default and CVA revaluation affect different risk measures.
SA-CCR supplies prescribed exposure measurement. Current Basel CVA capital uses BA-CVA or SA-CVA, rather than an arbitrary internal CVA VaR. DVA reflects own-default effects in bilateral valuation; it is not a usable counterparty loss cushion. Return to SA-CCR and CVA capital →
Climate and sector stress · follow both capital and cash
For a ₹40 crore manufacturing sector, an illustrative PD rise from 4% to 6% and LGD rise from 60% to 65% increase EL from ₹0.96 to ₹1.56 crore. In the related one-factor model, sector loss VaR rises from ₹9.7484 to ₹12.8843. These are constructed assumptions, not an NGFS forecast.
Translate transition costs or physical damage into borrower cash flows, collateral, loan drawdowns and deposit behaviour. An impaired factory can raise credit losses and cause a borrower to draw its committed line. Assess liquidity alongside capital; do not assume a thirty-year scenario directly calibrates a one-year PD.
Climate overlays support risk assessment and supervisory dialogue. They do not establish a universal automatic climate risk weight. Document the causal mechanism, uncertainty and effects already included in ordinary ratings or sector stress.
Mountain Bank's capital lab
Change capital, risk exposures or loss assumptions. Watch how headroom changes. This teaching lab uses Basel global minimums and a conservation buffer only; it is not a jurisdiction-specific compliance assessment.
₹10 cr loss preset: adjusted CET1 = 64 − 10 = 54; Tier 1 = 54 + 8 = 62; total capital = 62 + 16 = 78. RWA stays 800. CET1 ratio = 54 / 800 = 6.75%. This is the same ₹64 → ₹54 example used in the glossary.
Loss is assumed to reduce CET1 directly while RWA and leverage exposure remain as entered. Taxes, provisions, regulatory adjustments, output floor and local add-ons are excluded. Market and operational charges are user-supplied outputs, not model calculations.
Read Basel through the Indian rules
For commercial banks covered by RBI’s capital-adequacy directions, the minimum total capital ratio is 9%, CET1 is 5.5% and Tier 1 is 7%. Add the 2.5% CET1 capital conservation buffer: CET1 8%, Tier 1 9.5%, total capital 11.5%, before applicable systemic or other additional requirements. The leverage minimum is 4% for D-SIBs and 3.5% for other covered banks. The teaching lab above uses global Basel thresholds, so its green status does not certify Indian compliance.
RBI’s revised Standardised Approach for credit risk directions take effect on 1 April 2027 for their specified commercial-bank banking-book exposures. That commencement date does not by itself establish BA-CVA or SA-CVA adoption.
RBI current capital-adequacy directions · paragraphs 16–17, 85, 249 and 262 · Current RBI PDF · RBI 2026 credit-risk directions · commencement and scope
The output floor, illustrated
At full phase-in, aggregate RWA cannot fall below 72.5% of the prescribed standardised benchmark. It is a floor on RWA, not a 72.5% capital ratio. [Final reforms]
Applied RWA = max(pre-floor RWA, calibration × standardised benchmark). Global Basel schedule shown; local dates differ. Optional transitional caps and other local treatments are excluded. Transitional arrangements
Three risks, different methods
| Risk | Historical Basel II | Final Basel III direction | Key learning point |
|---|---|---|---|
| Credit | SA · F-IRB · A-IRB | Revised SA, constrained IRB and parameter floors | IRB estimates inputs; regulatory functions remain prescribed |
| Market | Standardised · VaR-based IMA | FRTB SA · FRTB IMA | SA = SBM + DRC + RRAO; IMA uses ES plus other components |
| Operational | BIA · TSA · AMA | Single standardised methodology | Revised SA differs from historical TSA |
Common questions and misconceptions
Is FRTB part of Basel II or Basel III?
FRTB is the revised Basel III market-risk framework. Basel II and Basel 2.5 provide the historical context.
Are the three pillars the same as the three risks?
No. Credit, market and operational risk are Pillar 1 risk categories. Pillar 2 adds supervisory review; Pillar 3 adds disclosure and market discipline.
Does expected loss equal regulatory credit capital?
No. PD × LGD × EAD estimates expected loss. The IRB capital calculation uses prescribed functions and further treatment of inputs and provisions.
Does an internal model always produce less capital?
No. Model approval, parameter floors, conservative calibration and the aggregate output floor constrain the results.
Is 10.5% the final requirement for every bank?
No. It is total capital with the conservation buffer alone. Countercyclical, systemic-bank, supervisory and local requirements can add to it.
Are BIA, TSA and AMA still the final Basel operational-risk methods?
They are historical Basel II approaches. The final Basel III standard introduces a single standardised methodology, subject to domestic implementation.
Four practice questions from the lecture
1. Historical Basel I: qualifying government exposure ₹200cr, mortgages ₹100cr and corporate loans ₹300cr. What is capital?
Using the assumed applicable 0%, 50% and 100% weights: RWA = 0 + 50 + 300 = ₹350 crore. Capital at 8% is ₹28 crore.
2. Corporate IRB: PD 2%, LGD 45%, M 2.5 years. What is the risk weight?
Using the displayed revised corporate function: correlation 0.164146, WCDR 19.0259%, MA 1.19926 and K 9.18834%. Risk weight = 12.5 × K = 114.8542%, before other applicable adjustments.
Basics & Glossary
Banking & Basel, in plain language
Click any linked term in the article to reach its explanation. Each card includes an example and a link back to your reading position. These are learning definitions; detailed eligibility and calculation rules are in the official references.
Stand-alone CVA capital (SCVA)
A counterparty's supervisory CVA risk measure before portfolio aggregation and the BA-CVA discount scalar.
Bank C has SCVA $15.79994 million; the portfolio aggregates it with Firm T before applying 0.65.
Single-name hedge recognition (SNH)
A weighted measure of eligible single-name CDS protection recognised against a counterparty's CVA credit-spread risk.
A directly referenced five-year CDS of $71.42857 million offsets Bank C's SCVA in this matched illustration.
Index hedge recognition (IH)
The BA-CVA quantity recognising eligible index CDS hedges in the systematic risk term.
IH is zero in the single-name hedge example because no index hedge is used.
Hedging misalignment (HMA)
The BA-CVA allowance for indirect hedges that do not move perfectly with the counterparty's credit spread.
Direct-reference hedging has no proxy misalignment in the illustration; related-name and sector proxies require the prescribed treatment.
Internal Models Method (IMM)
An approved method for measuring counterparty credit exposure using modelled future exposure profiles.
In BA-CVA, IMM uses DF = 1 because its effective maturity already includes discounting; alpha remains 1.4.
Net-to-gross ratio (NGR)
In the historical netted derivative add-on calculation, net replacement cost divided by gross replacement cost. A lower ratio indicates more offsetting in current values.
Net current exposure ₹8 crore divided by gross positive exposure ₹13 crore gives NGR 0.6153846.
Current Exposure Method (CEM)
A historical Basel derivative exposure method combining positive current replacement cost with a prescribed add-on for potential future exposure. Qualifying netting changes the calculation.
The Basel I example has ₹8 crore net replacement cost plus ₹3.8461538 crore netted add-on, giving ₹11.8461538 crore credit equivalent.
Credit equivalent
An exposure amount used to translate certain off-balance-sheet transactions into the credit-risk calculation. Its computation depends on the transaction and regulatory method.
Under historical CEM, current replacement cost ₹13 crore plus gross add-on ₹5 crore gives ₹18 crore credit equivalent before the counterparty risk weight.
Payment netting
Combining payments to reduce settlement flows. Payment netting alone may leave gross contractual obligations on default and therefore need not qualify for regulatory exposure netting.
Two scheduled payments can be settled as one smaller transfer, but default exposure depends on the legally enforceable agreement.
Credit conversion factor (CCF)
A prescribed factor that converts a contingent or undrawn obligation into a credit exposure equivalent. The factor depends on the type of commitment and applicable rules.
A ₹100 crore performance guarantee at an assumed applicable 50% CCF gives ₹50 crore credit exposure before applying a risk weight.
Haircut
A reduction in the recognised value of an asset or collateral to allow for potential adverse value changes under prescribed assumptions.
₹80 crore collateral with a 4% haircut has ₹76.8 crore adjusted value.
Standardised Approach to Counterparty Credit Risk (SA-CCR)
The Basel standardised method for calculating derivatives exposure at default using replacement cost and potential future exposure. Margining and netting-set treatment matter.
Assumed RC ₹2 crore and calculated PFE ₹0.5 crore give EAD = 1.4 × 2.5 = ₹3.5 crore.
Basic Approach for CVA risk (BA-CVA)
A supervisory formula for CVA risk capital. Its reduced version does not recognise hedges; its full version recognises eligible counterparty spread hedges.
The article's two-counterparty reduced calculation gives about $10.6671 million capital, distinct from the pricing CVA deduction.
Standardised Approach for CVA risk (SA-CVA)
A sensitivities-based regulatory CVA capital method requiring supervisory approval and prescribed modelling capabilities.
A bank measures sensitivities of regulatory CVA and eligible hedges to spreads and other market risk factors.
Credit default swap (CDS)
A credit derivative in which a protection buyer pays a premium and receives contractual protection if a specified credit event occurs. CDS quotes can inform market-implied default curves.
A quoted 200 bp annual spread is 2% of reference notional per year before contract-specific details.
Hazard rate
An instantaneous default intensity conditional on survival. With a constant intensity λ, survival to time t is exp(−λt).
An approximate λ of 3.3333% gives a first-year default probability of 3.2784%, not exactly 3.3333%.
Worst-case default rate (WCDR)
A conditional default rate at a specified adverse systematic-factor quantile in a credit model. It is not an absolute maximum possible default rate.
In the illustrated corporate function with PD 1%, WCDR at the 99.9% calibration is about 14.0273%.
Maturity adjustment (MA)
A prescribed factor reflecting effective maturity and PD in the relevant IRB corporate risk-weight function.
At PD 1% and M 2.5 years, the illustrated MA is 1.25981.
Business Indicator (BI)
A financial-statement-based measure used as a proxy for operational risk, constructed under regulatory definitions.
An assumed BI of €20 billion yields BIC €2.97 billion using marginal coefficients.
Potential future exposure (PFE)
A measure of possible future counterparty exposure. The regulatory calculation depends on the method and transaction characteristics.
The SA-CCR example assumes its prescribed PFE calculation has produced ₹0.5 crore, which is added to replacement cost.
Replacement cost (RC)
The current exposure measure for replacing transactions, calculated under the applicable margining, collateral and netting rules.
A positive uncollateralised net value of ₹2 crore can contribute ₹2 crore RC in a simplified case.
Zero-coupon bond
A bond with no periodic coupon payments. The investor receives the contractual redemption amount at maturity if the issuer pays.
A one-year ₹100 payment has a default-free present value of ₹95.24 at a 5% discount rate.
Coupon bond
A bond that promises periodic interest payments, called coupons, and repayment of principal under its terms.
A two-year ₹100 face-value bond with a 5% annual coupon pays ₹5 after year one and ₹105 after year two if the issuer pays in full.
Interest-rate swap
An agreement to exchange interest cash flows, commonly a fixed rate for a floating rate, on a reference notional amount. A plain single-currency interest-rate swap usually does not exchange principal.
On ₹1 crore notional, paying 5% and receiving a 7% fixing gives a ₹2 lakh net receipt for a one-year period before credit adjustments.
Credit Valuation Adjustment (CVA)
A valuation adjustment reflecting the market value of counterparty default risk on covered transactions. It reduces value from the bank's perspective when future amounts owed to it may not be paid.
One-period illustration: ₹10 crore positive exposure × 2% risk-neutral default probability × 60% LGD = ₹0.12 crore CVA, assuming discount factor one.
Debit Valuation Adjustment (DVA)
An own-credit valuation adjustment reflecting the reporting bank's possible non-payment of future liabilities. It is not cash received, and regulatory CVA excludes own default.
₹8 crore exposure owed to the counterparty × 1% own risk-neutral default probability × 60% LGD gives an illustrative ₹0.048 crore DVA.
Netting
Combining covered obligations within a legally enforceable netting arrangement to determine a net exposure. Regulatory recognition has eligibility conditions.
Covered positive and negative values of ₹10 crore and ₹7 crore can produce ₹3 crore net current exposure when the agreement qualifies.
Collateral
Assets posted to secure obligations. Recognised collateral can reduce unsecured exposure, subject to valuation, legal and operational conditions.
Against a ₹10 crore exposure, ₹6 crore recognised collateral leaves ₹4 crore unsecured in a simplified illustration.
Bank capital
The loss-absorbing funding layer of a bank. It is not a separate cash reserve. Regulatory eligibility determines what counts.
Assets of ₹1,000 crore minus liabilities of ₹920 crore leave ₹80 crore of equity.
Tier 1 capital
Core regulatory capital intended to absorb losses while the bank remains a going concern. Tier 1 = CET1 + AT1.
₹64 crore CET1 plus ₹8 crore AT1 gives ₹72 crore Tier 1.
Tier 2 capital
Additional qualifying regulatory capital designed for gone-concern loss absorption. It can include qualifying subordinated debt and eligible provisions within limits.
₹72 crore Tier 1 plus ₹16 crore Tier 2 gives ₹88 crore total capital. Ordinary borrowing does not automatically qualify.
Common Equity Tier 1 (CET1)
Qualifying common shares, retained earnings and eligible reserves after regulatory adjustments: the core equity cushion.
If an assumed ₹10 crore loss reduces CET1 of ₹64 crore, the remaining amount is ₹54 crore before other adjustments.
Additional Tier 1 (AT1)
Qualifying capital instruments with prescribed permanence, distribution and loss-absorption features. Their terms differ from ordinary debt.
An eligible instrument may require principal write-down or conversion at a specified trigger; holders must understand its contractual terms.
Total regulatory capital
The sum of eligible Tier 1 and Tier 2 capital after applicable adjustments.
₹64 crore CET1 + ₹8 crore AT1 + ₹16 crore Tier 2 = ₹88 crore total capital.
Equity
The residual interest in assets after liabilities. Accounting equity is a starting point, not necessarily the regulatory capital amount.
₹1,000 crore assets − ₹920 crore liabilities = ₹80 crore equity.
Liabilities
Amounts a bank owes, including customer deposits and borrowing. They fund assets but usually do not provide the same loss cushion as common equity.
A customer's ₹5 lakh deposit is money owed by the bank to that customer.
Goodwill
An accounting asset arising from an acquisition. It is generally deducted when determining CET1 because it is not a dependable prudential loss cushion.
Reported equity of ₹80 crore including ₹5 crore goodwill can yield lower eligible CET1 after the deduction.
Credit risk
Risk of loss when a borrower or counterparty does not meet an obligation.
A manufacturer fails to repay a loan; the bank loses the unrecovered amount.
Market risk
Risk of losses from movements in market prices, rates, spreads and volatility.
Bond prices fall when yields rise, reducing a trading portfolio's value.
Operational risk
Risk of loss from inadequate or failed processes, people, systems or external events. The regulatory definition includes legal risk but excludes strategic and reputational risk.
A payment-processing error or cyber incident produces a financial loss.
Liquidity risk
Funding liquidity risk is difficulty meeting payments when due without unacceptable losses. Market liquidity risk is difficulty selling or hedging positions at reasonable prices.
A solvent bank holds long-term loans but cannot quickly obtain cash to meet a surge in withdrawals.
Solvency
The capacity to meet obligations supported by an adequate asset and capital position. It differs from having cash available today.
A bank may have assets worth more than liabilities while temporarily lacking cash; asset losses can instead erode solvency.
Concentration risk
Risk from large exposures to one borrower, industry, geography or connected set of risks.
Loans to many developers in one city can all deteriorate in the same property downturn.
Counterparty credit risk
Risk that the other party defaults before a transaction is finally settled, leaving a loss. Derivatives and financing transactions are important examples.
A swap counterparty defaults while owing the bank a positive replacement value.
Interest-rate risk in the banking book (IRRBB)
Risk that interest-rate changes damage banking-book earnings or economic value. It is addressed through supervision and relevant local rules.
Loan yields reset slowly while deposit costs rise quickly, squeezing net interest income.
Risk-weighted assets (RWA)
A regulatory measure of risk used as the denominator of risk-based capital ratios. It includes equivalents for different risk categories, not just a list of balance-sheet assets.
A hypothetical ₹100 crore loan at a 50% weight produces ₹50 crore credit RWA.
Risk weight
A prescribed percentage or formula-derived factor used to translate an exposure into credit RWA.
₹100 crore exposure × 100% weight = ₹100 crore RWA. A low weight does not guarantee no loss.
Capital adequacy ratio
Eligible regulatory capital divided by total RWA. Separate CET1, Tier 1 and total-capital ratios apply.
₹88 crore total capital ÷ ₹800 crore RWA = 11%.
Capital headroom
The amount by which available capital exceeds a specified requirement. Always state which threshold is used.
₹88 crore capital − 10.5% × ₹800 crore RWA = ₹4 crore headroom.
Capital conservation buffer
A CET1 buffer above minimum requirements, designed to be built in normal times and usable during stress. Entering it restricts distributions.
The Basel baseline is 2.5% of RWA, in addition to minimum requirements.
Countercyclical capital buffer
An additional buffer adjusted by authorities in response to system-wide credit risk. Actual rates depend on relevant jurisdictions.
A credit boom may prompt an authority to increase the buffer for exposures in its jurisdiction.
Leverage and the leverage ratio
Leverage is the use of liabilities to support exposures relative to capital. The regulatory leverage ratio compares Tier 1 with a prescribed exposure measure without risk weighting.
₹72 crore Tier 1 ÷ ₹2,400 crore leverage exposure = 3%.
Liquidity Coverage Ratio (LCR)
Eligible high-quality liquid assets divided by prescribed net cash outflows over 30 days of stress.
₹150 crore HQLA ÷ ₹120 crore net outflows = 125% LCR.
High-quality liquid assets (HQLA)
Assets meeting prescribed liquidity eligibility and operational conditions. Haircuts and composition limits apply.
Eligible reserves and qualifying securities may help meet withdrawals; every saleable security is not automatically HQLA.
Net Stable Funding Ratio (NSFR)
Available stable funding divided by required stable funding, assessing funding resilience over a one-year horizon.
₹850 crore ASF ÷ ₹800 crore RSF = 106.25% NSFR.
Available stable funding (ASF)
Capital and liabilities weighted according to their expected stability under NSFR rules.
Stable retail deposits can receive different funding weights from short-term wholesale borrowing.
Required stable funding (RSF)
The stable funding needed for assets and off-balance-sheet exposures under prescribed NSFR factors.
A long-term illiquid loan generally needs more stable funding than a readily available cash asset.
Probability of default (PD)
The likelihood that a borrower defaults over a specified horizon. Regulatory estimates must meet prescribed standards.
A 1% one-year PD corresponds to an estimated one-in-100 chance, not a promise that exactly one borrower defaults.
Loss given default (LGD)
The proportion of exposure lost conditional on default, reflecting relevant recovery assumptions.
If ₹100 crore is exposed and ₹60 crore is recovered, a simple LGD illustration is 40%.
Exposure at default (EAD)
The amount expected to be exposed when default occurs, including relevant potential drawings or other prescribed exposure treatment.
A borrower may draw an undrawn commitment before default; EAD can exceed today's drawn loan.
Expected loss (EL)
An average credit-loss estimate. A simple illustration is PD × LGD × EAD; it is not the full regulatory capital requirement.
1% PD × 40% LGD × ₹100 crore EAD = ₹0.4 crore expected loss.
Internal Ratings-Based approach (IRB)
An approved credit-risk approach using permitted internal parameter estimates in regulatory risk-weight functions.
A bank estimates eligible risk inputs, while the regulatory formula and minimum standards still apply.
Foundation IRB (F-IRB)
For eligible exposures, the bank generally estimates PD while other components use supervisory treatment.
The bank's own default estimate is combined with prescribed LGD and EAD treatment, subject to applicable rules.
Advanced IRB (A-IRB)
For permitted exposures, the bank estimates more inputs such as PD, LGD and EAD under supervisory standards and floors.
A bank's recovery data may support an LGD estimate, but approval and regulatory constraints still apply.
Standardised approach (SA)
A rule-based calculation using prescribed classifications, weights or parameters. Each risk category has its own standardised methodology.
Credit SA uses exposure weights; FRTB SA aggregates sensitivity, default and residual-risk charges.
Internal Capital Adequacy Assessment Process (ICAAP)
The bank's process for assessing risks, capital needs and capital strategy, reviewed by supervisors.
Management tests whether capital remains adequate under a recession and concentrated loan losses.
Stress testing
Analysis of how adverse conditions could affect losses, earnings, capital or funding. Scenarios should connect shocks with financial outcomes.
A recession scenario raises defaults and lowers collateral values, eroding capital.
Trading book
Positions meeting regulatory criteria for trading-book treatment. Assignment is governed by rules rather than simply selecting a cheaper charge.
A position held for short-term resale may belong in the trading book if it meets the criteria.
Banking book
Positions outside the regulatory trading book, typically including lending exposures. They still face relevant credit and other risk requirements.
A conventional loan held as part of lending activity is a typical banking-book exposure.
Fundamental Review of the Trading Book (FRTB)
The Basel III redesign of market-risk capital, including revised standardised and internal-model approaches and a clearer book boundary.
A trading desk may use the standardised route or an approved model route under the applicable rules.
Sensitivities-based method (SBM)
The FRTB standardised component aggregating weighted delta, vega and curvature risks under prescribed correlations.
A bond's rate sensitivity and an option's volatility sensitivity contribute to the calculation.
Default risk charge (DRC)
A market-risk charge for jump-to-default risk, distinct from ordinary spread movements.
A bond issuer suddenly defaults, producing a loss larger than a small spread-change estimate.
Residual risk add-on (RRAO)
An additional FRTB standardised charge for specified residual risks inadequately captured by the other components.
Certain exotic underlyings or complex payoff risks attract separate prescribed treatment.
Value at Risk (VaR)
A loss threshold at a chosen confidence level and horizon. It does not describe the severity of losses beyond the threshold.
A 99% one-day VaR of ₹5 crore means the estimated distribution places about 1% of losses beyond ₹5 crore.
Expected Shortfall (ES)
The average loss in the specified worst tail of a distribution. FRTB uses 97.5% ES with stress and liquidity-horizon treatment.
Worst five of 200 equally likely losses of 10, 12, 15, 20 and 43 crore average ₹20 crore.
Delta
First-order sensitivity to a change in an underlying risk factor.
A bond's interest-rate delta indicates how its value changes for a small rate movement.
Vega
Sensitivity to implied volatility changes, especially relevant to options.
An option can change value when expected future volatility rises even if its underlying price stays unchanged.
Curvature
In FRTB, incremental risk from nonlinear price changes under prescribed upward and downward shocks beyond delta treatment.
An option's value under a large move differs from a straight-line approximation.
Liquidity horizon
The time assumed necessary to exit or hedge risk in stressed markets under the relevant framework.
An illiquid credit exposure needs a longer horizon than a highly liquid risk factor.
Backtesting
Comparing model predictions with observed outcomes to assess performance.
Repeated losses exceeding a VaR forecast can indicate inadequate risk measurement.
Profit and loss attribution (PLA)
An FRTB test comparing risk-theoretical with hypothetical P&L to assess whether the risk model captures desk value changes.
Material unexplained differences may reveal risk factors missing from the model.
Non-modellable risk factors
Factors failing prescribed modellability conditions require separate capital treatment under FRTB.
Sparse qualifying price observations can prevent a factor from being treated as modellable.
Basic Indicator Approach (BIA)
Historical Basel II operational-risk method using 15% of average positive gross income over the preceding three years.
₹100 crore average positive gross income gives ₹15 crore capital.
Historical Standardised Approach (TSA)
Historical Basel II operational-risk method applying beta factors to income in eight business lines.
Retail income ₹100 crore × 12% contributes ₹12 crore before annual aggregation rules.
Advanced Measurement Approaches (AMA)
Historical Basel II approved internal operational-risk measurement systems using loss data, scenarios and control factors.
A bank combines routine loss experience with severe disruption scenarios.
Business Indicator Component (BIC)
A component of revised operational-risk capital, derived from the financial-statement-based Business Indicator using marginal coefficients.
If the resulting BIC is ₹20 crore, it is multiplied by the applicable ILM.
Internal Loss Multiplier (ILM)
A multiplier reflecting historical operational losses relative to BIC under prescribed rules; national discretion can set it to one.
BIC ₹20 crore × assumed ILM 1.2 = ₹24 crore capital.
Output floor
An aggregate lower bound on RWA relative to a prescribed standardised benchmark. The fully phased-in calibration is 72.5%.
Pre-floor RWA ₹500 crore and benchmark ₹800 crore give a ₹580 crore full floor and applied RWA.
Modified duration
A first-order measure of bond-price sensitivity to yield changes, subject to assumptions.
Modified duration 5 and a one-percentage-point yield rise imply about a 5% price fall before convexity.
Convexity
Curvature of the bond price–yield relationship, refining a linear duration estimate.
For larger yield moves, the actual price change can differ from the duration-only approximation.
Asset encumbrance
An asset is tied to an obligation, such as a pledge, which can restrict availability for other funding needs. Treatment depends on legal and regulatory conditions.
A security pledged to secure borrowing may be unavailable to meet unrelated withdrawals.
Maturity ladder
A schedule of expected cash inflows and outflows in time buckets that reveals funding gaps.
Cash can become negative in week one even if expected receipts later in the month cover total payments.
Contingency funding plan
A practical plan for obtaining funding and escalating decisions when normal funding becomes difficult.
A bank identifies available collateral, tested funding sources and withdrawal-trigger thresholds.
Rollover risk
The risk that maturing funding cannot be renewed, or can be renewed only on costly terms.
A bank funds a five-year loan with borrowing due next month and cannot refinance it.
Expected positive exposure (EPE)
A time average of expected positive derivative exposure over a specified period. It differs from exposure at one date and from a tail quantile.
A profile of average positive swap values is averaged over time; this alone does not determine default-loss VaR.
Expected exposure (EE)
Expected positive exposure at a particular future date, under the stated netting, collateral and probability assumptions.
Equal probabilities of ₹10 and ₹30 positive exposure give EE ₹20 at that date.
Loss provision
An allowance recognising expected credit losses or another required loss estimate. Accounting and prudential definitions and eligibility can differ.
An additional ₹2 crore expense reduces pre-tax retained earnings; the capital impact depends on regulatory adjustments.
Definitions follow the Basel Framework and the historical standards cited in this guide. Examples are hypothetical.
Read the standards behind the illustrations
Sources checked on 10 October 2026. Historical versions are labelled. National rules determine actual obligations.
- Teaching examples adapted from Ravichandran Vaidyanathan’s Financial Risk Management, Lecture 10, “Regulation: Basel I, II and III”. Assumptions and historical labels are clarified for this guide.
- BCBS history and evolution
- 1988 Basel Capital Accord
- Basel II comprehensive framework, 2006
- Basel III initial framework, revised 2011
- Finalising Basel III post-crisis reforms, 2017
- Revised market-risk standard, 2019
- Consolidated Basel Framework: capital, RWA, supervision and disclosures
- FSI: revised market-risk framework overview
- RCAP implementation monitoring
- BCBS MAR50 · current CVA framework and supervisory weights
- BCBS implementation release · 5 October 2026
- RBI current commercial-bank capital-adequacy directions
- RBI revised standardised credit-risk directions · effective April 2027
Educational illustrations; amounts and scenarios are hypothetical. Simplified calculators do not replace regulatory reporting calculations. Check current domestic standards and bank-specific requirements.