Abstract
The trading book consists of actively traded positions which are facing financial losses due to the fluctuation of the underlying market risk factors. Since the latest market risk framework did not adequately capture the severity of such losses, the BCBS proposed a new framework for the estimation of the minimum capital requirements for market risk, also known as the Fundamental Review of the Trading Book (FRTB) framework (BCBS, Fundamental Review of the Trading Book: A revised market risk framework, 2013; BCBS, 2016a).
The FRTB proposals revise the changes in the philosophy for the valuation of market risk under both the standardised approach (SA) and the internal model approach (IMA). The new framework considers market liquidity risk under both approaches, whereas under the advanced IMA it introduces the estimation of the expected shortfall (ES) substituting the value at risk (VaR) as a measure for the assessment of market risk.
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Notes
- 1.
The proposed four scaling factors are [1.50–2.00], [3.00–3.50], [1.50–2.50] and [1.25–1.50] (BCBS, 2018: 13 table 1).
- 2.
As shown in Eq. (6.6) for bucket b, Sb = ∑kWSk and bucket c, SC = ∑kWSk; however, if \( \sum \limits_b{k}_b^2+\sum \limits_b\sum \limits_{c\ne b}{\gamma}_{bc}{S}_b{S}_c<0 \) then Sb = max [min(∑kWSk, kb), −kb] for all risk factors in bucket b. This rule is not applicable under the R-SbA.
- 3.
The same buckets used in in delta sensitivities.
- 4.
The curvature correlation parameters ρkl and γbc are the same as defined in delta sensitivities; however, the values in both parameters ρkl and γbc should be squared.
- 5.
As illustrated in Eq. (6.10), the formulae which estimate the sensitivities for all risk factors in bucket b and c are given by Sb = ∑kCVRk and Sc = ∑kCVRk, respectively; however, if the value under square root in Eq. (6.9) is negative, sensitivities are defined as Sb = max [min(∑kCVRk, kb), −kb] and SC = max [min(∑kCVRk, kc), −kc] for all risk factors in corresponding buckets b and c.
- 6.
- 7.
The new framework distinguishes vertices amongst periods of a quarter of a year, half a year, 1, 2, 3, 5, 10, 15, 20, and 30 years. For assigning risk factors to the above vertices, banks may use linear interpolation or a method consistent to pricing functions used internally.
- 8.
The vertices are 0.5, 1, 3, 5, and 10 years.
- 9.
The curvature risk charge does not include inflation and cross-currency basis risks.
- 10.
The maturity vertices are set to 0.5, 1, 3, 5, and 10 years.
- 11.
Vega risk capital charge does not apply to equity repo rates.
- 12.
Contract grade of the commodity is the minimum accepted standard that a commodity must meet to be accepted as the actual physical deliverable against the contract (also known as the “basis grade” or “par grade”) (BCBS, 2016a: 24, para 65).
- 13.
The time vertices are 0, 0.25, 0.5, 1, 2, 3, 5, 10, 15, and 20 years.
- 14.
The ten vertices are 0.25, 0.5, 1, 2, 3, 5, 10, 15, 20, and 30 years. Based on the proposed amendments the RWs correspondingly assigned to the five vertices modified and set from 2.4%, 2.25%, 1.88%, and 1.73% (BCBS, 2016a), to the ranges of [1.5–1.9%], [1.4–1.8%], [1.1–1.5%], [1.0–1.4%] (BCBS, 2018) respectively, while the RW assigned to the last five vertices is modified and set from 1.5% (BCBS, 2016a) to the range of [0.9–1.2%] (BCBS, 2018).
- 15.
The RWs may at the discretion of the bank be divided by \( \sqrt{2}. \)
- 16.
EUR, USD, GBP, AUD, JPY, SEK, CAD, and domestic reporting currency of a bank.
- 17.
Note that in reference to endnote number \( \sum \limits_b{k}_b^2+\sum \limits_b\sum \limits_{c\ne b}{\gamma}_{bc}{S}_b{S}_c>0. \)
- 18.
The RWs for the 16 buckets {1, …, 16} are 0.5%, 1.0%, 5.0%, 3.0%, 3.0%, 2.0%, 1.5%, 4.0%, 3.0%, 4.0%, 12.0%, 7.0%, 8.5%, 5.5%, 5.0%, and 12.0%, respectively.
- 19.
Sectors’ allocation on buckets 1 (IG ) and 9 (HY&NR) to sovereigns include central banks, multilateral development banks; buckets 2 (IG) and 10 (HY&NR) to local government, government-backed non-financials, education, public administration; buckets 3 (IG) and 11 (HY&NR) to financials including government-backed financials; buckets 4 (IG) and 12 (HY&NR) to basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying; buckets 5 (IG) and 13 (HY&NR) to consumer goods and services, transportation and storage, administrative and support service activities; buckets 6 (IG ) and 14 (HY&NR) to technology, telecommunications; buckets 7 (IG) and 15 (HY&NR) to health care, utilities, professional and technical activities; bucket 8 (IG) to covered bonds; and bucket 16 to other sectors.
- 20.
Excluding covered bonds.
- 21.
The correlations between buckets having different sectors are defined as in the table below:
Bucket
1/9
2/10
3/11
4/12
5/13
6/14
7/15
8
1/9
75%
10%
20%
25%
20%
15%
10%
2/10
5%
15%
20%
15%
10%
10%
3/11
5%
15%
20%
5%
20%
4/12
20%
25%
5%
5%
5/13
25%
5%
15%
6/14
5%
20%
7/15
5%
8
- 22.
Sectors’ allocation on buckets 1 (IG) and 4 (HY&NR) to sovereigns include central banks, multilateral development banks, local government, government-backed non-financials, education, public administration; buckets 2 (IG ) and 5 (HY&NR) to financials including government-backed financials; buckets 3 (IG) and 6 (HY&NR) to other sectors.
- 23.
For the sectors sovereigns including central banks, multilateral development banks’ RWs, associated with buckets 1 and 4 (HY&NR) the RWs are set to 1.0% and 5.0%, respectively, to these buckets; whereas for the sectors local government, government-backed non-financials, education, public administration, also associated with buckets 1 and 4 (HY&NR), the RWs are set to 1.0% and 5.0%, respectively, to these buckets. The RWs for buckets 2, 3, 5, and 6 are 10%, 15.0%, 25.0%, and 30.0%, respectively.
- 24.
The correlation parameter γbc defined as in the table below:
Bucket
1
2
3
4
5
6
1
10%
0%
50%
5%
0%
2
0%
5%
50%
0%
3
0%
0%
50%
4
10%
0%
5
0%
6
- 25.
The RWs for the 16 buckets {1, …, 16} are 4.0%, 4.0%, 8.0%, 5.0%, 4.0%, 3.0%, 2.0%, 6.0%, 13.0%, 13.0%, 16.0%, 10.0%, 12.5%, 12.0%, 12.0%, 13.0%, respectively.
- 26.
The sectors assigned to each of the eight buckets of all three groups of the non -correlation trading portfolio are residential mortgage-backed securities (RMBS)—prime, RMBS—mid-prime, RMBS—subprime, commercial mortgage-backed securities (CMBS), asset-backed securities (ABS)—student loans, asset-backed securities (ABS)—credit cards, asset-backed securities (ABS)—auto, and collateralised loan obligations (CLO).
- 27.
The RWs for the eight buckets are 0.9%, 1.5%, 2.0%, 2.0%, 0.8%, 1.2%, 1.2%, and 1.4%, respectively.
- 28.
The credit quality for the three groups of buckets is defined identically for both SbM and R-SbM , that is, as SIG, NSIG, and HY&NR, respectively.
- 29.
The sectors assigned to the three groups of four buckets {1, …, 4} are RMBS, non-mortgage retail securitisations, CMBS, other.
- 30.
The risk weights for the 12 buckets {1, …, 12} are set at 2.0%, 5.0%, 5.0%, 10.0%, 5.0%, 6.25%, 6.25%, 12.5%, 3.5%, 8.75%, 8.75%, 17.5%, respectively.
- 31.
Defined as the sum of the global market capitalisations (across all stock markets) of the same legal entity or group of legal entities: small market cap < US $2 billion and large market cap ≥ US $2 billion.
- 32.
Advanced economies: Canada, the US, Mexico, the Euro area, the non-Euro area Western European countries (the UK, Norway, Sweden, Denmark, and Switzerland), Japan, Oceania (Australia and New Zealand), Singapore, and Hong Kong SAR.
- 33.
Sectors of consumer goods and services, transportation and storage, administrative and support service activities, health care, and utilities are allocated to buckets 1, 5, 9, and 10; sectors of telecommunications and industrials are allocated to buckets 2, 6, 9, and 10; sectors of basic materials, energy, agriculture, manufacturing, mining and quarrying are allocated to buckets 3, 7, 9, and 10; and sectors of financials including government-backed financials, real estate activities, and technology are allocated to buckets 4, 8, 9, and 10.
- 34.
Based on the proposed amendments for the 11 buckets {1, …, 11} the RWs for equity spot price modified and set from 55%, 60%, 45%, 55%, 30%, 35%, 40%, 50%, 70%, 50%, and 70% (BCBS 2016a), to the ranges of [27.5–41.25%], [30–45%], [22.5–33.75%], [27.5–41.25%], [15–22.5%], [17.5–26.25%], [20–30%], [25–37.5%], [35–52.5%], [25–37.5%] and [35–52.5%] (BCBS, 2018); whereas the RWs for equity repo rate modified and set from 0.55%, 0.60%, 0.45%, 0.55%, 0.30%, 0.35%, 0.40%, 0.50%, 0.70%, 0.50%, and 0.70% (BCBS 2016a), to the ranges of [0.275–0.4125%], [0.30–0.45%], [0.225–0.3375%], [0.275–0.4125%], [0.15–0.225%], [0.175–0.2625%], [0.20–0.30%], [0.25–0.375%], [0.35–0.525%], [0.25–0.375%] and [0.35–0.525%] (BCBS, 2018), respectively.
- 35.
Sectors of financials including government-backed financials, real estate activities, technology are allocated to buckets 1 and 3, other sectors are allocated to buckets 2 and 4, and finally all sectors are allocated to buckets 5 and 6.
- 36.
For the six buckets {1, …, 6}, the RWs for equity spot price are 60%, 60%, 50%, 40%, 70%, and 60%, respectively.
- 37.
For the six buckets {1, …, 6} the correlation ρkl is set to 15%, 15%, 25%, 25%, 7.5%, and 12.5% accordingly.
- 38.
The RWs for the 11 buckets {1, …, 11} are 30%, 35%, 60%, 80%, 40%, 45%, 20%, 35%, 25%, 35%, and 55%, respectively.
- 39.
For the 11 buckets {1, …, 11} the corresponding commodity categories are defined by the regulators as: (1) energy—solid combustibles, (2) energy—liquid combustibles, (3) energy—electricity and carbon trading, (4) freight, (5) metals—non-precious, (6) gaseous combustibles, (7) precious metals (including gold), (8) grains and oilseed, (9) livestock and dairy, (10) softs and other agriculturals, and (11) other commodity.
- 40.
The risk weights for the 11 buckets {1, …, 11} are 40%, 45%, 70%, 90%, 50%, 55%, 30%, 45%, 35%, 45%, and 60%, respectively.
- 41.
The correlation ρkl between non-identical commodities for each of the 11 buckets is set at 55%, 95%, 40%, 80%, 60%, 65%, 55%, 45%, 15%, 40%, and 15%, respectively.
- 42.
The following currency pairs have been selected by the Basel Committee: USD/EUR, USD/JPY, USD/GBP, SD/AUD, USD/CAD, USD/CHF, USD/MXN, USD/CNY, USD/NZD, USD/RUB, USD/HKD, USD/SGD, USD/TRY, USD/KRW, USD/SEK, USD/ZAR, USD/INR, USD/NOK, USD/BRL, EUR/JPY, EUR/GBP, EUR/CHF, and JPY/AUD and based on the proposed amendments (BCBS, 2018) currency pairs forming first-order crosses across these specified currency pairs.
- 43.
The liquidity horizon assigned to risk class is set for GIRR at 60 days, CSR non -securitisations at 120 days, CSR securitisations (CTP) at 120 days, CSR securitisations (non-CTP) at 120 days, equity (large cap) at 20 days, equity (small cap) at 60 days, commodity at 120 days, and FX at 40 days.
- 44.
The Basel framework assigns LGD = 100% to non-senior debt instruments, LGD = 75% to senior debt instruments, and LGD = 25% to covered bond.
- 45.
The proposed classification of the credit quality assigns rating grades AAA (Aaa), AA (Aa), A (A), BBB (Baa), BB (Ba), B (B), CCC (Caa), unrated, and defaulted to the following default RWs: 0.5%, 2%, 3%, 6%, 15%, 30%, 50%, 15%, and 100%, respectively.
- 46.
Offsetting is not allowed among securitisation exposures with different underlying securitised portfolios as well as exposures arising from different tranches with the same securitised portfolio (see: BCBS, 2016a: 46 para 159).
- 47.
The asset classes are asset-backed commercial paper (ABCP), auto loans/leases, residential mortgage-backed securities (RMBS), credit cards, commercial mortgage-backed securities (CMBS), collateralised loan obligations (CLOs), collateralised debt obligations (CDOs)-squared, small and medium corporate entities (SMEs ), student loans, other retail, and other wholesale.
- 48.
Asia, Europe, North America, and all others.
- 49.
CDX North America IG , iTraxx Europe IG, CDX HY, iTraxx XO, LCDX (loan index), iTraxx LevX (loan index), Asia Corp, Latin America Corp, Other Regions Corp, Major Sovereign (G7 and Western Europe), other Sovereign.
- 50.
But excluding smile, dividend, cheapest-to-deliver option and some types of correlation risks.
- 51.
In trading, risk control, auditing, back-office areas.
- 52.
For example, board of directors and senior management.
- 53.
Or could be unwound hedged.
- 54.
Artzner (1997) describes sub-additivity based on the idea that “merging assets will not create extra risk”; otherwise, if risk were not sub-additive, then one could be exposed to two assets 1 and 2 and would be better off opening a separate account for each of them due to the fact that the risk-based margin requirement would be lower than if both are held in the same account.
- 55.
In fact, most definitions of ES lead to same results when applied to continuous loss distributions. Differences may appear when the underlying loss distributions have discontinuities. In this case, even the coherence property of ES could cease to exist, unless the bank carefully calibrates the confidence levels of VaR and ES to the right degree.
- 56.
In case no extreme tail event is expected to emerge, the ES would be equal to the VaR.
- 57.
The new framework (BSBS, 2016a: 55, para 181 (k)) assigns one out of the five liquidity horizons {1, …5}, that is, LH = {10,20,40,60,120}, to each of the risk factor categories: interest rates—widespread currencies: EUR, USD, GBP, AUD, JPY, SEK, CAD, and the domestic currency of a bank have LH = 10 days, interest rate—other currencies—LH = 20 days, interest rate volatility: LH = 60 days, interest rate—other types: LH = 60 days, credit spread—sovereign (IG): LH = 20 days, credit spread—sovereign (HY), LH = 40 days, credit spread—corporate (IG): LH = 40 days, credit spread—corporate (HY): LH = 60 days, credit spread—volatility: LH = 120 days, credit spread—other types: LH = 120 days, equity price (large cap): LH = 10 days, equity price (small cap): LH = 20 days, equity price (large cap)—volatility: LH = 20 days, equity price (small cap)—volatility: LH = 60 days, equity—other types: LH = 60 days, FX rate—specified currency pairs: LH = 20 days, FX rate other currency pairs: LH = 20 days, FX volatility: LH = 40 days, FX—other types: LH = 40 days, energy and carbon emissions trading price: LH = 20 days, precious metals and non-ferrous metals price: LH = 20 days, other commodities price: LH = 60 days, energy and carbon emissions trading price—volatility: LH = 60 days, precious metals and non-ferrous metals price—volatility: LH = 60 days, other commodities price—volatility: LH = 120 days, commodity—other types: LH = 120 days.
- 58.
Banks may use a subset of risk factors as far as they do not have at their disposal a sufficiently long history of good-quality data.
- 59.
As long as the supervisor judges that the ES model captures, through the P&L attribution and back -testing, all material risks which the bank is exposed to.
- 60.
Empirical correlations between risk factors can also be used.
- 61.
Default risk is the risk of direct loss due to an obligor’s failure to fulfil his or her contractual obligations.
- 62.
- 63.
Interest rate risk, equity risk, foreign exchange risk, commodity risk, and credit spread risk.
- 64.
Notably, according to (BCBS, 2016a: 63 paras 189), the aggregate capital charge for market risk refers to the previous day’s observation.
- 65.
The standard level of multiplication factor mc is set at 1.5; however, supervisory authorities may increase this level depending on the assessed quality of risk management system; they may also increase it by 0 to 0.5 depending on the performance of back-testing results against hypothetical and actual P&L as described in Sect. 6.8.3.
- 66.
Any risk factor that is not included in the risk management model of the trading desk cannot be considered in the estimation of the risk-theoretical P&L which is the P&L that would be produced by the bank’s pricing models for the desk (BCBS, 2016a: 71).
- 67.
The hypothetical P&L of the trading desk’s instruments is estimated daily at the desk level and is based on the MTM value of the instruments derived from the bank’s pricing models, for the desk, including all risk factors (BCBS, 2016a: 71). In hypothetical P&L bank must remove the commissions, fees, the impact of intraday trading and certain valuation adjustments.
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Akkizidis, I., Kalyvas, L. (2018). Market Risk: Fundamental Review of the Trading Book (FRTB). In: Final Basel III Modelling. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-70425-8_6
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