FRTB Standardised and Internally modelled Approach

by riskderivatives

Introduction

The Basel Committee published in May 2012 a consultation paper proposing a more robust boundary between Trading and Banking books to avoid regulatory arbitrage, capture market illiquidity more effectively, strengthen the risk measurement and valuation requirements under both standardised and internal model based approaches along with strengthening the relationship between the two approaches.

Background

The 2008 crisis highlighted the severe undercapitalisation of the trading book exposures. This characteristic was to a large extent the result of the risk measurement and valuation methodologies used by banks.

The crisis exposed a series of fundamental weaknesses of the overall design of the trading book regime which contributed or amplified the impact of the crisis.

Basel 2.5 introduced some changes but they were recognised to be insufficient.

Chronology of the MR Changes

1995	Internal Model Based approach to MR VaR
2009	Stressed VaR
	Standard Rules
	IRC
	CRM (Comprehensive Risk Measure)
	CVA
	Risk not in VaR and Stressed RNiV
2017	FRTB

Shortcomings:

Consistency and Coherence: there is no consistent view of risk categorisation and capitalisation

Tail Risk: Not consistently or fully captured

Market Liquidity Risk: Not consistently or fully captured

Bank-Specific variability: Supervisory multiplier, historical window length, weighting scheme, scaling, aggregation

Pro-cyclicality: risk measures and capital increase as economic conditions worsen

Overalapping of models: double counting VaR, SVaR, IRC

Hedging and diversification: Benefits from using these techniques are overstated

 

A new clearer distinction

The BIS proposed to reconsider what constitutes an asset in the TB and BB.
The initial distinction was dictated by the bank’s intent to hold an asset for trading purpose or to hedge a position held for trading purposes. Prior to FRTB, the boundary between TB and BB was subject to regulatory arbitrage giving rise to lightly capital charged trading books.

The BIS proposed two alternative definitions:

1. A trading evidence based boundary
2. A valuation based boundary

The trading evidence based boundary

Unlike the existing boundary the trading evidence based boundary is designed to be objective. The trading evidence is based on the trading intent, hence inclusion of trades in the TB requires proof of such intent.

Such proof may be the product of statistics on the position turnover, rebalancing frequency for their hedges and their average age. Banks would be required to produce evidence of the feasibility of trading an instrument. This now includes proofs of access to relevant markets for trading and hedging, owning historical data and market data for the underlying and a plausible plan to justify why and how the bank would trade on a market in which it had limited experience.

Banks would also be required to demonstrate active management of trading positions ad to do so they may need to set and enforce limits both on an instrument and on a risk position basis. Another new requirement would be for banks to actively monitor market liquidity levels (including market data records) and to specify an expected maximum holding period for an instrument with penalties if that period is exceeded.

The Valuation Based Boundary

This approach would dispense altogether with trading intent and instead apply market risk capital requirements to all fair valued financial instruments for which valuation changes could lead to a reduction in a bank’s capital resources.

This would significantly increase the size of bank’s TB and increase the number of banks subject to market risk capital requirements. IN accounting terms the new TB would include held for financial instruments, available for sale financial instruments and other financial instruments to which fair value is applied either as an option or a requirement.

Common Changes

Regardless of which of these boundaries is finally adopted, the proposal includes some common changes:

1. Banks will be subject to more stringent public disclosure requirements regarding their trading positions
2. Banks will be restricted from changing the book destination. This limitation is imposed by the trading evidence based boundary or through the fair value accounting requirements in the valuation approach
3. All fair valued financial instruments either in the TB or BB will be subject to more specific stringent prudent valuation requirements.

New Approach to Risk Assessment

In addition to the new boundaries the committee has proposed a series of changes designed to make the market risk calculation more risk sensitive.

1. BIS proposed to replace the VaR risk metric with a new ES method (Expected Shortfall). ES considers a broader range of potential outcomes than VaR and measures risk by considering both size and likelihood of losses above a certain confidence level. ES is expected to capture the tail risk (the risk of unforeseen events not factored into a bank’s VaR model)
2. BIS proposes to recalibrate the TB framework such that market risk capital charges are sufficient not only in benign market conditions but also in periods of stress.
3. The Committee is moving away from the assumption of market liquidity which was central to the market risk framework prior to the financial crisis. The Paper proposes to incorporate market illiquidity risks as an integrated component of the market risk framework.
   To achieve this, it proposes three key changes designed to capture market illiquidity at a bank-specific and market-wide levels:
   a) Market liquidity would be assessed using the concept of “liquidity horizons” – which is the time required to exit or hedge a risk position in a stressed market without materially affecting market prices;
   b) “endogenous” liquidity risk that might imply that the cost of unwinding portfolios might be affected by the bank’s own trading behaviour or other idiosyncratic factors should be accounted for by further increasing liquidity horizons;
   c) banks would be required to hold capital for potential future jumps in liquidity premia for instruments that could become particularly illiquid under stressed conditions (captured on a forward looking basis)

Calculation frequency

Market Risk capital will be required to be calculated daily at trading desk level. Approval to use internal models is to be assessed daily at same level using two new tests:

1. Back testing
2. P&L attribution

As already mentioned, ES will replace the VaR whilst Incremental Default Risk will replace the Incremental Risk Charge. Time series data will also be subject to quality assessment.

Key FRTB ingredients

Liquidity Modelling	Eligibility	Capital Calculations
Stricter Data Requirements	TB vs BB Boundary	Capital Aggregation
Granular Trading Desk level focus	Model Backtesting	Internal Model (ES)
Conservative treatment of hedging and diversification	RBPL	Non Modellable Stress Scenarios
Tail risk capture	Leverage Ratio	STD Approach
Increased granular disclosure requirements	Market Data Eligibility	Incremental Default Risk
Coherent approach
Consistent treatment of credit risk

Internal Model Based Approach: Eligibility

 

Internal Model Method: Market Data Eligibility

Modellable risk factor eligibility

Real Price: this is the price at which the institution has made transactions on arm-length basis, or  between two or other independent third parties. This price is taken from a firm quote.

Acceptable frequency: with a minimum of 24 observations per year and a maximum period of one month between two consecutive transactions.

Data	Description	Real Price Criteria Met
Equity Prices, FX rates, Commodity Prices	Prices available daily on exchanges quoted directly	YES
CDS spreads	Reliable spread data available through Markit (but held to be non modellable)	Unknown as at 25/04/2016
Yield curves, Volatility surfaces, Model Parameters, CDS Spreads	Calculated on the basis of a proprietary model on top of the traded instruments and used as an input to the pricing models.	Unknown as at 25/04/2016
Indexes	Calculated on the basis of a model on top of traded instruments.	Unknown as at 25/04/2016

Other market data may not satisfy eligibility. These include IPOs, Bonds issued for the first time for which no historical data exists for that particular issuance. Peer analysis or industry average can be a good start as a proxy. Likewise, a risk factor model can be calibrated by enriching it with data for a sufficiently longer period until the model replaces the data set with real data going forward.

Industry proposed alternatives include reasonable proxies  with good data, statistical models which can leverage the relationship with other variables with good historical data.  Proxies for volatilities are reasonable if they are based on financial/economic reasoning or risk factor parametrisation with similar characteristics and supporting empirical evidence. RNIV (Risk not in Var) style add ons capture the missing risks.

Expected Shortfall (Internal Model)

 

 

In Summary

FRTB concerns with new rules to determine the scope of the instruments eligible for inclusion in the TB.

There are now more stringent requirements governing internal risk transfer between the BB and the TB.

The introduction of the Liquidity Horizons in the ES calculation is to reflect the period of time required to sell or hedge a given position during a period of stress.

The replacement of VaR and Stressed VaR with a single expected shortfall risk measure aims at capitalising for the loss event in the tail of the P&L distribution.

Back testing requirements of internal models at trading desk level will determine the validation of the models in use. Should backtesting fail, the trading desk will have to apply the standardised approach.

The replacement of the IRC with a Default Risk Model, aims at capturing the default risk in the market risk framework.

The revised Standardised Approach for market risk is now based on price sensitivities, therefore more risk sensitive. BIS intention to set up the new STD approach was to reduce the gap with the Internal Models results.

Public disclosure on market risk capital charges under STD and Internal Models is now enhanced.

Standardised Approach

Under the existing framework, there are material differences between the Standardised and Internal Models based methodologies. The current standard rules are based on a simple Risk Weighted and Notionals or Mark to Market based Approach.

Banks in the past have been criticised for overusing the internal models in order to achieve lower capital requirements. The current Standard methodology did not allow for wide diversification and hedging benefits. The new framework would provide a method for calculating capital requirements for banks without sophisticated measuring model in place and would ensure a more appropriate fall back calculator should the Trading Desk fail the internal model eligibility test.

Alignment to Internal Models Method

The new Standard Rules are more aligned to the Internal Models Method in terms of capital requirements. Instruments are now bucketed as per their risk characteristics. The Risk Weights of each bucket are prescribed and they have been calibrated with the internal models for Expected Shortfall. There is now more recognition of hedging and diversification benefits through the use of an aggregation formula using the regulatory prescribed correlation parameters.

Standardised Capital Charge Calculation Process Flow

The STD capital requirement is the sum of:

Enhanced Delta Risk Capital Charge + Default Risk Capital Charge + Residual Risk Add On

Banks are required to calculate the ‘Enhanced delta plus Risk’ and ‘Default Risk’ capital charge at the following portfolios levels:

1. Complete trading desks
2. Non Internal Model Approach (Desks which failed the model eligibility tests)
3. Each desk as a portfolio on its own: no diversification or hedging benefits across desks

Delta, Vega and Curvature

The Basel Committee decided to implement the “enhanced delta plus method”, which is sensitivity-based, differentiating between three different risk components: delta risk as a foundation for capturing linear risks, and vega and curvature risk as two additional components which apply to products with optionality.

Vega risk assesses the risk of price changes based on market expectation on future volatility. In other words the sensitivity to the volatility.
Curvature risk captures the non-linear risk, which is not accounted for by delta risk.

STD Risk Class Definitions

Sensitivities are calculated for 7 Risk Classes in STD approach:

1. GIRR
2. Equity
3. Credit Spread Securitisations
4. Credit Spread Non Securitisations
5. Credit Spread Securitisations Non Correlation Trading Portfolios
6. Commodity
7. FX

The STD capital charge is also calculated on the above risk classes according to the relevant sensitivities: Delta, Vega, Curvature and Default Risk

The linear and non linear capital charges are calculated separately with no diversifation benefit recognised between them.

Options are subject to Vega and Curvature risks.

More specifically for each Risk Class:

Risk Class	Sensitivity	Risk Factor
General IR risk	Delta	Defined along two dimensions: 1) A risk-free yield curve for each ccy in which IR sensitive instruments are denominated 2) Vertices (maturity points): 0.25, 0.5, 1, 2, 3, 5, 10, 15, 20, 30 Also includes inflation and cross currency basis risk factors. (Delta is the rate of change of the theoretical option value with respect to changes in the underlying).
	Vega	Vega Rf are the implied volatilities of options that reference GIRR sensitive underlyings defined along two dimensions. (the Sensitivity to Volatility) 1) Maturity if the option mapped to the vertices :0.5, 1, 3, 5, 10 yrs
	Curvature	Defined along only one dimension: the constructed risk free yield curve per currency
Credit Spread Risk Non Sec.	Delta	Defined along 2 dimensions 1) the relevant issuer credit spread curves (Bond and CDS) 2) Vertices: 0.5, 1, 3, 5, 10 yrs
	Vega	The Vega Rf are implied volatilities of options that reference credit issuer names as underlyings (bonds and CDS). Further defined along maturity of the option mapped to the vertices: 0.5, 1, 3, 5, 10 yrs
	Curvature	The relevant issuer credit spread curves (Bond an CDS)
Credit Spread Risk Sec.	Delta	Rf are defined along 2 dimensions: 1) the relevant tranche credit spread curves 2) Vertices: 0.5, 1, 3, 5, 10
	Vega	Vega risk factors are the implied volatilities of options that reference non CTP credt spreads as underlying (bond and CDS) defined along maturity of the option mapped to the vertices: 0.5, 1, 3, 5, 10
	Curvature	The relevant tranche credit spread curves (Bond and CDS)
Credit Spread Sec (Correlation Trading Portfolio)	Delta	Risk factors are defined along two dimensions: 1) The relevant tranche credit spread curves 2) Vertices: 0.5, 1, 3, 5, 10
	Vega	Vega rf are the implied volatilities of options that reference non CTP credit spreads as underlyings
	Curvature	The relevant tranche credit spread curves (bonds and CDS)
Credit Spread Risk Securitisaitons (correlation trading portfolio)	Delta	Defined along two dimensions: 1) the relevant underlying credit spread curves (bonds and CDS) 2) Vertices: 0.5, 1, 3, 5, 10
	Vega	Vega rf are the implied volatilities of the options that reference CTP credit spreads as underlyings (Bonds and CDS) defined along maturity and the option mapped to the vertices: 0.5, 1, 3, 5, 10
	Curvature	The relevant underlying credit spread curves (bond and CDS)
Equity	Delta	Either: 1) Equity Spot prices 2) equity repo agreement rates
	Vega	The implied volatilities of the options that reference the equity spot prices as underlyings along maturity of the option dimension at the 0.5, 1, 3, 5, 10 yrs
	Curvature	Equity Spot prices
Commodity	Delta	Commodity spot prices depending on the contract grade of the physical commodity and time to maturity of the traded instrument
	Vega	The implied volatilities of the options that reference commodity spot prices as underlyings along maturity of the option dimension at the 0.5, 1, 3, 5, 10 years
	Curvature	Commodity spot prices
FX	Delta	All the exchange rates between the currency in which an instrument is denominated and the reporting currency
	Vega	The implied volatilities of the options that reference exchange rates between currency pairs with maturity of the option defined at the vertices 0.5, 1, 3, 5, 10
	Curvature	All the exchange rates between the currency in which an instrument is denominated and the reporting currency

Sensitivities Definition for STD approach

Linear Capital Charge Calculation under the STD approach: DELTA

Linear Capital Charge is calculated for each risk class separately. The Delta sensitivity is 1bp absolute in GIRR and CSR risk factors, or 1% relative move in EQ, FX and Comm Risk Factors.

The positions in a risk class are placed in buckets defined per risk class. Each bucket has a predefined RW. For example, Equity buckets are defined along 3 dimensions: region, market capitalisation and industry.

Net the sensitivity Sk across instruments to each risk factor k belonging to the same bucket. The Sensitivities cannot be netter across buckets

Calculation of the Risk Weighted net sensitivities follows: WSk=RWksk

In each of the buckets ‘b’, aggregate the weighted sensitivities across risk factors using the following:

 

The correlation parameter pkl between risk factors have been prescribed by the BIS. TO come up with delta capital charge for a risk class, bucket level capital Kb is aggregated as follows:

The Basel Committee prescribed similarities for across buckets aggregation, correlation parameter Ybc, between buckets for each risk class

Linear Capital Charge Calculation under the STD approach: VEGA

Calculation of Vega capital charge remains the same except for RW, correlations and sensitivity calculations. The RW used in Vega is calibrated to each risk class liquidity horizon and is not dependent on the bucket structure as Delta capital charge was.

Vega is defined along the option maturity at 5 tenor points. Hence, Vega of a position with a given maturity has to be allocated to one or two of the 5 tenor points.

Example:

Suppose an equity call option position with Vega of 100 and maturity of 4.5 years.

Vertices or maturity points are 0.5, 1. 3. 5. 10 years.

The position is linearly allocated between 3 and 5 years.

At yr 3 vertice, allocate 100*{(5-4.5)/(5-3)}

At yr 5 vertice, allocate 100 * {(1-[(5-4.5)/(5-3)]}

Vega sensitivity is calculated as a product of the option Vega as allocated above and its implied volatility at the relevant maturity tenor.

The BIS has prescribed the method to calculate the correlation parameter: one for the GIRR and another for the other asset classes.

Non-Linear Capital Charge Calculation under the STD approach: Curvature

Curvature capital charge calculation follows the same buckets and risk class foundations of linear capital charge with the only difference that this sensitivity is calculated by applying a stress move to the risk factor

from the above equation:
in 1. the risk factor is shocked equivalently to the RW of the bucket in which the position is placed. In 2. we strip the delta from the curvature sensitivity to avoid double counting.

The correlation parameters in the intra bucket and across bucket aggregation formulas are the same as those used in the delta capital charge calculation.

Example:

Suppose we have an option on IBM stock. (Large market capitalisation, Advanced economy, Technology, Bucket 8, RW 50%). Current Stock Price is USD 151.31

The stock price is bumped to USD 227.01 (151.341.5) and USD 75.67 (151.340.50). The position are revalued at the above stock market price level holding other risk factors constant.

The Curvature is calculated as:

CVR+= (227.01-151.31)-(Δ*RW)

CVR-= (75.67-151.31)+(Δ*RW)

CVR= min(CVR+, CVR-)

The FO system will ahve to provide the valuation for a position in the 2 scenarios and current price. Curvature is then calculated for the capital charge.

Default Risk Charge

Prior to FRTB, banks capture default and migration risk using the models for securitised and non securitised portfolios.

Namely: IRC for non Securitised Portfolios and All Price Risk (APR) or Comprehensive Risk Measure (CRM) for Securitised Portfolios (correlation trading portfolios).

The above are model based approaches, therefore no Standard default risk calculation exists except for securitisations trades. Default risk does not apply to equity portfolios either.

Going forward teh standardised default risk charge will be calcualted for all tradig desks in scope.

The capital requirement for default risk is the sum of the default risk of:

non-securitisations (including equity), Securitisations (non correlation trading portfolio) and Securitisations (correlation trading portfolios).

The DRC captures the Jump-To-Default risk at 1 year horizon and it’s calibrated on the basis of the banking book credit risk treatment in order to reduce the potential discrepancy in capital requirements for similar exposures in the Banking Book.

Similar to the ehanced delta plus component of the STD approach, it allows some hedging recognition at a bucket level.

The calculation steps are:

1. Categorise positions as long or short (a long position implies the default of the underlying obligor results in a loss)
2. Positions are assigned a seniority on the basis of the allocated LGD
3. Gross JTD is calculated per position. This value is a function of the LGD, notional amount (face value) and the cumulative P&L already realised on the position
4. Scaling and offsetting is performed on gross JTD to arrive at net JTD
5. Underlying obligors ratings are assigned in each of the net JTD position and placed in the defined buckets
6. Calculate hedge benefit ratio for each bucket
7. Calculate DRC for each bucket
8. Calculate total capital charge for DRC by sum of bucket level capital charges
9. No hedging or diversification is recognised across buckets in any given scope

 

Residual Risk Add On

The objective of this charge is to capture the risk which is not covered by the Enhanced Delta Plus Risk and Default Risk.

The scope of this add on is any instrument satisfying both conditions below:

1. It is subjec to Vega Sensitivity and Curvature capital charge in the Trading Book
2. Its pay off cannot be written as a linear combination of vanilla options

An example of instruments affected by residual risk add on are path dependent options.

The Add On calculation is straightforward:

N= total number of positions under scope

x = the add on multiplier (1% is the prescribed value)

Gross Notional is the notional amount of the instrument i.

In case the Notional amount is unavailable, then the maximum potential loss should be used.

General Interest Rate Risk Class Buckets and respective Risk Weights

Tenor	0.25Yr	0.5Yr	1Yr	2Yr	3Yr	5Yr	10Yr	15Yr	20Yr	30Yr
RW	1.6%	1.6%	1.5%	1.25%	1.15%	1.0%	1.0%	1.0%	1.0%	1.0%

Credit Spread Risk Non-Securitised/Securitised Correlation Traded Portfolios Risk Class Buckets and respective Risk Weights

Bucket	Credit Quality	Sector	RW
1	Investment Grade	Sovereigns, CTRL banks, Multilateral Dev Banks	2.5%
2		Financial including Gov backed financials	5%
3		Basic materials, energy, industrial agriculture, manufacturing, mining and quarrying	3.5%
4		Consumer Goods and Services, Transportation and Storage, Admin and support service activities	3%
5		Technology and telecom	2.5%
6		Health Care, utilities, Local Govt, Gov-backed non financial, education, public admin, professional and technical activities	2%
7	High Yield and Unrated	Sovereigns, CTRL banks, Multilateral Dev Banks	10%
8		Financial including Gov backed financials	12%
9		Basic materials, energy, industrial agriculture, manufacturing, mining and quarrying	9%
10		Consumer Goods and Services, Transportation and Storage, Admin and support service activities	10%
11		Technology and telecom	9%
12		Health Care, utilities, Local Govt, Gov-backed non financial, education, public admin, professional and technical activities	6%
13	Other Sectors		12%

Credit Spread Risk Securitised Non-Correlation Traded Portfolios Risk Class Buckets and respective Risk Weights

Bucket	Credit Quality	Sector	RW
1	Senior Investment Grade	RMBS Prime	4%
2		RMBS Mid Prime	6.5%
3		RMBS Sub Prime	8.5%
4		CMBS	8.5%
5		ABS Student Loans	3.5%
6		ABS Credit Cards	5%
7		ABS Auto	5%
8		CLO Non-CTP	6%
9	Non-Senior Investment Grade	RMBS Prime	8%
10		RMBS Mid Prime	13%
11		RMBS Sub Prime	17%
12		CMBS	17%
13		ABS Student Loans	7%
14		ABS Credit Cards	10%
15		ABS Auto	10%
16		CLO Non-CTP	12%
17-24	High Yield and Unrated	Same buckets as above	The RW for the buckets 17-24 are then equal to the corresponding RW for the buckets 1 to 8 scaled up by a multiplication of 4
25	Other Sector		34%

Equity Risk Class Buckets and respective Risk Weights

Bucket	Market Cap	Economy	Sector	RW
1	Large Market Capitalisation ≥USD2bn	Emerging Market Economy	Consumer Goods and Services, Transportation and Storage, Admin and Support Service activities, healthcare, utilities	55%
2			Telecom and Industry	60%
3			Basic materials, energy, agriculture, manufacturing, mining and quarrying	45%
4			Financials including Gov backed financials, RE activities, technology	55%
5		Adv Economy CAN, USA, MEX, €zone, non €zone, JAP, AUS, NZL, SIN, HK, SAR	Consumer Goods and Services, Transportation and Storage, Admin and Support Service activities, healthcare, utilities	30%
6			Telecom and Industry	35%
7			Basic materials, energy, agriculture, manufacturing, mining and quarrying	40%
8			Financials including Gov backed financials, RE activities, technology	50%
9	Small	EM	Same as above	70%
10		ADV Economies	Same as above	50%
11	Residual			70%

Commodity Risk Class Buckets ad respective Risk Weights

Bucket	Commodity Category	RW
1	Coal	30%
2	Crude Oil	35%
3	Electricity	60%
4	Freight	80%
5	Metals	40%
6	Natural Gas	45%
7	Precious Metals (+ gold)	20%
8	Grains and Oilseed	35%
9	Livestock and Dairy	25%
10	Softs and other Agric	35%
11	Other Commodities	50%

FX Risk Class Buckets ad respective Risk Weights

The Bucket structure is defined by each currency pair. (one bucket = one currency pair)

The FX weight is fixed at 15% and applied to all sensitivies or risk exposures. However for the following currency pairs, the 15% RW is divided by the SQRT of 2.

USD/EUR, USD/JPY, USD/GBP, USD/AUD, USD/CAD, USD/CHF, USD/MXN, USD/CNY, USD/NZD, USD/RB, USD/HKD, USD/SGD, USD/TRY, USD/KRW, USD/SEK, USD/ZAR, USD/INR, USD/NOK, USD/BRL, EUR/JPY, EUR/GBP, EUR/CHF, JPY/AUD