Managing Non-Modellable Risk Factors

REVISED FOR 2019 FRTB STANDARD

By: Sanjay Sharma, Ph.D. and John Beckwith

FRTB allows for risk factor (RF) modelling under IMA only where adequate observable data is available. It prescribes a framework for assessment of the modellability of RFs based on their observability and other factors, and for capital charges for NMRFs. FRTB requires that RFs that cannot be derived and evidenced from prescribed “real or committed prices” at defined frequency are treated as non-modellable (NMRF). Capital charge for trading positions associated with NMRFs is based on a specified methodology that entails conservative stress scenarios for each individual RF aggregated on a summative basis at the bank level. While the concept of NMRFs for computation of capital charge under IMA is logical and necessary, the underlying methodology and implementation will be challenging for both banks and supervisors alike, given vast sets of data sources and trading venues, and heterogeneity of instrument characteristics and trading frequencies.

There are three principal checks for appropriate usage of internal models under FRTB: a qualitative evaluation and approval by supervisors of the rigor and robustness of a banks’ overall framework (this includes internal and external model validation); continual observability of underlying RFs through market prices; and frequent P&L attribution tests that check for the alignment of front office and risk models. In this paper, we focus on the concept, practice, and management of NMRFs.

Criteria for price data and Risk Factor Eligibility Test (RFET) determination

The criteria for a price (the fundamental source of an RF) in FRTB is for it to be “real” and “continuously” available. Quantitative assessments of these two components collectively comprise the RFET.

A. Test for “reality” of price data

To be considered “real”, prices must pass one of the following 4 criteria.

1. It is a price at which the institution has conducted a transaction;
   OR
2. It is a verifiable price for an actual transaction between other arms-length parties;
   OR
3. The price is obtained from a committed quote; (footnote: this is not defined specifically in FRTB but likely to pass regulatory approval as it is based on the concept defined by Markets in Financial Instruments Directive MIFID).
   OR
4. If the price is obtained from a third-party vendor, where:
   1. the transaction has been processed through the vendor; AND
   2. the vendor agrees to provide evidence of the transaction to supervisors upon request; AND
   3. the price meets the three criteria immediately listed above, then it is considered to be real for the purposes of the modellable classification; AND
   4. the vendor communicates to the bank the number of corresponding real prices observed and the dates at which they have been observed; AND
   5. the vendor provides, individually, a minimum necessary set of identifier information to enable banks to map real prices observed to risk factors; AND
   6. the vendor is subject to an audit regarding the validity of its pricing information. The results and reports of this audit must be made available on request to the relevant supervisory authority and to banks as a precondition for the bank to be allowed to use real price observations collected by the third-party vendor. If the audit of a third-party vendor is not satisfactory to a supervisory authority, the supervisory authority may decide to prevent the bank from using data from this vendor.

B. Test for continual observation of “real” price data for RF extraction

To be considered “continuously observable”, the number of observations must meet one of the following two criteria.

1. Monthly Test:
   1. A RF must have at least 24 observable “real” prices per year (measured over the period used to calibrate the current expected shortfall model); AND
   2. Minimum 4 observations in every 90 days over the last 12 months;
      OR
2. Annual Test:
   1. At least 100 observations over the last 12 months.

Each of the above must be tested monthly and only one price observation can be counted per day.

A “real” price that is observed for a transaction can be included as an observation for all RFs concerned i.e. all RFs that are used to model the risk of the instrument that is transacted. Note that this test must be applied to all RFs, from the highest volume which trade continuously (e.g. USD 10Y) to the lowest volume which trade infrequently. While the former should easily pass the requirement, there will be numerous OTC derivatives that will not qualify easily e.g. swaption volatilities for long expiries and tenors.

Bucketing approaches for RFET

Under FRTB, the modellability test is applied to specific points or groups of points on a curve, cube or surface. For example, it is possible that the 1-week vector on a curve could be modellable whereas the 2-year vector on that same curve might not be modellable. In order to determine RF modellability, banks must have an approach for bucketing RF observations by vector. FRTB prescribes 2 allowed bucketing approaches for risk factors given as points on a curve, cube or surface.

1. The own bucketing approach. Under this approach, the bank may define the buckets it will use under the following requirements:
   1. Each bucket must include only one risk factor; AND
   2. All risk factors must correspond to RTPL RFs for purposes of the P&L attribution test; AND
   3. The buckets must be non-overlapping.
2. The regulatory bucketing approach. Under this approach, the bank must use the set of standard buckets as set out in Table 1.
   1. For interest rate, foreign exchange and commodity risk factors with one maturity dimension (excluding implied volatilities) (t, where t is measured in years), the buckets in row (A) below must be used.
   2. For interest rate, foreign exchange and commodity risk factors with several maturity dimensions (excluding implied volatilities) (t, where t is measured in years), the buckets in row (B) below must be used.
   3. Credit spread and equity risk factors with one or several maturity dimensions (excluding implied volatilities) (t, where t is measured in years), the buckets in row (C) below must be used.
   4. For any risk factors with one or several strike dimensions (delta, δ; ie the probability that an option is “in the money” at maturity), the buckets in row (D) below must be used. For options markets where alternative definitions of moneyness are standard, banks shall convert the regulatory delta buckets to the market-standard convention using their own approved pricing models.
   5. For expiry and strike dimensions of implied volatility risk factors (excluding those of interest rate swaptions), only the buckets in rows (C) and (D) below must be used.
   6. For maturity, expiry and strike dimensions of implied volatility risk factors from interest rate swaptions, only the buckets in row (B), (C) and (D) below must be used.

Table 1: Standard buckets for the regulatory bucketing approach

Note that the bucketing methodology a bank uses for its RFET will directly impact the trade-off between passage of the PLA test and the amount of NMRFs incurred by the bank. This trade-off stems from FRTB’s requirement to use the same buckets of RF observations for both the PLA test and the RFET. More granular buckets will better align HPL with RTPL, but additional granularity will also reduce the number of real observed prices per bucket, making RFET passage more difficult and NMRFs more numerous. This is a conscientious, embedded trade-off in the FRTB framework which banks must consider when designing their bucketing frameworks.

Computation methodology for capital charge

FRTB specifies that all trading book positions sensitive or exposed to NMRFs should be capitalized individually based on calibrated stress scenarios at the model/desk level with cross-trade and RTD aggregation to be done at the bank/enterprise level. The capital change is computed based on stress/shock scenarios for each NMRF with appropriate liquidity horizons.

The following describes the methodology for computing and aggregating individual NMRF capital charges.

FRTB divides NMRFs into three groups:

1. I-Type – Idiosyncratic credit spread risk factors that have been demonstrated to be appropriate to aggregate with zero correlation;
2. J-Type – Idiosyncratic equity risk factors that have been demonstrated to be appropriate to aggregate with zero correlation;
3. K-Type – Remaining non-modellable risk factors in IMA-approved trading desks.

The aggregate regulatory capital measure stress expected shortfall (SES) of all non-modellable risk factors (NMRFs) is:

Where,

• ISES_NM,i is the stress scenario capital requirement for idiosyncratic credit spread non-modellable risk i from the I risk factors aggregated with zero correlation;
• ISES_NM,j is the stress scenario capital requirement for idiosyncratic equity non-modellable risk j from the J risk factors aggregated with zero correlation;
• SES_NM,k is the stress scenario capital requirement for non-modellable risk k from K risk factors; and
• Rho (ρρ) is equal to 0.6.

Stress shocks and scenarios must be calibrated to be at least as prudent as the ES calibration used for modellable RFs, i.e. loss calibrated to 97.5% confidence threshold over a period of extreme stress for the underlying RFs. For each NMRF the liquidity horizon of the stress scenario must be greater than the longest interval between two consecutive price observations of the prior year, and the liquidity horizon assigned to the prescribed RFs.

Our interpretation of this requirement is that if adequate plausible historical price data is available to calibrate appropriate and acceptable shocks for an individual NMRF, an “ES equivalent” calculation should be acceptable as an RF-specific stress scenario. As data availability becomes sparse, the assumptions for shocks should be made increasingly conservative with longer liquidity horizons. This range can be specified with supervisory approval at 97.5% confidence and ES with holding periods scaling up based on data gaps and liquidity horizons as prescribed under IMA.

If the SES is positive, it will be capped at zero. For large RF shocks, pricing models may produce odd or unexpected results as arbitrage conditions that underlie the specific model change. In this case SES can be computed via a backup approach based on sensitivity.

Subject to supervisory approval, a bank may be permitted to calculate stress scenario capital requirements at the bucket level using the same buckets that the bank uses to disprove modellability of risk factors. The process for this is as follows:

1. For each NMRF, the liquidity horizon of the stress scenario must be the greater of the liquidity horizon assigned to the risk factor under the bucketing approach or 20 days. The bank’s supervisor may require a longer liquidity horizon.
2. For NMRFs arising from idiosyncratic credit spread or equity risk, banks may apply a common 12-month stress period. Additionally, a zero-correlation assumption may be used when aggregating gains and losses provided the bank conducts analysis to demonstrate to its supervisor that this is appropriate. Correlation or diversification effects between other non-idiosyncratic NMRFs are recognized through the formula above.
3. In the event that a bank cannot provide a stress scenario which is acceptable for the supervisor, the bank will have to use the maximum possible loss as the stress scenario.

NMRF Principles

Acknowledging that banks will employ many different types of models with varying data requirements and sources/types of data, BCBS developed 7 principles for determining modellability to be applied subjectively by banks and supervisors. These principles are designed to be incremental to the objective RFETs already described.

Banks will be required to demonstrate adherence to these principles at all times for their approved trading desks. Supervisors may disallow modellability for any number of risk factors, even those that pass objective RFETs, if compliance with these principles cannot be demonstrated. Because nuances can be important in compliance with subjective regulations, for each principle we recite below the exact FRTB language, followed by our comment on its implication to implementing banks.

“Principle 1. The data used may include combinations of modellable risk factors. Banks often price instruments as a combination of risk factors. Generally, risk factors derived solely from a combination of modellable risk factors are modellable. For example, risk factors derived through multifactor beta models for which inputs and calibrations are based solely on modellable risk factors, can be classified as modellable and can be included within the ES model. A risk factor derived from a combination of modellable risk factors that are mapped to distinct buckets of a given curve/surface is modellable only if this risk factor also passes the RFET.

(a) Interpolation based on combinations of modellable risk factors should be consistent with mappings used for PLA testing (to determine the RTPL) and should not be based on alternative, and potentially broader, bucketing approaches. Likewise, banks may compress risk factors into a smaller dimension of orthogonal risk factors (eg principal components) and/or derive parameters from observations of modellable risk factors, such as in models of stochastic implied volatility, without the parameters being directly observable in the market.

(b) Subject to the approval of the supervisor, banks may extrapolate up to a reasonable distance from the closest modellable risk factor. The extrapolation should not rely solely on the closest modellable risk factor but on more than one modellable risk factor. In the event that a bank uses extrapolation, the extrapolation must be considered in the determination of the RTPL.”

Implication: We call this the transitive principle because it allows for the construction of modellable but untraded instruments from a collection of modellable risk factors so long as those RFs each pass the RFET. This principle also ties RFET determination to the PLA through the requirement for alignment with the RTPL.

“Principle 2. The data used must allow the model to pick up both idiosyncratic and general market risk. General market risk is the tendency of an instrument’s value to change with the change in the value of the broader market, as represented by an appropriate index or indices. Idiosyncratic risk is the risk associated with a particular issuance, including default provisions, maturity and seniority. The data must allow both components of market risk to be captured in any market risk model used to determine capital requirements. If the data used in the model do not reflect either idiosyncratic or general market risk, the bank must apply an NMRF charge for those aspects that are not adequately captured in its model.”

Implication: We call this the robustness principle. RFs should be viable through systemic as well as idiosyncratic stress. An RF may be deemed to be non-modellable even if it passes the RFET if the bank or supervisor believes recent trading activity would not reflect future activity because of either idiosyncratic or systemic stress events.

“Principle 3. The data used must allow the model to reflect volatility and correlation of the risk positions. Banks must ensure that they do not understate the volatility of an asset (eg by using inappropriate averaging of data or proxies). Further, banks must ensure that they accurately reflect the correlation of asset prices, rates across yield curves and/or volatilities within volatility surfaces. Different data sources can provide dramatically different volatility and correlation estimates for asset prices. The bank should choose data sources so as to ensure that (i) the data are representative of real price observations; (ii) price volatility is not understated by the choice of data; and (iii) correlations are reasonable approximations of correlations among real price observations. Furthermore, any transformations must not understate the volatility arising from risk factors and must accurately reflect the correlations arising from risk factors used in the bank’s ES model.”

Implication: We call this the hidden volatility principle. RFs should not be chosen specifically to reduce volatility or correlation within a book or desk.

“Principle 4. The data used must be reflective of prices observed and/or quoted in the market. Where data used are not derived from real price observations, the bank must demonstrate that the data used are reasonably representative of real price observations. To that end, the bank must periodically reconcile price data used in a risk model with front office and back office prices. Just as the back office serves to check the validity of the front office price, risk model prices should be included in the comparison. The comparison of front or back office prices with risk prices should consist of comparisons of risk prices with real price observations, but front office and back office prices can be used where real price observations are not widely available. Banks must document their approaches to deriving risk factors from market prices.”

Implication: We call this the reconciliation principle. Just as the PLA test is designed to align front office and risk models, this principle is designed to align front office and risk data sources through periodic reconciliation and regular documentation.

“Principle 5. The data used must be updated at a sufficient frequency. A market risk model may require large amounts of data, and it can be challenging to update such large data sets frequently. Banks should strive to update their model data as often as possible to account for frequent turnover of positions in the trading portfolio and changing market conditions. Banks should update data at a minimum on a monthly basis, but preferably daily. Additionally, banks should have a workflow process for updating the sources of data. Furthermore, where the bank uses regressions to estimate risk factor parameters, these must be re-estimated on a regular basis, generally no less frequently than every two weeks. Calibration of pricing models to current market prices must also be sufficiently frequent, ideally no less frequent than the calibration of front office pricing models. Where appropriate, banks should have clear policies for backfilling and/or gap-filling missing data.”

Implication: We call this the stale data principle and will be a clear target for both auditors and supervisors to determine whether policies and procedures are clear, well documented, and rigorously followed.

“Principle 6. The data used to determine stressed expected shortfall (ES_R,S) must be reflective of market prices observed and/or quoted in the period of stress. The data for the ES_R,S model should be sourced directly from the historical period whenever possible. There are cases where the characteristics of current instruments in the market differ from those in the stress period. Nevertheless, banks must empirically justify any instances where the market prices used for the stress period are different from the market prices actually observed during that period. Further, in cases where instruments that are currently traded did not exist during a period of significant financial stress, banks must demonstrate that the prices used match changes in prices or spreads of similar instruments during the stress period.

(a) In cases where banks do not sufficiently justify the use of current market data for products whose characteristics have changed since the stress period, the bank must omit the risk factor for the stressed period and meet the requirement of [the ES_R,S regime within the IMCC];

(b) that the reduced set of risk factors explain 75% of the fully specified ES model. Moreover, if name-specific risk factors are used to calculate the ES in the actual period and these names were not available in the stressed period, there is a presumption that the idiosyncratic part of these risk factors are not in the reduced set of risk factors. Exposures for risk factors that are included in the current set but not in the reduced set need to be mapped to the most suitable risk factor of the reduced set for the purposes of calculating ES measures in the stressed period.”

Implication: We call this the stress period principle because it’s focus is specific to historic stress periods and the modellability of instruments or even sensitivities which did not exist historically. Of all the principles, we believe principle 6 will have the most room for dispersion in supervisory interpretation across jurisdictions.

Principle 7. The use of proxies must be limited, and proxies must have sufficiently similar characteristics to the transactions they represent. Proxies must be appropriate for the region, quality and type of instrument they are intended to represent. Supervisors will assess whether methods for combining risk factors are conceptually and empirically sound.

(a) For example, the use of indices in a multifactor model must capture the correlated risk of the assets represented by the indices, and the remaining idiosyncratic risk must be demonstrably uncorrelated across different issuers. A multifactor model must have significant explanatory power for the price movements of assets and must provide an assessment of the uncertainty in the final outcome due to the use of a proxy. The coefficients (betas) of a multifactor model must be empirically based and must not be determined based on judgment. Instances where coefficients are set by judgment generally should be considered as NMRFs.

(b) If risk factors are represented by proxy data in the current period ES model, the proxy data representation of the risk factor – not the risk factor itself – must be used in the RTPL unless the bank has identified the basis between the proxy and the actual risk factor and properly capitalized the basis either by including the basis in the ES model (if the risk factor is a modellable) or capturing the basis as a NMRF. If the capital requirement for the basis is properly determined, then the bank can choose to include in the RTPL either:
(i) the proxy risk factor and the basis; or
(ii) the actual risk factor itself.”

Implication: We call this the proxy-basis principle. It is both self-explanatory and very useful.

Aggregate Capital Calculation

The internal model capital charge C_A for all desks with internal model approval is calculated based on the scaled expected shortfall and the aggregated NMRF charges using the following formula:

C_A=max (IMCC_t-1+SES_t-1;m_c×IMCC_avg+SES_avg)

Where:

• IMCC_t is the internal model capital charge calculated with the scaled expected shortfall model at time t
• SES_t is the aggregated NMRF charge as described above, and m_c is a multiplier that is set individually for each bank by the regulators with a floor of 1.5

NMRF capital charge principal contributing factors

Initial estimates point to NMRF capital charge being significantly higher than for ES-based IMA capital charge for modellable RFs. This stems from a combination of three underlying FRTB methodology prescriptions:

1. Conservative stress scenarios
   Under FRTB, capital charge for NMRFs has to be computed based on conservative stress scenarios proposed by banks and approved by supervisors.
2. Longer liquidity horizons
   The liquidity period for NMRF capital charge is assumed to be longer of the proposed risk class-specific charge prescribed under IMA, or the time period between the two “real price” quotes that are most further apart over the prior year.
3. Limited correlation, diversification and hedging benefit at the RTD level. FRTB prescribes that correlation or diversification benefits across NMRFs are to be netted and adjusted for at the bank level. The genesis of this is that because NMRFs arise from endemic or episodic absence of verifiable real prices, and making correlations between NMRFs and across modellable RFs are difficult to estimate reliably.

NMRF workflow

For desks that are deemed eligible for internal model approval the underlying RFs for each model will be categorized vis‑à‑vis their observability in the RF analysis process. RFs that can be objectively verified using “real prices” are hence classified as modellable and capital charge can be computed through the ES approach. All other RFs are categorized as non‑modellable and are to be capitalised using the NMRF charge, based on individual stress scenarios and a conservative aggregation framework.

Addressing the NMRF compliance obligation for banks will have several components requiring both sequential and simultaneous workflows.

The panel below illustrates a high-level process for management of NMRFs.

We describe a three-step RF identification methodology for establishing an FRTB compliant RF framework.

Implementing a systematic identification process

A bank’s NMRF identification process should be focused on objectively validating RF values based on real transactions. To that end, the identification process can be divided into three steps:

A. Identify relevant RFs

All relevant RFs of a bank’s trading book portfolio should to be identified in a structured and comprehensive manner on a regular basis for all trading desks eligible for IMA based on a common RF definition.

RFs that are omitted from internal models (i.e. both for the Expected Shortfall and NMRF calculations) should be flagged. The omission should be justified and documented as prescribed by jurisdictional supervisors, e.g. by providing the appropriate P&L attribution test statistics.

B. Create instrument to RF Mapping

1. Modelability assessment of individual RFs is based on “real prices” of representative transactions. Towards that end, a mapping between RFs and representative products should be defined. This mapping should link RFs to instruments with demonstrable materiality and tractable relationship between an RF and the price of the respective instrument. Generally, several instruments may be available to evidence the same RF.
2. Identification and regrouping of RFs

The list created in Step 1 should be redrawn to identify common RFs and their sources based on commonality, materiality, frequency and robustness.

This analysis has to be performed across all internal and external data sources. The most optimal combinations of RF sources and price data can be identified, listed and prioritized for each model.

3. Calibration of models with new RF source

In situations where a unified model framework and RF mapping involves changes, calibration should be performed to ensure compatibility and avoid surprises.

C. Selection and inclusion of RFs

Listing and grouping of existing models with FRTB prescribed risk buckets. Since 2008, banks’ model organization and validation documentation for risk models have undergone substantial transformation as required by supervisory bodies. However, given the flexibility provided to banks under Basel 2.5 IMA, current model frameworks are siloed by asset class, trading desks and business units. Siloed frameworks are not conducive for RF identification and NMRF minimization under FRTB. It is strongly advisable that were it does not exist, banks conduct a comprehensive listing and categorization of individual risk and pricing models along with RFs and their sources.

D. Observability check

Any “real price” that is observed for a transaction should be counted as an observation for all the RFs concerned i.e., all RFs which are used to model the risk of the instrument that is bought, sold or generated through the transaction as part of the overall portfolio.

To check observability, “real price and committed quote” data can be sourced from internal transactions or third parties. In the latter case, the data will most likely be procured from a vendor, who can process the transactions and record the necessary observability evidence and audit trail that can be provided to supervisors by the banks. The “real price” data is then projected back onto the RFs to assess their modelability based on the mapping rules created in the previous step.

Qualified price observations are mapped to the RFs and two data fields are recorded: the count of observations within the last year; and the longest gap between two consecutive observations. Mapping has to be done such that instruments and transactions have to be linked to specific RFs across materiality and historical consistency availability of prices. It will be possible to link several RFs to a single instrument across risk class buckets and asset class. This classification can be guided by the SA risk class bucket classification and IMA liquidity buckets.

The following steps can then be followed:

1. If the data is near fail thresholds examine alternate RF sources and substitute with impacted capital.
2. If other RF sources are also close to the disqualifications range qualifying prepare to apply proxy and basis. This will increase the capital charge because of the NMRF charge associated with the non-modellable basis.
3. Although FRTB does not allow for transfer of trades across desks future trades should be booked under SA desks.
4. If IMA capital charge is high with NMRFs, create a process for adopting SA.

Considerations

To summarize, the following three considerations for utilizing the flexibility afforded under FRTB for RF selection should be integral to the workflow:

A. Systematic approach

The mapping between RF sources and instruments should be systematic and thorough. If not well planned and executed the flexibility to select RFs from multiple sources can result in a disorganized model environment with ad hoc choices lead to inconsistency that may be hard to document and justify to supervisors.

B. Materiality

Due consideration given to materiality of RFs factors in the valuation and risk models. Defining the materiality of RF can be a straightforward sensitivity assessment of simulated movement in prices vs. redefined RFs across alternate instruments.

C. Reliable frequency of the real prices of source instruments

The choice of instruments as RF sources should incorporate their historical trading volume and frequency of the availability. At a minimum, the choice of RF sources is a balancing and organizing act.

Additional points for RF selection

Market data that is used to illustrate RF modelability may not be suitable for computing ES. Once an RF is proven to be modellable, banks are allowed to use all available data sources to calibrate an internal model.

Categorization of RFs for NMRF are allowed to be distinct from other representations. For instance, in a standard volatility model, e.g. SABR, the parameters of the volatility model are considered as RFs. The underlying parameters of these models are calibrated from swaption prices with combinations of expiry, tenor and strike/moneyness.

1. Under FRTB, if the underlying parameters are demonstrably derived from modellable RFs with “real price” and specified observation frequency, the calibrated parameters are clearly modellable as well. For instance, for interest rate derivatives, the underlying RFs can be extracted from interest rate volatility surfaces for each currency demonstrate the availability of price data for applicable and modellable transactions then the SABR models can be used.

The following sections provide guidelines on computation of capital charge, selection and management of RFs and calibration of shocks that incorporate appropriate liquidity horizons.

Strategies for NMRF management and optimization

The conservative aggregation structure prescribed by FRTB scales linearly with the number of NMRFs and can result in economically unrealistic NMRF capital charges. As no diversification benefits are granted across NMRFs, banks would be less motivated to hedge and diversify their portfolios. If an NMRF is hedged with a modellable RF, the overall capital consumption can potentially become very punitive. Positions with NMRFs will have to be capitalized on a standalone basis, separate from associated hedges leading to an additional capital charge as part of the Expected Shortfall calculation. This implies that FRTB will lead to economically sensible risk management and hedging strategies being discouraged due to a potentially punitive capital treatment wherein a hedged portfolio has a higher capital consumption than a non-hedged portfolio.

To mitigate these undesired effects, several techniques can be employed that are provided below. We describe and illustrate some straightforward methodologies below.

Representative NMRF Workflow

A. RF decomposition

FRTB allows for the decomposition of NMRFs into modellable benchmarks and “residual basis” that would be capitalized as non-modellable. This is logical because RFs that are observable generally have an underlying basis that is modellable. The simplest example is the case of a corporate bond wherein idiosyncratic credit risk in the mind of a trader/investor is generally relative to that of an index or other liquid bonds. In these cases, the additional risk premium that may be truly non-modellable is an add-on to the other components that include credit risk of similar issuers and prevailing interest rates, i.e. credit risk spread for small and illiquid issuers can be decomposed into a liquid credit spread index that is modellable to which a nonmodellable basis or spread is added. In a similar fashion, long tenor points for interest rate curves that may not be frequently traded and observed and do not pass the observable price criteria can be decomposed into shorter-tenor observable points and cross-tenor basis spread.

Banks and RTDs should consider the following general guidelines for decomposing NMRFs. Several factors will determine if the decomposition of a RF is more capital efficient than modelling the non-modellable RF as an outright NMRF:

• Proportional variation of the NMRF that can be explained by the modellable RF proxy.
• Relative size of the trading book/position vis‑à-vis risk offsets.
• Chosen proxies should have a demonstrable causal relationship with the modellable proxy that can be observed and recorded on a regular basis.
• The RTD should be prepared to reduce the overall NMRF positon in case there is an episodic divergence with the modellable proxy and unexpected increase in the NMRF capital charge.
• The relative sizes of NMRF and proxy positons that are balanced and managed as a “pair trades.” This function can be extended to an NMRF portfolio but only with sophisticated risk management and FRTB systems.
• Proxies should be chosen carefully with due consideration to the balance between their liquidity and proximity to the NMRF. In general, a well-chosen liquid single-name CDS as a proxy will have a smaller basis compared to a CDS index, and thus lower volatility and lower NMRF capital charge.
• A proxy itself may have high volatility resulting in a net increase in NMRF capital charge. This can be true of an index as well.
• The proxy may itself become non-observable to the capital charge.
• Particular attention should be paid to instrument specific idiosyncratic risks that may not be proxy-able. Consider the case of credit risk of a corporate bond is represented across the following RFs:
  1. Issuer-specific default probability
  2. Recovery rate
  3. Issue-specific idiosyncratic risk

The default probability and the recovery rate can both be observed from bonds of the same issuer with identical seniority and maturity. However, the issue-specific idiosyncratic risk of the the specific bond can only be observed from market prices of bonds that have the same default provisions, other terms, and covenants, etc.

B. Calibration of stress scenarios for computation of SES

RFs classified as non-modellable must be capitalized at the bank level, based on stress scenario for each NMRF. We suggest a methodology for calibrating shocks according to FRTB guidelines and applicable liquidity horizons. These shocks drive the computation of capital charge individually for each non-modellable RF.

FRTB requires that stress scenarios used for computing capital should to be calibrated to be “at least as prudent as the expected shortfall calibration used for modeled risks (i.e. a loss calibrated to a 97.5% confidence threshold over a period of extreme stress for the RF value)”.

Our interpretation of this requirement is that if sufficient data is available to calibrate an appropriate shock for an individual NMRF, an ES-equivalent calculation would be sufficient as an RF stress scenario. However, as data availability becomes scarce, more conservative shock approaches for stress must be used. Where a modellable RF is not available during the historical period used for stressed calibration (e.g. 2007‑08), proxy data can be used, provided the general approach for replicating missing data is justified and documented as part of the independent review of the internal models, as well as approved by the bank’s supervisory body. Although the FRTB guidelines have not stated this explicitly, it should be noted that this does not apply to ongoing observation and validation of data availability.

A rational and practical approach is to reprice all instruments for which the models are impacted by the NMRF classification as an impact with calibrated stress scenarios at 97.5% confidence level. The stressed expected shortfall is computed by shocking the RF twice with same parameter interval up and down. The higher loss of the two scenarios is selected at the bank level.

We propose a three-step for creation and calibration of SES.

1. If an applicable historical time series is available, the NMRF shock should be calculated over a period of stress for the specific RF1 as an expected shortfall at 97.5% confidence level.
2. If the historical market data is unavailable and/or is of poor quality, the maximum loss observed over the liquidity horizon should be used as stress scenario.
3. For cases where the historical market data is incomplete and unreliable such that the justification for its usage is questionable, the bank should calibrate the stress scenario based on expert judgement based on historical and or hypothetical assumption sets.

All stress scenarios have to be approved by banks’ supervisors. If they do not deem a stress scenario to be sufficiently conservative, they can ask for an NMRF capital charge equivalent to a maximum loss of the principal amount at risk.

C. Mechanism for “break-glass” SA fallback

SA is designed to be the IMA fallback under FRTB. In situations where the alternatives for managing NMRFs are cumbersome or not robust, SA can be a feasible alternative. The capital change will be higher than IMA, but not if the NMRF component is large.

The decision to select SA for an RTD can be based on the following comparison criteria:

1. The relative impact of correlation assumptions under IMA/NMRF (which can be zero for demonstrably non-correlated credit risks)
2. The comparison between SES scenarios under NMRF capital change computation vis-à-vis prescribed risk weights in SA

It should be noted that for idiosyncratic credit risk the comparison may not be tractable because of the size of proxies for NMRF computation. This is because the concept of an inherently a non-zero correlation. Thus, by using a shared proxy across idiosyncratic credit risks is unspecified (correlation assumption a zero). The impact of proxy-related correlation would be diluted at the bank-level e.g. computation can also be hedged perfectly with liquid credit investments. A quantitative comparison algorithm can be designed that incorporates SA risk weights, correlations, regression R squared the impact of proxies and residual variances.

Summary

Management of NMRFs and P&L Attribution Tests are where the FRTB rubber meets the capital road. It is very likely that BCBS will make this road smoother by providing clarity and more rational criteria for IMA implementation and regulation. However, it is highly unlikely that these tests will be withdrawn from FRTB. Banks and trading desks will do well to be armed with flexible technology systems and models framework to face the bumps on the road and ensuring a smooth ride towards capital optimization.