Response to consultation Paper on draft RTS on criteria for assessing risk factors modellability under the IMA
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For level playing field issues, not to raise problems, audit conditions should be internationally agreed, not applying uneven requirements from a jurisdiction to another.
Recourse to parametric functions might vary across institutions and it is difficult to provide an exhaustive list of possible use cases.
Nevertheless, it is expected that the use of parametric functions could increase with FRTB standards, as eligibility rules (e.g. PLA) or capitalization rules may lead institutions to review their risk factor definition towards less redundant and somewhat more orthogonal risk factors.
That being said, the EBF considers that the general modellability criteria outlined in articles 5.3(a) and 5.3(b) of the draft RTS (whereby the function parameters are modellable if and only if all the buckets covering the related dimensions are modellable) are far more stringent than the BCBS provision [MAR 31.19] itself and shares EBA’s concern that a full curve, surface or cube could be pushed into the SSRM “just because one bucket is non-modellable”.
We believe the general eligibility criteria should be adaptive to the nature specific of parameters and offer recognition for a potential hierarchy between parameters where relevant. For instance, the ATM vol parameter plays a central role in the calibration of a SABR model. Assessing its modellability based on the ATM bucket makes sense, whether or not DITM bucket passes the RFET.
• Option 1 requires recalibration of historical parameters beyond capacity
o From an operational standpoint, the marking of a set of parameters {a,b,c} is driven by the market information available at a given point in time, and completed if needed by human expertise. Stripping a set of alternative parameters {a’,b’,c’} only from RFET qualifying data is possible only if a full history of RFET qualifying data (since 2007) is still available and if the human expertise is replaced by some algorithmic intelligence to solve operational issues.
o The modellability of the underlying instrument buckets evolve through time. If N is the number of buckets supporting the modellability of the parameters {a,b,c}, then there are 2^(N-1) versions of possible alternative sets {a’,b’,c’} to maintain.
• Option 2 requires the alternative pricing functions to be built in the risk engine
o If {x1,x2,x3,x4} are the “output risk factors” chosen to discretize the curve, surface or cube, then the pricing function ф(a,b,c) has to be replaced by an equivalent pricing function of the form Ψ(x1,x2,x3,x4) . Otherwise it would be impossible to unshock x1 separately from the other risk factors in the ES, or shock it separately from the other in the SSRM, should it be NMRF.
o Ultimately, the introduction of new pricing functions makes the parametric function almost useless in the risk engine
We will focus on volatility cube representations where the maturity and tenor dimensions are not parameterised but the strike dimension is. We believe this is a common representation of a volatility cube though some banks may have different approaches.
For the non-parameterised dimensions, maturity and tenor in our example, a usual own or supervisory bucketing may be used.
The parameterised dimension, strike in our example, is often represented by the ATM volatility and a skew and smile parameters. The ATM volatility (for a given maturity and tenor bucket) modellability may be assessed directly from a strike bucket around the ATM volatility. We could for instance use bucket 3 of Table 1 – Row iv for that purpose.
The skew and the smile generally are calibrated based on the differences between OTM, ATM and ITM volatilities. For that reason, we may consider that skew and smile may be modellable only if the ATM volatility is. In such cases, the skew will be deemed modellable if either the OTM or the ITM bucket passes the RFET, the smile will be deemed modellable if both the OTM and ITM buckets pass the RFET.
When doing so, OTM may be defined as all strikes lower than strikes of the ATM bucket, i.e. the union of supervisory buckets 1 and 2 of Table 1, Row iv while ITM may be defined as all strikes higher than the strikes of the ATM bucket, i.e. the union of supervisory buckets 4 and 5 of Table 1, Row iv. In such way, there is a bucketing consistent with the parameterisation granularity (3 parameters, 3 non-overlapping buckets).
Some models may involve more parameters and the above proposal would need adaptation. Due consideration should be taken to the importance of a parameter in the strike dimension calibration: the modellability assessment of additional parameters that are rarely updated and have limited effect may be linked to those of other parameters (ex. skew and smile).
Grandfathering conditions should be given more precision.
Q5. Do you see any problems with requiring that institutions are allowed to use data from external data providers as input to the modellability assessment only where the external data providers are regularly subject to an independent audit (independent of whether the price is shared with the institution or not)? If so, please describe them thoroughly (i.e. for which data providers and the reasons for it).
The EBF supports the use of data from external data providers as input to the modellability assessment, where external data providers are regularly subject to an independent audit.For level playing field issues, not to raise problems, audit conditions should be internationally agreed, not applying uneven requirements from a jurisdiction to another.
Q6. Do you have any proposals on additional specifications that could be included in the legal text in order to ensure that verifiable prices provided by third-party vendors meet the requirements of this Regulation?
We have no proposal on additional specifications.Q7. How relevant are the provisions outlined above for your institution? How many and which curves, surfaces or cubes are (planned to be) represented by a mathematical function with function parameters chosen as risk factors in your (future) internal model?
Curve, surface or cube parameterization is of practical use in risk modelling as it enables to represent the joint dynamic of a whole set of market data in a vector space of smaller dimension. A common example is the use of SABR model to summarize the dependency of implied volatility on option strikes through three parameters (ATM level, skew and smile).Recourse to parametric functions might vary across institutions and it is difficult to provide an exhaustive list of possible use cases.
Nevertheless, it is expected that the use of parametric functions could increase with FRTB standards, as eligibility rules (e.g. PLA) or capitalization rules may lead institutions to review their risk factor definition towards less redundant and somewhat more orthogonal risk factors.
Q8. Do you have a preference for any of the options outlined above? For which reasons? Please motivate your response.
The Industry does not support any of the proposed options, both of them being considered as impractical. Please refer to the answer to question 9 for more details and motivated answers.That being said, the EBF considers that the general modellability criteria outlined in articles 5.3(a) and 5.3(b) of the draft RTS (whereby the function parameters are modellable if and only if all the buckets covering the related dimensions are modellable) are far more stringent than the BCBS provision [MAR 31.19] itself and shares EBA’s concern that a full curve, surface or cube could be pushed into the SSRM “just because one bucket is non-modellable”.
We believe the general eligibility criteria should be adaptive to the nature specific of parameters and offer recognition for a potential hierarchy between parameters where relevant. For instance, the ATM vol parameter plays a central role in the calibration of a SABR model. Assessing its modellability based on the ATM bucket makes sense, whether or not DITM bucket passes the RFET.
Q9. Do you consider any of the options outlined above as impossible or impractical? For which reasons? Please motivate your response.
The Industry believes that both options are impractical (if not impossible).• Option 1 requires recalibration of historical parameters beyond capacity
o From an operational standpoint, the marking of a set of parameters {a,b,c} is driven by the market information available at a given point in time, and completed if needed by human expertise. Stripping a set of alternative parameters {a’,b’,c’} only from RFET qualifying data is possible only if a full history of RFET qualifying data (since 2007) is still available and if the human expertise is replaced by some algorithmic intelligence to solve operational issues.
o The modellability of the underlying instrument buckets evolve through time. If N is the number of buckets supporting the modellability of the parameters {a,b,c}, then there are 2^(N-1) versions of possible alternative sets {a’,b’,c’} to maintain.
• Option 2 requires the alternative pricing functions to be built in the risk engine
o If {x1,x2,x3,x4} are the “output risk factors” chosen to discretize the curve, surface or cube, then the pricing function ф(a,b,c) has to be replaced by an equivalent pricing function of the form Ψ(x1,x2,x3,x4) . Otherwise it would be impossible to unshock x1 separately from the other risk factors in the ES, or shock it separately from the other in the SSRM, should it be NMRF.
o Ultimately, the introduction of new pricing functions makes the parametric function almost useless in the risk engine
Q10. Do you have alternative proposals to define the consequence on the modellability of the parameters where some buckets of a curve, surface or cube are modellable whilst others are nonmodellable?
It is not possible to cover all type of models, hence the alternative proposal put forward below may not address all cases and models. However, it sets an approach that should be adapted to other types of models.We will focus on volatility cube representations where the maturity and tenor dimensions are not parameterised but the strike dimension is. We believe this is a common representation of a volatility cube though some banks may have different approaches.
For the non-parameterised dimensions, maturity and tenor in our example, a usual own or supervisory bucketing may be used.
The parameterised dimension, strike in our example, is often represented by the ATM volatility and a skew and smile parameters. The ATM volatility (for a given maturity and tenor bucket) modellability may be assessed directly from a strike bucket around the ATM volatility. We could for instance use bucket 3 of Table 1 – Row iv for that purpose.
The skew and the smile generally are calibrated based on the differences between OTM, ATM and ITM volatilities. For that reason, we may consider that skew and smile may be modellable only if the ATM volatility is. In such cases, the skew will be deemed modellable if either the OTM or the ITM bucket passes the RFET, the smile will be deemed modellable if both the OTM and ITM buckets pass the RFET.
When doing so, OTM may be defined as all strikes lower than strikes of the ATM bucket, i.e. the union of supervisory buckets 1 and 2 of Table 1, Row iv while ITM may be defined as all strikes higher than the strikes of the ATM bucket, i.e. the union of supervisory buckets 4 and 5 of Table 1, Row iv. In such way, there is a bucketing consistent with the parameterisation granularity (3 parameters, 3 non-overlapping buckets).
Some models may involve more parameters and the above proposal would need adaptation. Due consideration should be taken to the importance of a parameter in the strike dimension calibration: the modellability assessment of additional parameters that are rarely updated and have limited effect may be linked to those of other parameters (ex. skew and smile).
Q11. Do you intend to apply paragraph 4? If so, for which risk factors will it be relevant? Do you expect any implementation issues related to it? Please explain expected issues thoroughly.
Paragraph 4 of Article 6 of the draft technical standard on criteria for assessing the modellability of risk factors under the Internal Models Approach (IMA) under Article 325be(3) seems operationally very complex.Q12. Do you agree with the outlined methodology for the assessment of modellability of risk factors? If not, please explain why.
NAQ13. Do you expect any problems for the modellability assessment arising from the upcoming benchmark rate transition that could be addressed via this regulation? If so, please provide a thorough description and potential solutions if any
EBF member banks expect problems raised by the reuse set of deals without migration agreement.Grandfathering conditions should be given more precision.