General Interest Rate Risk (GIRR)
Relevant provisions: Paragraphs 47 (c), 53 (b) and 67 (a) of the January 2016 market risk framework.
BCBS response: Paragraph 47 (c) states that banks must determine each delta sensitivity, vega sensitivity and curvature scenario based on instrument prices or pricing models that an independent risk control unit within a bank uses to report market risks or actual profits and losses to senior management. Banks should use zero rate or market rate sensitivities consistent with the pricing models referenced in that paragraph.
Referenced FRTB text:
47 (c) The bank must determine each delta and vega sensitivity and curvature scenario based on instrument prices or pricing models that
an independent risk control unit within a bank uses to report market risks or actual profits and losses to senior management.
53 (b) The curvature risk charge for curvature risk factor k can be formally written as follows:
where:
■ i is an instrument subject to curvature risks associated with risk factor k;
■ xk is the current level of risk factor k;
■ Vi(xk) is the price of instrument i depending on the current level of risk factor k;
■ – Vi(xk(RW(curvature)+)) and Vi(xk(RW(curvature)-)) both denote the price of instrument i after xk is shifted (ie, “shocked”) upward and downward;
■ under the FX and equity risk classes:
● RWk(curvature) is the risk weight for curvature risk factor k for instrument i determined in accordance with paragraph 131; and
● sik is the delta sensitivity of instrument i with respect to the delta risk factor that corresponds to curvature risk factor k
■ under the GIRR, CSR and commodity risk classes:
● RWk(curvature) is the risk weight for curvature risk factor k for instrument i determined in accordance with paragraph 132; and
● sik is the sum of delta sensitivities to all tenors of the relevant curve of instrument i with respect to curvature risk factor k.
67(a) Delta GIRR: Sensitivity is defined as the PV01 (sensitivity) of an instrument i with respect to vertex t of the risk-free yield curve (or curves, as appropriate) used to price the instrument i for the currency in which i is denominated. PV01 is determined by calculating the change in the market value of the instrument (Vi (.)) as a result of a one basis point shift in the interest rate r at vertex t (rt) of the risk-free yield curve in a given currency, divided by 0.0001 (ie, 0.01%). In notation form:
where:
■ rt is the risk-free yield curve at vertex t;
■ cst is the credit spread curve at vertex t; and
■ Vi (.) is the market value of the instrument i as a function of the risk-free interest rate curve and credit spread curve.
Authors’ comment: This question replaces the prior Q1 from this section found in the 2017 FAQ. Here we see some relief granted by the BCBS. Rather than prescribing zero or market rate sensitivities be used in GIRR delta and curvature charges, BCBS simply states that the choice must be consistent with that approved by the IPV and used within the bank for management reporting of P&L. In this instance, the BCBS response is quite constructive as it creates alignment within the bank between risk, front office and management views of both risk and return.
Relevant provisions: paragraph 59 (a) (iii) of the January 2016 market risk framework.
BCBS response: Paragraph 59 (a) (iii) states that for the purpose of constructing the risk-free yield curve per currency, an overnight index swap curve (such as EONIA) and an interbank offered rate curve (such as three-month Euribor) must be considered two different curves, with distinct risk factors in each tenor bucket, for the purpose of computing the risk charge.
Referenced FRTB text:
59 (a) (iii) For the purpose of constructing the risk-free yield curve per currency, an OIS curve (such as Eonia) and a BOR swap curve
(such as Euribor 3M) must be considered two different curves. Two BOR curves at different maturities (eg, Euribor 3M and Euribor 6M)
must be considered two different curves. An onshore and an offshore currency curve (eg, onshore Indian rupee and offshore Indian rupee)
must be considered two different curves.
Authors’ comment: The question seeks to address money market basis risk, in this case between EONIA and three-month Euribor.BCBS clarifies that for any curve derived through another, in this case Euribor derived from EONIA, both the underlying curve and the spread (basis) must be modelled. It is not sufficient to simply model the derived three-month Euribor curve
Relevant provisions: Paragraph 59 (c) of the January 2016 market risk framework.
BCBS response: Yes. Banks may use a term structure-based CCBS curve and aggregate sensitivities to individual tenors by simple sum.Referenced FRTB text:
59 (c) The GIRR delta risk factors also include one of two possible cross-currency basis risk factors for each currency (ie, each GIRR
bucket) with term structure not recognised as a risk factor (ie, both cross-currency basis curves are flat).
Authors’ comment: This BCBS response is self-explanatory.
Relevant provisions: Paragraph 59 (c) of the January 2016 market risk framework.
BCBS response: Yes. All cross-currency basis risk for a currency (ie,“Curr/US$” or “Curr/€”) for both onshore and offshore curves may be aggregated via a simple sum of weighted sensitivities.
Referenced FRTB text:
59 (c) The GIRR delta risk factors also include one of two possible cross-currency basis risk factors for each currency (ie, each GIRR
bucket) with term structure not recognised as a risk factor (ie, both cross-currency basis curves are flat).
Authors’ comment: The BCBS response here is constructive;however, definitions of “onshore” and “offshore” cross-currency basis risk may diverge within the ring-fenced jurisdictions of global banks, adding to the complexity of CCBS management. For example, the US intermediate holding company (IHC) of a Japanese bank will treat US dollars as domestic at the IHC level, but “offshore” from the consolidated parent company perspective.
Relevant provisions: Paragraph 59 (d) of the January 2016 market risk framework.
BCBS response: Yes. Inflation and cross-currency bases are included in the GIRR vega risk charge. As no maturity dimension is specified for the delta charge for inflation or cross-currency bases (ie, the possible underlying of the option), the vega charge for inflation and cross-currency bases should be considered only along the single dimension of the maturity of the option.
Referenced FRTB text:
59 (d) Vega GIRR: Within each currency, the GIRR vega risk factors are the implied volatilities of options that reference GIRR-sensitive
underlyings; further defined along two dimensions:
(i) Maturity of the option: The implied volatility of the option as mapped to one or several of the following maturity vertices: 0.5
years, one year, three years, five years, 10 years.
(ii) Residual maturity of the underlying of the option at the expiry date of the option: The implied volatility of the option as
mapped to two (or one) of the following residual maturity vertices: 0.5 years, one year, three years, five years, 10 years.
Authors’ comment: Once again, BCBS’s interpretation is constructive here. By excluding the requirement for residual maturities of inflation and cross currency underlyings to be included within vega GIRR, BCBS acknowledges that the quantification of these elements is impractical, if not impossible. At the same time, BCBS still allows inclusion of these risk factors without the more punitive option which they could have considered of adding a more punitive RRAO charge. This interpretation will be particularly helpful for European banks with substantial, long-dated inflation swaps residing in their legacy portfolios.
Relevant provisions: Paragraph 59 (d) of the January 2016 market risk framework.
BCBS response: The implied volatilities for a regular forward starting cap, which would start in one year and last for 12 months, should be defined along the following dimensions: maturity of the option’s individual components (caplets) – 12, 15, 18, 21 months; and residual maturity of the underlying of the option – three months.
Referenced FRTB text:
59 (d) Vega GIRR: Within each currency, the GIRR vega risk factors are the implied volatilities of options that reference GIRR-sensitive
underlyings; further defined along two dimensions:
(i) Maturity of the option: The implied volatility of the option as mapped to one or several of the following maturity vertices: 0.5 years, one year, three years, five years, 10 years.
(ii) Residual maturity of the underlying of the option at the expiry date of the option: The implied volatility of the option as mapped to two (or one) of the following residual maturity
vertices: 0.5 years, one year, three years, five years, 10 years.
Authors’ comment: The BCBS response is self-explanatory.
Relevant provisions: Paragraphs 59 and 60 of the January 2016 market risk framework.
BCBS response: For the specified instruments, delta, vega and curvature charges must be computed for both general interest rate risk (GIRR) and credit spread risk (CSR).
Referenced FRTB text:
59. General Interest Rate Risk (GIRR) risk factors
(a) Delta GIRR: The GIRR delta risk factors are defined along two dimensions: a risk-free yield curve for each currency in which interest rate-sensitive instruments are denominated and the following vertices: 0.25 years, 0.5 years, one year, two years,three years, five years, 10 years, 15 years, 20 years, 30 years, to which delta risk factors are assigned.
i. The risk-free yield curve per currency should be constructed using money market instruments held in the trading book which have the lowest credit risk, such as overnight index swaps (OIS). Alternatively, the risk-free yield curve should be based on one or more market-implied swap curves used by the bank to mark positions to market. For example, interbank offered rate (BOR) swap curves.
ii. When data on market-implied swap curves described in (a) (i) is insufficient, the risk-free yield curve may be derived from the most appropriate sovereign bond curve for a given currency. In such cases the sensitivities related to sovereign bonds is not exempt from the credit spread risk charge:when a bank cannot perform the decomposition y = r + cs,any sensitivity of cs to y is allocated to the GIRR and to CSR
risk classes as appropriate with the risk factor and sensitivity definitions in the standardised approach. Applying swap curves to bond-derived sensitivities for GIRR will not change the requirement for basis risk to be captured between bond and CDS curves in the CSR risk class.
iii. For the purpose of constructing the risk-free yield curve per currency, an OIS curve (such as Eonia) and a BOR swap curve (such as Euribor 3M) must be considered two different curves. Two BOR curves at different maturities (eg, Euribor 3M and Euribor 6M) must be considered two different curves. An onshore and an offshore currency curve (eg,onshore Indian rupee and offshore Indian rupee) must be considered two different curves.
(b) The GIRR delta risk factors also include a flat curve of market-implied inflation rates for each currency with term structure not recognised as a risk factor.
i. The sensitivity to the inflation rate from the exposure to implied coupons in an inflation instrument gives rise to a specific capital requirement. All inflation risks for a currency must be aggregated to one number via simple sum.
ii. This risk factor is only relevant for an instrument when a cash flow is functionally dependent on a measure of inflation(eg, the notional amount or an interest payment depending on a consumer price index). GIRR risk factors other than for inflation risk will apply to such an instrument notwithstanding.
iii. Inflation rate risk is considered in addition to the sensitivity to interest rates from the same instrument, which must be allocated, according to the GIRR framework, in the term structure of the relevant risk-free yield curve in the same currency.
(c) The GIRR delta risk factors also include one of two possible cross-currency basis risk factors for each currency (ie, each GIRR bucket) with term structure not recognised as a risk factor (ie, both cross-currency basis curves are flat).
i. The two cross-currency basis risk factors are basis of each currency over US$ or basis of each currency over €. For instance, an A$-denominated bank trading a ¥/US$ cross-currency basis swap would have a sensitivity to the ¥/US$ basis but not to the ¥/€ basis.
ii. Cross-currency bases that do not relate to either basis over US$ or basis over € must be computed either on “basis over US$” or “basis over €” but not both. GIRR risk factors other than for cross-currency basis risk will apply to such an instrument notwithstanding.
iii. Cross-currency basis risk is considered in addition to the sensitivity to interest rates from the same instrument, which must be allocated, according to the GIRR framework, in the term structure of the relevant risk-free yield curve in the same currency.
(d) Vega GIRR: Within each currency, the GIRR vega risk factors are the implied volatilities of options that reference GIRR-sensitive
underlyings; further defined along two dimensions:
i. Maturity of the option: The implied volatility of the option as mapped to one or several of the following maturity vertices: 0.5 years, one year, three years, five years, 10 years.
ii. Residual maturity of the underlying of the option at the expiry date of the option: The implied volatility of the option as mapped to two (or one) of the following residual maturity vertices: 0.5 years, one year, three years, five years,10 years.
(e) Curvature GIRR: The GIRR curvature risk factors are defined along only one dimension: the constructed risk-free yield curve (ie, no term structure decomposition) per currency: For example,the Euro, Eonia, Euribor 3M and Euribor 6M curves must be shifted at the same time in order to compute the Euro-relevant
risk-free yield curve curvature risk charge. All vertices (as defined for delta GIRR) are to be shifted in parallel. There is no curvature risk charge for inflation and cross-currency basis risks.
(f) The treatment described in paragraph 59(a)(ii) for delta GIRR also applies to vega GIRR and curvature GIRR risk factors.60. Credit spread risk (CSR) non-securitisation risk factors:
(a) Delta CSR non-securitisation: The CSR non-securitisation delta risk factors are defined along two dimensions: the relevant
issuer credit spread curves (bond and CDS) and the following vertices: 0.5 years, one year, three years, five years, 10 years to
which delta risk factors are assigned.
(b) Vega CSR non-securitisation: The vega risk factors are the implied volatilities of options that reference the relevant credit
issuer names as underlyings (bond and CDS); further defined along one dimension:
i. Maturity of the option: The implied volatility of the option as mapped to one or several of the following maturity vertices: 0.5 years, one year, thee years, five years, 10 years
(c) Curvature CSR non-securitisation: The CSR non-securitisation curvature risk factors are defined along one dimension: the relevant
issuer credit spread curves (bond and CDS). For instance, the bond-inferred spread curve of Électricité de France and the CDS-inferred spread curve of Électricité de France should be considered a single spread curve. All vertices (as defined for CSR) are to be shifted in parallel.
Authors’ comment: The BCBS response is self-explanatory.
Relevant provisions: Paragraphs 59 and 64 of the January 2016 market risk framework.
BCBS response: Repo rate risk factors for fixed income funding instruments are subject to the GIRR capital charge. A relevant repo curve should be considered by currency.
Referenced FRTB text:
59. See 1.4, Q7 on page 27 above
Authors’ comment: BCBS’s response here is a bit enigmatic, but we provide our interpretation below.
First is the question of what repos will fall into the banking book and what repos will fall into the trading book. BCBS clarifies in the
March 2018 CP that repo-style transactions that are entered into for liquidity management purposes and that are valued using the accrual method for accounting purposes need not be held in the trading book, but rather can be held in the banking book.9 Later in the FAQ (Section 3.1, Q7), BCBS narrows the interpretation further by specifying that trading related repos must have as their purpose market-making, locking in arbitrage profits, or creating short credit or equity positions.
Having determined what repos paragraphs 59–60 apply to (ie,not banking book repos), we can then say that for the remaining repos in the trading book backed by fixed income instruments, only the GIRR charge related to a relevant repo curve is applicable. We do not interpret this to mean that trading book repos backed by fixed instrument collateral should be subject to equity treatment.
Relevant provisions: Paragraph 72 of the January 2016 market risk framework.
BCBS response: To compute vega GIRR, banks may choose a mix of lognormal and normal assumptions for different currencies.
Referenced FRTB text:
72. When computing a vega GIRR or CSR sensitivity, banks may use either the lognormal or normal assumptions. When computing a vega equity, commodity or FX sensitivity, banks must use the lognormal assumption.10
(a) If, for internal risk management, a bank computes sensitivities using definitions differing from the definitions provided in the present standards, this bank may use linear transformations to deduce from the sensitivities it computes the one to be used for the vega risk measure, knowing that the difference between these transformations and the exact price movements shall be captured through the curvature risk measure.
(b) All sensitivities must be computed ignoring the impact of credit valuation adjustments (CVA).
Authors’ comment: In this answer, BCBS confirms that banks may compute their vega GIRR differently in different currencies. Either lognormal or normal assumptions may be used, so long as these assumptions are consistently applied against all currency positions.