IRRBB - Interest rate in the banking book

Used in the following modules

• IRRBB

Legal references

• Finma circ. 2019/02
• Finma circ. 2016/01 annexe 2
  • Calculation of EVE and NII
• Basel Framework SRP31

Description

Interest rate curves

Steps (SPR31.95)

1. ZIR Categories

• core_positions_calc.ZIRCategoryused in v_IRRBB_U/v_IRRBB_K.
• Categories:
  • I: Positions with determined repricing maturities
  • II: Positions with undetermined repricing maturities
  • III: Positions with no repricing maturities
  • IV: Own funds
  • V: Non-linear derivatives

2. Repricing cash flow generation

• Definition (EBA, 2021): Notional repricing cash flows refers to interest payments or principal amounts of fixed rate instruments that mature or principal amounts of floating rate instruments that reprice
• Each repricing cash flow is generated in the views v_IRRBB_U/v_IRRBB_K which can be of 3 different types (v_IRRBB_U.RCFType):
  • InterestPayment
  • PrincipalPayment
  • PrincipalRepricing
    • PrincipalReplicationKey → generated with replication key
    • PrincipalReplicationKeyDefault → generated with default replication key
• The scope of positions for which repricing cash flow have to be considered, which will in turn enter the views v_IRRBB_U/v_IRRBB_K are those which carry a floating or fixed interest rate, i.e. those were core_posiitons.IRTypeOf in ('Fixed','Floating').
• Remarks:
  • Simplification: in this version, among derivatives, only the interest rate swaps (IRS) are taken into account.
  • A zero coupon bond should still be delivered with an IRTypeOf, even if the the IR payment is 0%.

2.1 Slotting

• Scope: RCFType in ('PrincipalPayment','PrincipalRepricing')
• The slotting is the division of a position into the repricing cash flows PrincipalPayment or PrincipalRepricing, and the assignement of their repricing slots/bucket.
• Simplification: In this first version amortizations are ignored.

2.1.1 Slotting of fixed rate positions

• Scope: core_positions.IRTypeOf = 'Fixed'
• Whole principal (core_positions.BookAmount) assigned to the maturity of the position (core_positions.MaturityDate) → RCFType = 'PrincipalPayment'.

2.1.2 Slotting of floating rate position with IR fixing date

• Scope: core_positions.IRTypeOf = 'Floating' and core_positions.IRNextFixingDate > core_load_collections.ReportingDate
• Whole principal (core_positions.BookAmount) assigned to the next IR fixing date (core_positions.IRNextFixingDate) → RCFType = PrincipalRepricing.

2.1.3 Slotting of floating rate position without IR fixing date

• Scope: core_positions.IRTypeOf = 'Floating' and core_positions.IRNextFixingDate < core_load_collections.ReportingDate
• The scope corresponds to the ZIR category 2 (v_IRRBB_U/K.ZIRCategory = 2) → typically includes banks and clients checking account.
  • See SPR31.103.
• This distribution is done with replication keys which generate principal repricing and their corresponding repricing date.
• Category 2 subcategories and their replication keys → repricing date = time bucket midpoint:
  • Due from banks
    • 100% → 0 - 1 M
  • Due from customers (on sight)
    • 70% → 0 - 1 M
    • 30% → 9 - 12 M
  • Due from customers (on call and cancellable)
    • 25% → 9 - 12 M
    • 50% → 18 - 24 M
    • 25% → 2 - 3 Y
  • Floating rate mortgage loans
    • 25% → 9 - 12 M
    • 50% → 18 - 24 M
    • 25% → 4 - 5 Y
  • Other exposures
    • 100% → 0 - 1 M
  • Current accounts
    • 100% → 0 - 1 M
  • Due to banks
    • 100% → 0 - 1 M
  • Due to customers
    • 70% → 0 - 1 M
    • 30% → 9 - 12 M
  • Other liabilities
    • 100% → 0 - 1 M
  • Default replication key (if the position does not fit in any of the categories above):
    • 100% → 0 - 1 M
• Replication keys can be parametrized by the bank if necessary in the config file irrbbReplicationKeys.csv

2.1.4 Slotting of derivatives

• As interest rate derivatives need information from various tables, the most important ones are gathered in the view v_derivatives_ir (vds). For simplicity purpose, references will be made to fields of this view when it comes to derivatives in the IRBB.
  • v_derivatives_ir distinguishes the information related to the receivable and payable legs by prefixing the fields of the view with R or P.
• Scope: vds.TypeOf in ('IRS','CCS')
• Interest rate swaps (IRS) and cross currency swaps (CCS) which pays two stream of cash flows are treated as two positions, one long, one short.
• Each leg can either pay a fixed rate or a floating rate, although the common type of IRS is fix vs floating.
• The fixed leg of an IRS/CCS is treated as a fixed rate position (see section 2.1.1): the whole notional (vds.R/PNotional) is assigned to the maturity of the position (vds.MaturityDate) → RCFType = 'PrincipalPayment'.
• The floating leg of an IRS is treated as a floating rate position with IR fixing date (see section 2.1.2): the whole notional (core_positions.Notional) is assigned to the next IR fixing date (vds.P/RNextFixingDate) → RCFType = PrincipalRepricing.

3. Repricing cash flow: interest payment (RCFType = 'InterestPayment')

• The following fields of core_positions are relevant for the calculation of the interest payments of on-balance sheet positions:
  • IRPaymentFrequency
  • IRNextPaymentDate
  • MaturityDate
  • IRNextFixingDate

3.1 Interest payment of derivatives

• As for slotting interest payments are treated separately for each leg of the derivatives.

Case 1: IRPaymentFrequency and IRNextPaymentDate provided

• In a perfect world the algorithm to generate the IR payment is the following:
  1. The next IR payment is generated at the next IR payment date (core_positions.IRNextPaymentDate or vds.R/PNextPaymentDate).
  2. The following IR payment are generated by adding the IR payment period (based on the IR payment frequency (core_positions.IRPaymentFrequency or vds.R/PPaymentFrequency)) to the next IR payment date as long as 1) the maturity date is not exceeded for fixed interest rate instruments (core_posiitons.IRTypeOf = 'Fixed' or vds.R/PIRType = 'Fixed') or 2) the IR next fixing date for floating interest rate instruments is not exceeded (core_posiitons.IRTypeOf = 'Floating' or vds.R/PIRType = 'Floating').
  • Remark: It is assumed that for floating interest rate instruments, the interest rate risk is limited to the next cash flows until refixing. Consequently, only the IR payments until that date are considered in this case (SPR31.103).
  3. If the last IR payment does not fall on the maturity date, a last interest payment is computed on the maturity date, based on the duration between the penultimate IR payment and maturity date of the contract.
  • Remark: For floating interest rates, no IR is computed on the IR next fixing date. This would be equivalent to computing an accrual interest rate, which is irrelevant in this context.
• With contradictory information: In a less perfect world where the IRPaymentFrequency and IRNextPaymentDate are in contradiction, the IRPaymentFrequency prevails. For instance if the interest payment frequency is 1 month, and the next interest payment is in 2 month. In this case, IR payments are generated backward from the IRNextPaymentDate:
  1. IR payments between the IRNextPaymentDate and the reporting date are generated by substracting the IR period (based on the IR payment frequency) from the IRNextPaymentDate, as long as the reporting date is not exceeded.
  2. For what happens after the IR next payment date provided in input and the maturity date or the IR next fixing date, follow the algorithm of case 1.

Case 2: IRPaymentFrequency provided, but not IRNextPaymentDate

• IR payments are generated backwards from the maturity date for fixed interest rate instruments (core_posiitons.IRTypeOf = 'Fixed' or vds.R/PIRType = 'Fixed')or the IR next fixing date for floating interest rate instruments (core_posiitons.IRTypeOf = 'Floating' or vds.R/PIRType = 'Floating'):
  1. Set the last IR payment at maturity or IR next fixing date.
  2. IR payments generated backward until the reporting date.

Case 3: IRPaymentFrequency not provided, but IRNextPaymentDate is

• We set a default IR payment frequency at 1 year which leads to the following algorithm:
  1. First cash flow takes place at the IR next payment date provided.
  2. The subsequent IR payment takes place every year after the IR next payment date until the maturity date or IR next fixing date.

Case 4: IRPaymentFrequency and IRNextPaymentDate not provided

• We set a default IR payment frequency at 1 year and generate IR payments backwards from the maturity date or IR next fixing date.

Remarks

• Positions delivered with a negative BookAmount will be treated as follow:
  • Category 1: only the notional is considered, and the cash flow treated as PrincipalPayment or PrincipalRepricing depending if the interest rate carried by the position is fixed or floating, respectively. Interest payments are not generated.
  • Category 2: the slotting is performed as regular category 2 positions using replication keys.
• Param for currencies to report

Parameters

• IRRBB_K_LIST_CURRENCIES & IRRBB_U_LIST_CURRENCIES
  • Legal ref. Finma Notes Le formulaire d’enquête comprend une liste énumérant 22 monnaies, y compris la position collective «Autres monnaies». Si la part des actifs u des passifs de l’une de ces monnaies représente 10% ou plus de la somme du bilan, un formulaire ZIR1 doit être rempli pour chacune de ces monnaies
• IRRBB_TB
  • Set to 1 to include trading book positions.

Risk Indicators

Net interest income (NII)

• The net interest income is a financial performance measure that reflects the difference between the revenue generated from a bank's interest-bearing assets and the expenses associated with paying on its interest-bearing liabilities (source)
• The $\Delta$NII (change in NII) is measured by assessing the impact of interest rate shocks over a one year period, with a constant balance sheet view. For this reason, only the positions with a repricing date within one year are considered: those are the ones that would be impacted by changes in interest rates, if rolled over.
• The calculation implies computing the net shock (impact on assets - liabilities) from the repricing date of the RCF until the one year after the reporting date (since it is assumed positions are rolled over because of the constant balance sheet).

Base scenario

• The base scenario intends to reflect the net interest income generated by the maturing position if reinvested, from its maturity until a one year horizon, with no shock applied.
• The reinvestment rate of a position is estimated using the forward rate applicable between its maturity and its rolled-over maturity plus the spread carried by the position.
• Spread: if not delivered, it is estimated as the difference between the interest rate carried by the position and the interest rate applicable for the original maturity of the position using today's interest rate curve:
  • core_positions.InterestRate - $r_\text{original duration}$
• Forward rate:
  • The forward rate $r_{12}$ between the maturity of the position $T_1$ and it's rolled-over maturity $T_2$ is today's best approximation of what will be the interest rate applicable at $T_1$ when rolling over the position for an equivalent duration.
  • Reminder → the followings are equivalent (where T is expressed as a number of years, and r as an annual interest rate):
    • Discrete compounding: $(1 + r)^T$
    • Continuous compounding: $e^{r T}$
  • Calculation:
    $$\begin{align} e^{r_2 T_2} = e^{r_1 T_1} * e^{r_{12} (T_2 - T_1)} \\ e^{r_{12} (T_2 - T_1)} = \frac{e^{r_2 T_2}}{e^{r_1 T_1}} \\ e^{r_{12} (T_2 - T_1)} = e^{r_2 T_2 - r_1 T_1} \\ r_{12} (T_2 - T_1) = r_2 T_2 - r_1 T_1 \\ r_{12} = \frac{r_2 T_2 - r_1 T_1}{T2 - T_1} \\ \end{align}$$

$$\begin{align} (1+r_2)^{T_2} = (1+r_1)^{T_1}*(1+r_{12})^(T_2 - T_1) \\ (1+r_{12})^(T_2 - T_1) = \frac{(1+r_2)^{T_2}}{(1+r_1)^{T_1}}\\ (1+r_{12}) = \sqrt[(T_2 - T_1)]{\frac{(1+r_2)^{T_2}}{(1+r_1)^{T_1}}} \\ r_{12} = \sqrt[(T_2 - T_1)]{\frac{(1+r_2)^{T_2}}{(1+r_1)^{T_1}}} -1 \\ \end{align}$$

• where:
  • $T_1$ = time to maturity in years of the position ($T_1$)
  • $r_1$ = rate implied by the interest rate curve until the maturity of the position
  • $T_2$ = time to maturity in years of the rolled over position, i.e. $T_1 + \text{original duration}$
    • Note that if $T_1 + \text{original duration} < \text{1 year}$, then $T_2 = T_1 + 1$
      • This treatment which sets the minimal original duration at one year approximates the rollover of the transaction as many times as necessary to exceed the one year horizon.
  • $r_2$ = rate implied by the interest rate curve until the maturity of the rolled over position ($T_2$)
  • $r_{12}$ = forward rate between the maturity of the position ($T_1$) and its rolled over maturity ($T_2$)
• NII:
  • It is made of the expected net interest income perceived during a one year horizon, both effective and accrued. It is therefore composed of (1) the paid interest of the position at expiration and (2) the accrued interest of the rolled over position between its maturity ($T_1$) and the end of the one year time horizon.
    • Reinvested amount = Notional + Interest paiement
    • Reinvestment rate:
      $$\begin{align} r = e^{(r_{12} + \text{spread})(1-T_1)}-1 \end{align}$$
    • NII
      $$\begin{align} NII_{\text{Base scenario}} = \text{Reinvested amount * Reinvestment rate + Interest paiement} \\ NII_{\text{Base scenario}} = \text{Reinvested amount} * (e^{(r_{12} + \text{spread})(1-T_1)}-1) + \text{Interest paiement} \end{align}$$

Scenarios 1 & 2

• The parallel shifts of the yield curve of the scenarios 1 and 2 impact the calculation of the forward rate calculation, by shifting $r_1$ and $r_2$ by the amount of the shock. Compared to the base scenario, the NII is impacted only by this change of forward rate, all other variable staying constant.

Complementary information for category 1 positions with floating rates

• The maturity date and corresponding time to maturity ($T_1$) are defined by the maturity of the repricing cash flow as defined above
• Original duration (which enters the calculation of $T_2$ = the time to maturity of the rolled over position):
  • Option 1: Set to one year by default.
  • Option 2:The original duration which enters the calculation of $T_2$ (the time to maturity of the rolled over position) is defined by the interest rate refixing frequency core_positions.IRReFixingFrequency.
    • Remark: the condition if $T_1 + \text{original duration} < \text{1 year}$, then $T_2 = T_1 + 1$ still applies.

Complementary information for category 2 positions

• The maturity date and corresponding time to maturity ($T_1$) are defined by the middle of the time bucket to which the repricing cash flow is assigned.
• Original duration:
  • Option 1: Set to one year by default.
  • Option 2: The original duration is defined by the interest rate refixing frequency core_positions.IRReFixingFrequency. It means that all the repricing cash flows generated by a given position and its replication keys (not matter the time bucket) will have the same original duration, which is equal to the interest rate refixing frequency.
    • Remark: the condition if $T_1 + \text{original duration} < \text{1 year}$, then $T_2 = T_1 + 1$ still applies.

Economic value of equity (EVE)

• The economic value of equity (EVE) is a cash flow calculation that takes the present value of all asset cash flows and subtracts the present value of all liability cash flows. (source)
• The $\Delta$EVE is computed as the impact of interest rate shocks on the EVE, through the discount factor.
• Reminder about present value: Present value (PV) is the current value of a future sum of money or stream of cash flows given a specified rate of return. Present value takes the future value and applies a discount rate or the interest rate that could be earned if invested. (source)
  • $\text{Present value of cash flow} = \frac{\text{Future value of cash flow}}{\text{Discount factor}} = \frac{\text{Future value of cash flow}}{(1 + i)^T}$, where:
    • $i$ = interest rate
    • $T$ = time in years
• Calculation:
  1. Compute the discount rate rate of the RCF before applying shocks. Interest rates for a given currency are provided for some tenors, and the RCF maturity will usually fall between this tenors. In order to compute the appropriate discount rate, the appropriate interest rate must be interpolated based on the interest rate of the previous and next tenor (linear interpolation to start with). With the interpolated (discount) interest rate, the discount factor and the present value of the position can be computed.
  • Fields
    • v_IRRBB_U/K.InterpolatedDiscountIR
    • v_IRRBB_U/K.DiscountFactor
    • v_IRRBB_U/K.DiscountedRCF
  2. Apply the shocks of the corresponding maturity bucket to the interpolated interest rates for each scenario to obtain successively the shocked interpolated discount rate, the shocked discount factor and shocked discounted RCF:
  • v_IRRBB_U/K.ShockedXInterpolatedDiscountIR
  • v_IRRBB_U/K.ShockedXDiscountFactor
  • v_IRRBB_U/K.ShockedXDiscountedRCF

ZIR2_B

• Pas prendre en compte payment d'intérêt
• Moyenne des RCFDuration days

Input fields

internal_indicator/scenarios

• The shock applied to the positions for the calculation of the EVE (l.22-25 ZIR2_A).
• One line per Finma scenarios possibility for the user to add their own scenarios.
• One column to flag the scenario that should be used for the internal indicator.

core_positions

• InterestRate
• IRTypeOf
• IRNextFixingDate
• IRRefixingFrequency
• IRNextPaymentDate
• IRPaymentFrequency

list_interest_rate_curves

• Category
• ReportingDate
• Currency
• Tenor
• InterestRate

param_IRRBB_shocks → is param_ the good prefix?

• Currency
• TimeBand

Output views/tables

v_IRRBB_U/K

• lcId
• Id
• rcfNum
• LegalAccountNumber
• Currency
• IRBBCurrency
  • Value can be 'U'
• AccountGroupLevel1
• PositionType
• PositionSubType
• SecurityType
• SecuritySubType
• CommodityType
• ReportingDate
• StartDate
• MaturityType
• IRType
• Subordination
• RCFType → Repricing cash flow type
  • legal ref.: SRP31.98
• MainRCFlag → Interest rate main cash flow flag
  • Legal ref.: Finma Notes Les actifs dont le volume nominal représente moins de 1% des opérations au bilan ainsi que les passifs et opérations hors-bilan dont le volume nominal représente moins de 1% de la somme des opérations au bilan et hors-bilan ne sont pas considérés comme principaux dans les cas où ils devraient être rapportés uniquement dans les échéances allant jusqu'à 12 mois
• RCF → repricing cash flow
• RCFDate → Repricing cash flow date
• RCFDurationDays
• ZIRCategory → 1 to 5
  • Rules for non-derivatives positions
• ZIRTimeBand
  • Legal ref.: Finma circ. 2019/02 Annexe 2
  • Value 1 to 19
• InterpolatedDiscountIR
• DiscountFactor
• DiscountedRCF
• Shocked1InterpolatedDiscountIR
• Shocked2InterpolatedDiscountIR
• Shocked3InterpolatedDiscountIR
• Shocked4InterpolatedDiscountIR
• Shocked5InterpolatedDiscountIR
• Shocked6InterpolatedDiscountIR
• Shocked1DiscountFactor
• Shocked2DiscountFactor
• Shocked3DiscountFactor
• Shocked4DiscountFactor
• Shocked5DiscountFactor
• Shocked6DiscountFactor
• Shocked1DiscountedRCF
• Shocked2DiscountedRCF
• Shocked3DiscountedRCF
• Shocked4DiscountedRCF
• Shocked5DiscountedRCF
• Shocked6DiscountedRCF
• DeltaNIIUpShock
• DeltaNIIDownShock
• DeltaNIIBaseShock