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sbm

Calculate sensitivity-based method (SBM) charge results for each portfolio

Since R2024b

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Syntax

SBMResults = sbm(frtbsaObject)

Description

SBMResults = sbm(frtbsaObject) computes the sensitivity-based method (SBM) charge results for each portfolio using the frtbsa object. For more information, see Sensitivity-Based Method.

example

Examples

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Open Live Script

Use a frtbsa object and the sbm function to calculate the sensitivity-based method (SBM) charge results for each portfolio. FRTB-SA (Standardized Approach for Fundamental Review of Trading Book) is a Basel Committee on Banking Supervision framework for calculating market capital risk requirements that is based on a set of standardized risk factors.

Create frtbsa object

Use bank format for numeric data to use two decimal places.

format bank

Define the ISDA® FRTB-SA CRIF file.

FRTBSACRIF = "FRTBSA_CRIF.csv";

Define the DRC reference date.

DrcRefCOBDate = datetime(2023,9,21);

Use frtbsa to create the FRTB-SA object.

myFRTBSA = frtbsa(FRTBSACRIF,DRCValuationDate=DrcRefCOBDate)
myFRTBSA = 
  frtbsa with properties:

                CRIF: [159x18 table]
       NumPortfolios: 2.00
        PortfolioIDs: [2x1 string]
          Portfolios: [2x1 frtbsa.Portfolio]
          Regulation: "Basel_d491"
    DomesticCurrency: "USD"
    DRCValuationDate: 21-Sep-2023
         NumDaysYear: 365.00

Examine Output

Display the contents of the ISDA FRTB-SA CRIF file.

myFRTBSA.CRIF
ans=159×18 table
    PortfolioID    TradeID       Variant       SensitivityID      RiskType      Qualifier     Bucket     Label1        Label2        Amount      AmountCurrency    AmountUSD    Label3    EndDate    CreditQuality    LongShortInd    CoveredBondInd    TrancheThickness
    ___________    ________    ____________    _____________    ____________    __________    ______    _________    ___________    _________    ______________    _________    ______    _______    _____________    ____________    ______________    ________________

       "P1"        "EQD_a1"    <missing>        "P1_EQD_a1"     "EQ_DELTA"      "ISSUER A"     "1"      <missing>    "SPOT"           8250.00        "USD"           8250.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQD_a2"    <missing>        "P1_EQD_a2"     "EQ_DELTA"      "ISSUER A"     "1"      <missing>    "REPO"           8333.33        "USD"           8333.33     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQD_b1"    <missing>        "P1_EQD_b1"     "EQ_DELTA"      "ISSUER B"     "2"      <missing>    "SPOT"          22000.00        "USD"          22000.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQV_a1"    "Variant 1"      "P1_EQV_a1"     "EQ_VEGA"       "ISSUER A"     "1"      "0.5"        <missing>         -50.00        "USD"            -50.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQV_a2"    "Variant 1"      "P1_EQV_a2"     "EQ_VEGA"       "ISSUER A"     "1"      "1"          <missing>         200.00        "USD"            200.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQV_b1"    "Variant 1"      "P1_EQV_b1"     "EQ_VEGA"       "ISSUER B"     "2"      "0.5"        <missing>        -166.67        "USD"           -166.67     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQC_a1"    "Variant 1a"     "P1_EQC_a1"     "EQ_CURV"       "ISSUER A"     "1"      "0.5"        <missing>      -18910.00        "USD"         -18910.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQC_a1"    "Variant 1a"     "P1_EQC_a1"     "EQ_CURV"       "ISSUER A"     "1"      "-0.5"       <missing>        6526.25        "USD"           6526.25     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQC_b1"    "Variant 1a"     "P1_EQC_b1"     "EQ_CURV"       "ISSUER B"     "2"      "0.5"        <missing>       -6288.00        "USD"          -6288.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "EQC_b1"    "Variant 1a"     "P1_EQC_b1"     "EQ_CURV"       "ISSUER B"     "2"      "-0.5"       <missing>        6120.00        "USD"           6120.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMD_a1"    <missing>        "P1_CMD_a1"     "COMM_DELTA"    "COAL"         "1"      "0"          "NEWCASTLE"      2000.00        "USD"           2000.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMD_a2"    <missing>        "P1_CMD_a2"     "COMM_DELTA"    "COAL"         "1"      "0"          "LONDON"         -500.00        "USD"           -500.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMD_b1"    <missing>        "P1_CMD_b1"     "COMM_DELTA"    "BRENT"        "2"      "0"          "LE HAVRE"        666.67        "USD"            666.67     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMD_c1"    <missing>        "P1_CMD_c1"     "COMM_DELTA"    "WTI"          "2"      "2"          "OKLAHOMA"       -875.00        "USD"           -875.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMV_a1"    "Variant 1"      "P1_CMV_a1"     "COMM_VEGA"     "COAL"         "1"      "0.5"        <missing>         333.33        "USD"            333.33     NaN        NaT        <missing>       <missing>        <missing>             NaN       
       "P1"        "CMV_a2"    "Variant 1"      "P1_CMV_a2"     "COMM_VEGA"     "COAL"         "1"      "1"          <missing>        -100.00        "USD"           -100.00     NaN        NaT        <missing>       <missing>        <missing>             NaN       
      ⋮

Display the number of portfolios and their IDs.

myFRTBSA.NumPortfolios
ans = 
          2.00


myFRTBSA.PortfolioIDs
ans = 2x1 string
    "P1"
    "P2"

Display the properties of the first Portfolio object.

myFRTBSA.Portfolios(1)
ans = 
  Portfolio with properties:

    PortfolioID: "P1"
         Trades: [69x1 frtbsa.Trade]
      RiskTypes: [69x1 string]

Display the risk types of the portfolio.

myFRTBSA.Portfolios(1).RiskTypes
ans = 69x1 string
    "EQ_DELTA"
    "EQ_DELTA"
    "EQ_DELTA"
    "EQ_VEGA"
    "EQ_VEGA"
    "EQ_VEGA"
    "EQ_CURV"
    "EQ_CURV"
    "COMM_DELTA"
    "COMM_DELTA"
    "COMM_DELTA"
    "COMM_DELTA"
    "COMM_VEGA"
    "COMM_VEGA"
    "COMM_VEGA"
    "COMM_VEGA"
    "COMM_CURV"
    "COMM_CURV"
    "COMM_CURV"
    "GIRR_DELTA"
    "GIRR_DELTA"
    "GIRR_DELTA"
    "GIRR_VEGA"
    "GIRR_VEGA"
    "GIRR_VEGA"
    "GIRR_CURV"
    "GIRR_CURV"
    "FX_DELTA"
    "FX_DELTA"
    "FX_VEGA"
      ⋮

Display some of the trades of the portfolio.

myFRTBSA.Portfolios(1).Trades(1)
ans = 
  Trade with properties:

             TradeID: "EQD_a1"
             Variant: <missing>
       SensitivityID: "P1_EQD_a1"
            RiskType: "EQ_DELTA"
           Qualifier: "ISSUER A"
              Bucket: "1"
              Label1: <missing>
              Label2: "SPOT"
              Amount: 8250.00
      AmountCurrency: "USD"
           AmountUSD: 8250.00
              Label3: NaN
             EndDate: NaT
       CreditQuality: <missing>
        LongShortInd: <missing>
      CoveredBondInd: <missing>
    TrancheThickness: NaN


myFRTBSA.Portfolios(1).Trades(30)
ans = 
  Trade with properties:

             TradeID: "FXV_b1"
             Variant: "Variant 1"
       SensitivityID: "P1_FXV_b1"
            RiskType: "FX_VEGA"
           Qualifier: "EURCLP"
              Bucket: <missing>
              Label1: "0.5"
              Label2: <missing>
              Amount: 175.00
      AmountCurrency: "USD"
           AmountUSD: 175.00
              Label3: NaN
             EndDate: NaT
       CreditQuality: <missing>
        LongShortInd: <missing>
      CoveredBondInd: <missing>
    TrancheThickness: NaN


myFRTBSA.Portfolios(1).Trades(60)
ans = 
  Trade with properties:

             TradeID: "RRAO_a2"
             Variant: <missing>
       SensitivityID: "P1_RRAO_a2"
            RiskType: "RRAO_01_PERCENT"
           Qualifier: <missing>
              Bucket: <missing>
              Label1: <missing>
              Label2: <missing>
              Amount: 300000.00
      AmountCurrency: "USD"
           AmountUSD: 300000.00
              Label3: NaN
             EndDate: NaT
       CreditQuality: <missing>
        LongShortInd: <missing>
      CoveredBondInd: <missing>
    TrancheThickness: NaN

Compute SBM Charge

Under the SBM, banks calculate capital charges based on the sensitivities of their trading book positions to various risk factors. Use sbm to compute the SBM charge results for each portfolio using the frtbsa object.

SBMResults = sbm(myFRTBSA)
SBMResults = 
  sbmResults with properties:

       NumPortfolios: 2.00
        PortfolioIDs: [2x1 string]
          Regulation: "Basel_d491"
    DomesticCurrency: "USD"
             Charges: [2x1 double]
    ComponentResults: [2x1 frtbsa.sbmPortfolioResults]
        ResultsTable: [2x10 table]

The Charges output contains the SBM risk charge of the portfolios.

SBMResults.Charges
ans = 2×1

     124519.56
     122514.96

The ResultsTable output contains the high-level risk SBM charge calculations of the portfolio.

SBMResults.ResultsTable
ans=2×10 table
    PortfolioID    Correlation      Total        GIRR      CSR_NS     CSR_SC     CSR_SNC        FX          EQ        COMM  
    ___________    ___________    _________    ________    ______    ________    ________    ________    ________    _______

       "P1"           "Low"       124519.56    10183.45    815.24    40425.33    20169.47    21532.62    23991.46    7401.98
       "P2"           "Low"       122514.96     9941.02    503.07    40425.33    20169.47    21532.62    23954.45    5988.99

The ComponentResults output contains detailed SBM risk charge information for a given portfolio. Examine the SBM risk charge for the first portfolio.

SBMResults.ComponentResults(1)
ans = 
  sbmPortfolioResults with properties:

            PortfolioID: "P1"
                 Charge: 124519.56
    ChargeByCorrelation: [1x1 struct]
      ChargeByRiskClass: [21x5 table]
     IntrabucketCharges: [1x1 struct]

Display the charges by risk class.

SBMResults.ComponentResults(1).ChargeByRiskClass
ans=21×5 table
    RiskClass    RiskMeasure    LowCorrelation    MediumCorrelation    HighCorrelation
    _________    ___________    ______________    _________________    _______________

    "GIRR"       "Delta"             342.95             334.39              338.69    
    "GIRR"       "Vega"              516.67             514.22              515.45    
    "GIRR"       "Curvature"        9323.83            9323.83             9323.83    
    "CSR_NS"     "Delta"             265.17             262.20              263.68    
    "CSR_NS"     "Vega"              130.96             129.28              130.12    
    "CSR_NS"     "Curvature"         419.11             418.46              418.79    
    "CSR_SC"     "Delta"             590.07             575.70              582.93    
    "CSR_SC"     "Vega"              198.82             195.75              197.29    
    "CSR_SC"     "Curvature"       39636.44           39634.87            39635.66    
    "CSR_SNC"    "Delta"             456.21             455.99              456.10    
    "CSR_SNC"    "Vega"              506.86             489.20              498.11    
    "CSR_SNC"    "Curvature"       19206.41           19206.41            19206.41    
    "FX"         "Delta"               8.84               8.84                8.84    
    "FX"         "Vega"              150.00             150.00              150.00    
    "FX"         "Curvature"       21373.78           21373.78            21373.78    
    "EQ"         "Delta"           14762.60           14451.94            14608.10    
      ⋮

Display the low correlation scenario charges.

SBMResults.ComponentResults(1).ChargeByCorrelation.Low
ans=8×4 table
                Delta       Vega      Curvature     Charge  
               ________    _______    _________    _________

    GIRR         342.95     516.67      9323.83     10183.45
    CSR_NS       265.17     130.96       419.11       815.24
    CSR_SC       590.07     198.82     39636.44     40425.33
    CSR_SNC      456.21     506.86     19206.41     20169.47
    FX             8.84     150.00     21373.78     21532.62
    EQ         14762.60     157.31      9071.55     23991.46
    COMM         437.51     234.97      6729.51      7401.98
    Total      16863.33    1895.59    105760.63    124519.56

Display the intrabucket charges for this portfolio for the equity class and the delta risk sensitivity.

SBMResults.ComponentResults(1).IntrabucketCharges.EQ.Delta
ans=2×5 table
    Bucket       Sb       LowCorrelation    MediumCorrelation    HighCorrelation
    ______    ________    ______________    _________________    _______________

     1.00      4583.33        4583.24            4583.29             4583.33    
     2.00     13200.00       13200.00           13200.00            13200.00

Display the intrabucket charges for this portfolio for the GIRR class and the vega risk sensitivity.

SBMResults.ComponentResults(1).IntrabucketCharges.GIRR.Vega
ans=1×5 table
    Bucket      Sb      LowCorrelation    MediumCorrelation    HighCorrelation
    ______    ______    ______________    _________________    _______________

    "USD"     516.67        514.22             515.45              516.67

Input Arguments

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FRTB-SA object, specified as a frtbsa object. You create a frtbsa object using frtbsa.

Data Types: object

Output Arguments

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Sensitivity based market risk capital charge results, returned as a SBMResults object. The SBMResults object has the following properties:

  • NumPortfolios — Number of portfolios whose residual risk add-on capital charges are contained in the RRAOResults object.

  • PortfolioIDs — NumPortfolios-by-1 array of strings containing the portfolio IDs of each portfolio.

  • DomesticCurrency — Domestic currency. The default is "USD".

  • Regulation — Jurisdiction. The default is "Basel".

  • Charges — NumPortfolios-by-1 array of residual risk add-on capital charges.

  • ComponentResults — NumPortfolios-by-1 array of frtbsa.sbmPortfolioResults objects containing the calculation results for each portfolio. The frtbsa.sbmPortfolioResults object properties are:

    • PortfolioIDs — Scalar string indicating the ID of the portfolio.

    • ChargeByCorrelation — Struct for SBM risk capital charge calculation by correlation.

    • ChargeByRiskClass — Table displaying the SBM risk capital charge calculation by risk class.

    • IntracucketCharges — Table displaying the SBM risk capital charge calculation intrabucket calculations.

  • ResultsTable — Table displaying the high-level SBM calculation results for all portfolios.

More About

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Sensitivity-Based Method

Under the sensitivity-based method (SBM), banks calculate capital charges based on the sensitivities of their trading book positions to various risk factors.

These risk factors are determined by regulatory guidelines and include interest rate risk, credit spread risk, equity risk, foreign exchange risk, commodity risk, and others.

The SBM workflow involves the following steps:

  1. Identification of Risk Factors — Banks must identify the risk factors that affect the pricing of their trading book instruments. Risk factors are categorized into different risk classes (for example, interest rate risk, credit spread risk, equity risk, commodity risk, and FX risk) and further divided into liquidity horizons and buckets as defined by the FRTB-SA regulation.

  2. Sensitivities Calculation — Banks determine the sensitivities of their trading book positions to the prescribed risk factors. Sensitivities measure how the value of a position is expected to change in response to changes in the underlying risk factors.

  3. Aggregation of Sensitivities — Aggregate the following sensitivities:

    • Delta risk — Aggregate delta sensitivities within each risk class to calculate the delta risk charge.

    • Vega risk — Compute the vega risk charge for options and other positions sensitive to volatility changes.

    • Curvature risk — Calculate the curvature risk charge, which captures the nonlinear risk of options and instruments with option-like characteristics.

  4. Risk Weight Application — Each sensitivity is then multiplied by a corresponding risk weight, which is prescribed by the regulator. Risk weights are designed to reflect the risk associated with changes in the respective risk factors.

  5. Correlation Effects — The standardized approach also accounts for correlations between risk factors within the same risk factor category. The prescribed correlations are used to calculate the aggregated risk within each risk factor category.

  6. Capital Charge Aggregation — The risk-weighted sensitivities within each risk factor category are aggregated, taking into account the prescribed correlations, to determine the capital charge for each risk factor category.

  7. Overall Capital Requirement — The capital charges for all risk factor categories are then added together to determine the overall capital requirement for the trading book under the sensitivity-based method.

    SBM aggregation across asset classes and correlation scenarios

    The correlation calculations are done for each risk sensitivity (delta, vega, and curvature) and for three correlation scenarios. The three correlation scenarios take into consideration market stress times. FRTB-SA requires that the sensitivity-based charge of the portfolio is computed for these three correlation scenarios: high correlation, medium/base correlation, and low correlation. The medium/base scenario corresponds to the basic values of the correlation parameters. The low scenario consists of multiplying the correlation coefficients by 0.75 and the high scenario consists of multiplying these correlation coefficients by 1.25. These scenarios take into consideration market stress times. The total portfolio sensitivity-based capital risk charge is the largest of these three correlation scenarios.

Sensitvity-Based Method Components

Sensitvity-based method (SBM) components calculate capital requirements based on the sensitivities of the trading book positions to various risk factors.

SBM components

In this framework, the following terminology applies:

  • Risk Factor Classes — SBM categorizes risk factors into several classes, such as interest rate risk, credit spread risk, equity risk, commodity risk, and foreign exchange risk. Each class has its own risk-weighting scheme.

  • Sensitivities — Banks must calculate the sensitivities of their trading book positions to the various risk factors. Sensitivities measure how the value of a position changes in response to changes in an underlying risk factor.

  • Risk Factor — Each sensitivity is then multiplied by a corresponding risk weight, which is prescribed by the regulation based on the liquidity and riskiness of the risk factor. The SBM accounts for correlations between risk factors within a risk class using a prescribed correlation matrix. This correlation allows for some diversification benefit within a risk class.

  • Bucket — A bucket is a categorization of positions for market risk capital calculation. It is a set of instruments of the same risk class that are grouped together by similar characteristics. For each class, there is a bucket definition. For example, for the GIRR class, each bucket refers to a currency type. For the Equity Risk class, each bucket is classified in terms of market, economy, and sector type.

References

[1] Bank for International Settlements. "MAR21 — Standardised Approach: Sensitivities-Based Method." March 2020. https://www.bis.org/basel_framework/chapter/MAR/21.htm.

[2] Bank for International Settlements. "MAR22 — Standardised Approach: Default Risk Capital Requirement." March 2020. https://www.bis.org/basel_framework/chapter/MAR/22.htm.

[3] Bank for International Settlements. "MAR23 — Standardised Approach: Residual Risk Add-On." March 2020. https://www.bis.org/basel_framework/chapter/MAR/23.htm.

[4] Bank for International Settlements. "CRE42 — Securitisation: External-Ratings-Based Approach (SEC-ERBA)." January 2023. https://www.bis.org/basel_framework/chapter/CRE/42.htm.

[5] Bank for International Settlements. "Basel Committee on Banking Supervision: Minimum Capital Requirements for Market Risk"." January 2019. https://www.bis.org/bcbs/publ/d457.pdf.

Version History

Introduced in R2024b

See Also

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