Compute Capital Risk Charge Using FRTB-SA Framework

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This example creates a frtbsa object and uses the ISDA® FRTB-SA framework to support the workflows for calculating capital market risk charge. 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. To calculate the total market risk charge, you need to use only the charge method. However, for the purpose of illustration, this example also demonstrates the frtbsa component methods (sbm, drc, rrao).

Create frtbsa Object

Use bank format to display numeric data using 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: [159×18 table]
       NumPortfolios: 2.00
        PortfolioIDs: [2×1 string]
          Portfolios: [2×1 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 = 2×1 string
    "P1"
    "P2"

Display the properties of the first Portfolio object.

myFRTBSA.Portfolios(1)

ans = 
  Portfolio with properties:

    PortfolioID: "P1"
         Trades: [69×1 frtbsa.Trade]
      RiskTypes: [69×1 string]

Display risk types of the portfolio.

myFRTBSA.Portfolios(1).RiskTypes

ans = 69×1 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 DRC Charge

The default risk capital (DRC) charge captures the risk of default of issuers of debt and equity instruments in the trading book. Use drc to compute the DRC charge for each portfolio using the previously created frtbsa object.

DRCResults = drc(myFRTBSA)

DRCResults = 
  drcResults with properties:

       NumPortfolios: 2.00
        PortfolioIDs: [2×1 string]
          Regulation: "Basel_d491"
    DomesticCurrency: "USD"
             Charges: [2×1 double]
    ComponentResults: [2×1 frtbsa.drcPortfolioResults]
        ResultsTable: [2×4 table]

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

DRCResults.Charges

The ResultsTable output contains the high-level risk DRC charge calculations of the portfolios.

DRCResults.ResultsTable

ans=2×4 table
    PortfolioIDs      Total         NS          SNC   
    ____________    _________    ________    _________

        "P1"        177008.51    20750.00    156258.51
        "P2"         51024.29    20750.00     30274.29

The ComponentResults output contains the detailed DRC risk charge information for a given portfolio.

Examine the DRC risk charge for the first portfolio.

DRCResults.ComponentResults(1)

ans = 
  drcPortfolioResults with properties:

            PortfolioID: "P1"
                 Charge: 177008.51
    ChargeByCreditClass: [2×2 table]
     IntrabucketCharges: [1×1 struct]

Display charges by credit class. Portfolio P1 has non-securitization and securitization non-correlation trading portfolio (non-CTP) trades.

DRCResults.ComponentResults(1).ChargeByCreditClass

ans=2×2 table
    CreditClass     Charge  
    ___________    _________

       "NS"         20750.00
       "SNC"       156258.51

Display the intrabucket charges for the non-securitization trades.

DRCResults.ComponentResults(1).IntrabucketCharges.NS

ans=2×4 table
       Bucket       NetLongJtd    NetShortJdt     Charge 
    ____________    __________    ___________    ________

    "CORPORATES"     12750.00        0.00        12750.00
    "SOVEREIGNS"      8000.00        0.00         8000.00

Display the intrabucket charges for the securitization non-CTP trades.

DRCResults.ComponentResults(1).IntrabucketCharges.SNC

ans=1×9 table
       Bucket       NonSeniorLongJtd    NonSeniorShortJtd    SeniorLongJtd    SeniorShortJtd    NetLongJtd    NetShortJtd    HBR      Charge  
    ____________    ________________    _________________    _____________    ______________    __________    ___________    ____    _________

    "CORPORATES"          0.00                0.00             746666.67        -300000.00      746666.67      300000.00     0.71    156258.51

Compute RRAO Capital Charge

The residual risk add-on (RRAO) charge covers risks that are not fully captured by the other components of the FRTB capital charges, particularly those arising from positions with exotic or nonlinear payoffs, as well as other risks that are deemed to be residual in nature. Use rrao to compute the RRAO charge results for each portfolio using the previously created frtbsa object.

RRAOResults = rrao(myFRTBSA)

RRAOResults = 
  rraoResults with properties:

       NumPortfolios: 2.00
        PortfolioIDs: [2×1 string]
          Regulation: "Basel_d491"
    DomesticCurrency: "USD"
             Charges: [2×1 double]
    ComponentResults: [2×1 frtbsa.rraoPortfolioResults]
        ResultsTable: [2×4 table]

The Charges output contains the RRAO risk charge of the portfolio.

RRAOResults.Charges

The ResultsTable output contains the high-level risk RRAO charge calculations of the portfolios.

RRAOResults.ResultsTable

ans=2×4 table
    PortfolioIDs     Total     Exotic      ORR  
    ____________    _______    _______    ______

        "P1"        3310.00    3000.00    310.00
        "P2"        2800.00    2500.00    300.00

The ComponentResults output contains detailed RRAO risk charge information for a given portfolio.

Examine the RRAO risk charge for the first portfolio.

RRAOResults.ComponentResults(1)

ans = 
  rraoPortfolioResults with properties:

               PortfolioID: "P1"
                    Charge: 3310.00
     ChargeBySensitivityID: [4×5 table]
    ChargeByInstrumentType: [2×2 table]

Display charges by instrument type. Portfolio P1 has both exotic underlying instruments and other residual risk instruments.

RRAOResults.ComponentResults(1).ChargeByInstrumentType

ans=2×2 table
    InstrumentType    Charge 
    ______________    _______

       "Exotic"       3000.00
       "ORR"           310.00

Compute SBM Risk Capital Charge

Under the sensitivity-based market (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 previously created frtbsa object.

SBMResults = sbm(myFRTBSA)

SBMResults = 
  sbmResults with properties:

       NumPortfolios: 2.00
        PortfolioIDs: [2×1 string]
          Regulation: "Basel_d491"
    DomesticCurrency: "USD"
             Charges: [2×1 double]
    ComponentResults: [2×1 frtbsa.sbmPortfolioResults]
        ResultsTable: [2×10 table]

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

SBMResults.Charges

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: [1×1 struct]
      ChargeByRiskClass: [21×5 table]
     IntrabucketCharges: [1×1 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

Compute Market Risk Capital Charge

The charge is the sum of the capital charges for all risk factor categories, plus any applicable add-ons. Use charge to compute the capital market risk charge for all portfolios in the frtbsa object.

ChargeResults = charge(myFRTBSA)

ChargeResults = 
  chargeResults with properties:

       NumPortfolios: 2.00
        PortfolioIDs: [2×1 string]
          Regulation: "Basel_d491"
    DomesticCurrency: "USD"
             Charges: [2×1 double]
    ComponentResults: [2×1 frtbsa.chargePortfolioResults]
        ResultsTable: [2×5 table]

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

ChargeResults.Charges

The ResultsTable output contains the high-level risk charge calculations of the portfolios and includes the total portfolio charge, RRAO charge, DRC charge, and SBM charge.

ChargeResults.ResultsTable

ans=2×5 table
    PortfolioID      Total       RRAO         DRC          SBM   
    ___________    _________    _______    _________    _________

       "P1"        304838.07    3310.00    177008.51    124519.56
       "P2"        176339.24    2800.00     51024.29    122514.96

The ComponentResults output contains detailed capital risk charge information for a given portfolio.

Examine the market risk capital charge for the second portfolio.

ChargeResults.ComponentResults(2)

ans = 
  chargePortfolioResults with properties:

    PortfolioID: "P2"
         Charge: 176339.24
            SBM: [1×1 frtbsa.sbmPortfolioResults]
            DRC: [1×1 frtbsa.drcPortfolioResults]
           RRAO: [1×1 frtbsa.rraoPortfolioResults]

Examine the SBM component of this portfolio.

ChargeResults.ComponentResults(2).SBM

ans = 
  sbmPortfolioResults with properties:

            PortfolioID: "P2"
                 Charge: 122514.96
    ChargeByCorrelation: [1×1 struct]
      ChargeByRiskClass: [21×5 table]
     IntrabucketCharges: [1×1 struct]

Display charges by risk class.

ChargeResults.ComponentResults(2).SBM.ChargeByRiskClass

ans=21×5 table
    RiskClass    RiskMeasure    LowCorrelation    MediumCorrelation    HighCorrelation
    _________    ___________    ______________    _________________    _______________

    "GIRR"       "Delta"             300.52             296.23              298.38    
    "GIRR"       "Vega"              316.67             316.67              316.67    
    "GIRR"       "Curvature"        9323.83            9323.83             9323.83    
    "CSR_NS"     "Delta"              62.50              62.47               62.48    
    "CSR_NS"     "Vega"               46.67              47.79               47.24    
    "CSR_NS"     "Curvature"         393.90             393.90              393.90    
    "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"           14740.74           14432.78            14587.58    
      ⋮

Examine the DRC component of this portfolio.

ChargeResults.ComponentResults(2).DRC

ans = 
  drcPortfolioResults with properties:

            PortfolioID: "P2"
                 Charge: 51024.29
    ChargeByCreditClass: [2×2 table]
     IntrabucketCharges: [1×1 struct]

Display charges by credit class.

ChargeResults.ComponentResults(2).DRC.ChargeByCreditClass

ans=2×2 table
    CreditClass     Charge 
    ___________    ________

       "NS"        20750.00
       "SNC"       30274.29

Examine the RRAO component of this portfolio.

ChargeResults.ComponentResults(2).RRAO

ans = 
  rraoPortfolioResults with properties:

               PortfolioID: "P2"
                    Charge: 2800.00
     ChargeBySensitivityID: [2×5 table]
    ChargeByInstrumentType: [2×2 table]

Display charges by instrument type.

ChargeResults.ComponentResults(2).RRAO.ChargeByInstrumentType

ans=2×2 table
    InstrumentType    Charge 
    ______________    _______

       "Exotic"       2500.00
       "ORR"           300.00