com.quantfinlib.risk.FrtbSa

public final class FrtbSa extends Object

FRTB standardised approach, sensitivities-based method (SBM), styled after BCBS d457 (January 2019) chapter MAR21. Not certified.

Plain idea. Each risk factor sensitivity is multiplied by a supervisory risk weight. Weighted sensitivities are netted inside a bucket with a correlation, the bucket results are netted across buckets with a second correlation, and the whole calculation is run three times with the correlations scaled up, left alone and scaled down. The capital is the worst of the three totals.

Formal statement (per MAR21). With weighted sensitivities WS_k = RW_k·s_k:

  K_b = √max(0, Σ WS_k² + Σ_{k≠l} ρ_kl WS_k WS_l)
 S_b = max(min(Σ WS_k, K_b), −K_b)
 Δ   = √(Σ K_b² + Σ_{b≠c} γ_bc S_b S_c)

For delta and vega the first pass uses S_b = Σ WS_k unclamped (MAR21.4(5)(a)); only if that radicand is negative is the calculation repeated with the clamped S_b above, the alternative specification of MAR21.4(5)(b). If that is still negative this class returns 0. Curvature (MAR21.5) uses S_b = Σ CVR of the selected scenario, the ψ rule (cross term dropped when both terms are negative) and floors the radicand at 0; the bucket takes the larger of the up and down scenario (MAR21.5(3)(a)), see curvature(List, List, double[][], Scenario). Curvature correlations are the squared delta correlations, and the high and low scenarios are applied to the squared value (MAR21.100, MAR21.101). Correlation scenarios (MAR21.6): high = min(1.25ρ, 1), low = max(2ρ − 1, 0.75ρ), applied to ρ and γ alike.

Worked example (independent recomputation, not a BCBS worked number: MAR21 prints no capital example; own tests FrtbSaTest and FrtbSaTableTest, the latter from the printed Table 1 and Table 2): two GIRR sensitivities of 100 and −50 at tenors 1y and 2y in one currency, RW 1.6% and 1.3%: WS = 1.6, −0.65; ρ = exp(−0.03·1/1) = 0.97045; K = √(2.56 + 0.4225 − 2·0.97045·1.04) = 0.98182.

Correlation matrices are supplied by the caller; the supervisory parameter helpers FrtbSa.Girr, FrtbSa.Fx, FrtbSa.Equity, FrtbSa.Commodity and FrtbSa.Csr build the ones this library can take from d457 MAR21, each value checked against the text and cited on the constant (published reference, BCBS d457 January 2019). FrtbSa.SecNonCtp covers CSR securitisation (non-CTP). Bucketing decisions (sector, rating, market cap) stay with the caller.

Nested Class Summary

Nested Classes

Modifier and Type

Class

Description

static final record

FrtbSa.Bucket

One bucket: weighted sensitivities and the medium-scenario intra-bucket correlation matrix (diagonal ignored).

static final record

FrtbSa.BucketResult

Bucket-level result.

static final class

FrtbSa.Commodity

Commodity parameters, buckets 1-11.

static final class

FrtbSa.Csr

Credit spread risk, non-securitisation (MAR21.51 to MAR21.57).

static final class

FrtbSa.Equity

Equity (spot) parameters, buckets 1-13.

static final class

FrtbSa.Fx

FX parameters.

static final class

FrtbSa.Girr

General interest rate risk parameters.

static final record

FrtbSa.RiskClass

One risk class: delta, vega and curvature inputs (any may be empty).

static enum

FrtbSa.Scenario

Correlation scenarios of MAR21.

static final class

FrtbSa.SecNonCtp

CSR securitisation (non-CTP), buckets 1-25 (MAR21.62 to MAR21.71).
Field Summary

Fields

Modifier and Type

Field

Description

static final int

VEGA_LH_COMMODITY

static final int

VEGA_LH_CSR

static final int

VEGA_LH_EQUITY_LARGE_CAP

static final int

VEGA_LH_EQUITY_SMALL_CAP

static final int

VEGA_LH_FX

static final int

VEGA_LH_GIRR

Vega liquidity horizons, days (MAR21.92 Table 13, verified; CSR securitisation also 120).
Method Summary

Modifier and Type

Method

Description

static FrtbSa.BucketResult

bucket(FrtbSa.Bucket b, FrtbSa.Scenario sc)

K_b and clamped S_b of one bucket (delta or vega).

static double[][]

constant(int n, double rho)

Matrix with constant off-diagonal value.

static double

curvature(List<FrtbSa.Bucket> buckets, double[][] gamma, FrtbSa.Scenario sc)

Curvature capital of one risk class under one scenario.

static double

curvature(List<FrtbSa.Bucket> up, List<FrtbSa.Bucket> down, double[][] gamma, FrtbSa.Scenario sc)

Curvature capital with both shock directions (MAR21.5(3) and (4)).

static double

cvr(double vUp, double vBase, double vDown, double deltaPnlUp)

Curvature risk charge CVR_k = −min(V⁺ − V₀ − RW·s, V⁻ − V₀ + RW·s), where V± are values after an up/down shift of size RW (the curvature risk weight) and s is the delta sensitivity per unit of that shift, so RW·s is the delta-implied P&L of the up shift.

static double

deltaVega(List<FrtbSa.Bucket> buckets, double[][] gamma, FrtbSa.Scenario sc)

Delta or vega capital of one risk class under one scenario.

static double

deltaVega(List<FrtbSa.Bucket> buckets, double[][] gamma, FrtbSa.Scenario sc, Set<Integer> otherSector)

Delta or vega capital where some buckets are "other sector" buckets (equity 11, CSR non-securitisation 16, securitisation non-CTP 25): their K_b is Σ|WS_k| with no correlation (MAR21.56(1), MAR21.69(1), MAR21.79(1)).

static double

otherSectorCurvatureK(double[] cvrUp, double[] cvrDown)

Other-sector bucket curvature K_b = max(Σ max(CVR⁺, 0), Σ max(CVR⁻, 0)) (MAR21.56(2), MAR21.79(2)).

static double

otherSectorK(double[] weighted)

Other-sector bucket delta or vega K_b = Σ|WS_k| (MAR21.56(1), MAR21.79(1)).

static double

sbmCapital(List<FrtbSa.RiskClass> classes)

SBM capital: the maximum of the three scenario totals.

static double

total(List<FrtbSa.RiskClass> classes, FrtbSa.Scenario sc)

Total SBM charge of a set of risk classes under one scenario.

static double

vegaMaturityCorrelation(double tk, double tl)

Vega option-maturity correlation exp(−1%·|T_k − T_l|/min(T_k, T_l)) (MAR21.93(1), verified).

static double

vegaRiskWeight(int liquidityHorizonDays)

Vega risk weight min(RW_σ·√(LH/10), 1) with RW_σ = 0.55 (MAR21.92 footnote 24).

Methods inherited from class Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Details
- VEGA_LH_GIRR
  public static final int VEGA_LH_GIRR
  
  Vega liquidity horizons, days (MAR21.92 Table 13, verified; CSR securitisation also 120).
  
  See Also:
  
  Constant Field Values
- VEGA_LH_CSR
  public static final int VEGA_LH_CSR
  
  See Also:
  
  Constant Field Values
- VEGA_LH_EQUITY_LARGE_CAP
  public static final int VEGA_LH_EQUITY_LARGE_CAP
  
  See Also:
  
  Constant Field Values
- VEGA_LH_EQUITY_SMALL_CAP
  public static final int VEGA_LH_EQUITY_SMALL_CAP
  
  See Also:
  
  Constant Field Values
- VEGA_LH_COMMODITY
  public static final int VEGA_LH_COMMODITY
  
  See Also:
  
  Constant Field Values
- VEGA_LH_FX
  public static final int VEGA_LH_FX
  
  See Also:
  
  Constant Field Values
Method Details
- bucket
  
  public static FrtbSa.BucketResult bucket(FrtbSa.Bucket b, FrtbSa.Scenario sc)
  
  K_b and clamped S_b of one bucket (delta or vega).
- deltaVega
  
  public static double deltaVega(List<FrtbSa.Bucket> buckets, double[][] gamma, FrtbSa.Scenario sc)
  
  Delta or vega capital of one risk class under one scenario.
  
  Parameters:
  
  gamma - medium-scenario inter-bucket correlation, nb x nb
- curvature
  
  public static double curvature(List<FrtbSa.Bucket> buckets, double[][] gamma, FrtbSa.Scenario sc)
  
  Curvature capital of one risk class under one scenario. Each bucket's weighted entries are CVR_k (see cvr(double, double, double, double)); ρ and γ are the delta correlations, squared internally.
- deltaVega
  
  public static double deltaVega(List<FrtbSa.Bucket> buckets, double[][] gamma, FrtbSa.Scenario sc, Set<Integer> otherSector)
  
  Delta or vega capital where some buckets are "other sector" buckets (equity 11, CSR non-securitisation 16, securitisation non-CTP 25): their K_b is Σ|WS_k| with no correlation (MAR21.56(1), MAR21.69(1), MAR21.79(1)). otherSector holds zero-based indices into buckets.
- otherSectorK
  
  public static double otherSectorK(double[] weighted)
  
  Other-sector bucket delta or vega K_b = Σ|WS_k| (MAR21.56(1), MAR21.79(1)).
- otherSectorCurvatureK
  
  public static double otherSectorCurvatureK(double[] cvrUp, double[] cvrDown)
  
  Other-sector bucket curvature K_b = max(Σ max(CVR⁺, 0), Σ max(CVR⁻, 0)) (MAR21.56(2), MAR21.79(2)).
- curvature
  
  public static double curvature(List<FrtbSa.Bucket> up, List<FrtbSa.Bucket> down, double[][] gamma, FrtbSa.Scenario sc)
  
  Curvature capital with both shock directions (MAR21.5(3) and (4)). up.get(b) and down.get(b) hold CVR⁺_k and CVR⁻_k of bucket b with the delta ρ (squared internally). Each bucket takes the larger of K⁺ and K⁻; on a tie the up scenario is chosen if Σ CVR⁺ > Σ CVR⁻. S_b is Σ CVR of the selected scenario, and the selection is made afresh under each correlation scenario.
- cvr
  
  public static double cvr(double vUp, double vBase, double vDown, double deltaPnlUp)
  
  Curvature risk charge CVR_k = −min(V⁺ − V₀ − RW·s, V⁻ − V₀ + RW·s), where V± are values after an up/down shift of size RW (the curvature risk weight) and s is the delta sensitivity per unit of that shift, so RW·s is the delta-implied P&L of the up shift.
- total
  
  public static double total(List<FrtbSa.RiskClass> classes, FrtbSa.Scenario sc)
  
  Total SBM charge of a set of risk classes under one scenario.
- sbmCapital
  
  public static double sbmCapital(List<FrtbSa.RiskClass> classes)
  
  SBM capital: the maximum of the three scenario totals.
- vegaRiskWeight
  
  public static double vegaRiskWeight(int liquidityHorizonDays)
  
  Vega risk weight min(RW_σ·√(LH/10), 1) with RW_σ = 0.55 (MAR21.92 footnote 24). Verified: gives 100% for every class except equity large cap and indices, 0.55·√2 = 77.78% (MAR21.92 Table 13).
- vegaMaturityCorrelation
  
  public static double vegaMaturityCorrelation(double tk, double tl)
  
  Vega option-maturity correlation exp(−1%·|T_k − T_l|/min(T_k, T_l)) (MAR21.93(1), verified).
- constant
  
  public static double[][] constant(int n, double rho)
  
  Matrix with constant off-diagonal value.

Class FrtbSa

Nested Class Summary

Field Summary

Method Summary

Methods inherited from class Object

Field Details

VEGA_LH_GIRR

VEGA_LH_CSR

VEGA_LH_EQUITY_LARGE_CAP

VEGA_LH_EQUITY_SMALL_CAP

VEGA_LH_COMMODITY

VEGA_LH_FX

Method Details

bucket

deltaVega

curvature

deltaVega

otherSectorK

otherSectorCurvatureK

curvature

cvr

total

sbmCapital

vegaRiskWeight

vegaMaturityCorrelation

constant