com.quantfinlib.risk.SaCcr

public final class SaCcr extends Object

Standardised approach for counterparty credit risk, SA-CCR (Basel Committee, "The standardised approach for measuring counterparty credit risk exposures", BCBS 279, March 2014, Annex 4). Exposure at default of one netting set:

  EAD = alpha * (RC + PFE),  alpha = 1.4                      (para 128)
  RC  = max(V - C, 0)                          unmargined     (para 136)
  RC  = max(V - C, TH + MTA - NICA, 0)         margined       (para 144)
  PFE = multiplier * AddOn_aggregate,  AddOn_aggregate = sum over classes  (paras 146, 150)
  multiplier = min(1, F + (1 - F) * exp((V - C) / (2 (1 - F) AddOn_aggregate))),  F = 5%  (para 149)

Trade level (paras 155-159): adjusted notional d_i is the notional times the supervisory duration SD = (exp(-0.05 S) - exp(-0.05 E)) / 0.05 for rates and credit, the foreign leg for FX, price times units for equity and commodity. The maturity factor is MF = sqrt(min(max(M, 10/250), 1)) unmargined and MF = 1.5 sqrt(MPOR / 250) margined (MPOR in business days, a 250-day year as in the Annex 4a examples). Each trade contributes delta * d * MF.

Asset-class add-ons (paras 165-182), supervisory factors from Table 2:

Interest rates: hedging set per currency, three maturity buckets by E (under 1y, 1y-5y, over 5y), effective notional sqrt(D1^2 + D2^2 + D3^2 + 1.4 D1 D2 + 1.4 D2 D3 + 0.6 D1 D3), SF 0.5%, add-on is the sum over currencies.
FX: hedging set per currency pair, SF 4% times the absolute net effective notional, summed over pairs.
Credit and equity: entity-level add-on SF times net effective notional; then sqrt((sum rho_k A_k)^2 + sum (1 - rho_k^2) A_k^2) with rho 50% single name, 80% index.
Commodity: commodity-type add-on SF times net effective notional (40% electricity, 18% other types), the same systematic plus idiosyncratic formula with rho 40% inside each of the four hedging sets, summed over sets.

Basis and volatility transactions (paras 162-163) form their own hedging sets inside their asset class, with the supervisory factor times 0.5 (basis) or 5 (volatility); mark a trade with SaCcrTrade.asBasis() or SaCcrTrade.asVolatility(). For example a USD 3m/OIS basis swap with adjusted notional 78,694 in the over-5y bucket adds 0.5 * 0.5% * 78,694 = 196.7 on its own, where the same trade as an ordinary swap would add 393.5 and net against the other USD swaps.

Margin agreements and netting sets (paras 185-187, checked against the March 2014 text): oneMarginAgreementManyNettingSets(List, double) for one agreement covering several netting sets, subNettingSets(List) for one netting set under several agreements (or partly unmargined). Collateral C is passed already haircut; SaCcrHaircuts gives the supervisory haircuts. Times are year fractions the caller computes; the S and E floor of ten business days is applied as 10/250 years. The tests reproduce Annex 4a Examples 1 to 5. Research lane, deterministic.

Nested Class Summary

Nested Classes

Modifier and Type

Class

Description

static enum

SaCcr.AssetClass

The five SA-CCR asset classes.

static enum

SaCcr.CommoditySet

The four commodity hedging sets (para 161).

static enum

SaCcr.CreditGrade

Credit rating buckets and their supervisory factors (Table 2).

static enum

SaCcr.HedgingSetType

Hedging-set kind of a trade (paras 162-163) and its multiplier on the supervisory factor.

static final record

SaCcr.Margin

Margin agreement terms for a margined netting set.

static final record

SaCcr.Result

SA-CCR outputs for one netting set.

static final record

SaCcr.SubNettingSet

One part of a netting set for subNettingSets(List): the trades under one margin agreement (or the unmargined trades when margin is null) and the haircut collateral that belongs to them.
Field Summary

Fields

Modifier and Type

Field

Description

static final double

ALPHA

Alpha, para 128.

static final double

MULTIPLIER_FLOOR

Multiplier floor, para 149.

static final double

OPTION_VOL_COMMODITY_OTHER

Supervisory option volatility, other commodities (Table 2).

static final double

OPTION_VOL_CREDIT_INDEX

Supervisory option volatility, credit index (Table 2).

static final double

OPTION_VOL_CREDIT_SINGLE

Supervisory option volatility, single-name credit (Table 2).

static final double

OPTION_VOL_ELECTRICITY

Supervisory option volatility, electricity (Table 2).

static final double

OPTION_VOL_EQUITY_INDEX

Supervisory option volatility, equity index (Table 2).

static final double

OPTION_VOL_EQUITY_SINGLE

Supervisory option volatility, single-name equity (Table 2).

static final double

OPTION_VOL_FX

Supervisory option volatility, FX (Table 2).

static final double

OPTION_VOL_INTEREST_RATE

Supervisory option volatility, interest rates (Table 2).
Method Summary

Modifier and Type

Method

Description

static double

cdoTrancheDelta(double attachment, double detachment, boolean purchased)

Supervisory delta of a CDO tranche, para 159: 15 / ((1 + 14 A)(1 + 14 D)), positive for purchased protection.

static SaCcr.Result

margined(List<SaCcrTrade> trades, double collateralHeld, SaCcr.Margin margin)

EAD of a margined netting set.

static double

maturityFactor(double maturityYears, SaCcr.Margin margin)

Maturity factor of paras 164 and 171.

static double

multiplier(double vMinusC, double aggregate)

The PFE multiplier of para 149.

static SaCcr.Result

oneMarginAgreementManyNettingSets(List<List<SaCcrTrade>> nettingSets, double collateralHeld)

One margin agreement covering several netting sets (RC from BCBS 279 para 186, PFE from para 187, both checked against the March 2014 text).

static double

optionDelta(boolean call, boolean bought, double underlying, double strike, double expiryYears, double vol)

Supervisory option delta of para 159 (Black-Scholes delta with the supervisory volatility, zero rates).

static SaCcr.Result

subNettingSets(List<SaCcr.SubNettingSet> parts)

One netting set under several margin agreements, or mixing margined and unmargined trades (BCBS 279 para 185).

static double

supervisoryDuration(double startYears, double endYears)

Supervisory duration of para 157, with S and E in years.

static SaCcr.Result

unmargined(List<SaCcrTrade> trades, double collateralHeld)

EAD of an unmargined netting set.

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

Field Details
- ALPHA
  public static final double ALPHA
  
  Alpha, para 128.
  
  See Also:
  
  Constant Field Values
- MULTIPLIER_FLOOR
  public static final double MULTIPLIER_FLOOR
  
  Multiplier floor, para 149.
  
  See Also:
  
  Constant Field Values
- OPTION_VOL_INTEREST_RATE
  public static final double OPTION_VOL_INTEREST_RATE
  
  Supervisory option volatility, interest rates (Table 2).
  
  See Also:
  
  Constant Field Values
- OPTION_VOL_FX
  public static final double OPTION_VOL_FX
  
  Supervisory option volatility, FX (Table 2).
  
  See Also:
  
  Constant Field Values
- OPTION_VOL_CREDIT_SINGLE
  public static final double OPTION_VOL_CREDIT_SINGLE
  
  Supervisory option volatility, single-name credit (Table 2).
  
  See Also:
  
  Constant Field Values
- OPTION_VOL_CREDIT_INDEX
  public static final double OPTION_VOL_CREDIT_INDEX
  
  Supervisory option volatility, credit index (Table 2).
  
  See Also:
  
  Constant Field Values
- OPTION_VOL_EQUITY_SINGLE
  public static final double OPTION_VOL_EQUITY_SINGLE
  
  Supervisory option volatility, single-name equity (Table 2).
  
  See Also:
  
  Constant Field Values
- OPTION_VOL_EQUITY_INDEX
  public static final double OPTION_VOL_EQUITY_INDEX
  
  Supervisory option volatility, equity index (Table 2).
  
  See Also:
  
  Constant Field Values
- OPTION_VOL_ELECTRICITY
  public static final double OPTION_VOL_ELECTRICITY
  
  Supervisory option volatility, electricity (Table 2).
  
  See Also:
  
  Constant Field Values
- OPTION_VOL_COMMODITY_OTHER
  public static final double OPTION_VOL_COMMODITY_OTHER
  
  Supervisory option volatility, other commodities (Table 2).
  
  See Also:
  
  Constant Field Values
Method Details
- unmargined
  
  public static SaCcr.Result unmargined(List<SaCcrTrade> trades, double collateralHeld)
  
  EAD of an unmargined netting set.
  
  Parameters:
  
  trades - the trades of the netting set
  
  collateralHeld - C, haircut value of net collateral held (negative when posted)
  
  Returns:
  
  the result
- margined
  
  public static SaCcr.Result margined(List<SaCcrTrade> trades, double collateralHeld, SaCcr.Margin margin)
  
  EAD of a margined netting set.
  
  Parameters:
  
  trades - the trades of the netting set
  
  collateralHeld - C, haircut value of net collateral held, variation margin plus NICA
  
  margin - margin agreement terms
  
  Returns:
  
  the result
- oneMarginAgreementManyNettingSets
  
  public static SaCcr.Result oneMarginAgreementManyNettingSets(List<List<SaCcrTrade>> nettingSets, double collateralHeld)
  
  One margin agreement covering several netting sets (RC from BCBS 279 para 186, PFE from para 187, both checked against the March 2014 text). The agreement's collateral cannot be split between the netting sets, so RC_MA = max(sum_NS max(V_NS, 0) - C_MA, 0), and PFE_MA = sum_NS PFE_NS with each netting set's PFE computed as if unmargined. Each multiplier uses that set's own V_NS with no collateral, since C_MA belongs to no single set; para 187 says only that each PFE follows the unmargined methodology, so the choice of V_NS for the multiplier is this library's reading.
  Example (own hand computation): netting sets with V of 100 and -40 under one agreement holding C = 30 give RC = max(100 + 0 - 30, 0) = 70. Netting the two sets first would give 30, which the rule does not allow.
  
  Parameters:
  
  nettingSets - the netting sets, each non-empty
  
  collateralHeld - C_MA, haircut net collateral under the agreement
  
  Returns:
  
  a result whose add-on fields are sums over the netting sets and whose multiplier is PFE divided by the aggregate add-on
- subNettingSets
  
  public static SaCcr.Result subNettingSets(List<SaCcr.SubNettingSet> parts)
  
  One netting set under several margin agreements, or mixing margined and unmargined trades (BCBS 279 para 185). The netting set is divided into sub-netting sets aligned with their agreements, and para 185 states that this applies to both RC and PFE. So each part gets its own RC_k (margined: max(V_k - C_k, TH_k + MTA_k - NICA_k, 0); unmargined: max(V_k - C_k, 0)) and its own PFE with its own maturity factors and multiplier from V_k - C_k, and both are summed over the parts. Until 2.3 the RC was taken for the netting set as a whole with summed floors; that reading did not match para 185 and was corrected.
  Example (own hand computation): a margined part with V = -30, C = 0, TH + MTA - NICA = 5 and an unmargined part with V = 50 give RC = 5 + 50 = 55, where netting the parts first would give 20.
  
  Parameters:
  
  parts - the sub-netting sets
  
  Returns:
  
  a result whose add-on fields are sums over the parts and whose multiplier is PFE divided by the aggregate add-on
- multiplier
  
  public static double multiplier(double vMinusC, double aggregate)
  
  The PFE multiplier of para 149.
  
  Parameters:
  
  vMinusC - V - C
  
  aggregate - aggregate add-on (≥ 0); zero gives 1
  
  Returns:
  
  the multiplier in [0.05, 1]
- supervisoryDuration
  
  public static double supervisoryDuration(double startYears, double endYears)
  
  Supervisory duration of para 157, with S and E in years.
  
  Parameters:
  
  startYears - S (0 when started; a positive S is floored at ten business days)
  
  endYears - E (floored at ten business days)
  
  Returns:
  
  SD in years
- optionDelta
  
  public static double optionDelta(boolean call, boolean bought, double underlying, double strike, double expiryYears, double vol)
  
  Supervisory option delta of para 159 (Black-Scholes delta with the supervisory volatility, zero rates).
  
  Parameters:
  
  call - true for a call, false for a put
  
  bought - true when the bank bought the option
  
  underlying - P, the underlying price (forward, spot, swap rate), > 0
  
  strike - K, > 0
  
  expiryYears - T, latest exercise date, > 0
  
  vol - supervisory volatility, > 0
  
  Returns:
  
  the signed delta
- cdoTrancheDelta
  
  public static double cdoTrancheDelta(double attachment, double detachment, boolean purchased)
  
  Supervisory delta of a CDO tranche, para 159: 15 / ((1 + 14 A)(1 + 14 D)), positive for purchased protection.
  
  Parameters:
  
  attachment - A in [0, 1)
  
  detachment - D in (A, 1]
  
  purchased - true for long protection
  
  Returns:
  
  the signed delta
- maturityFactor
  
  public static double maturityFactor(double maturityYears, SaCcr.Margin margin)
  
  Maturity factor of paras 164 and 171.
  
  Parameters:
  
  maturityYears - M
  
  margin - null for unmargined
  
  Returns:
  
  MF

Class SaCcr

Nested Class Summary

Field Summary

Method Summary

Methods inherited from class Object

Field Details

ALPHA

MULTIPLIER_FLOOR

OPTION_VOL_INTEREST_RATE

OPTION_VOL_FX

OPTION_VOL_CREDIT_SINGLE

OPTION_VOL_CREDIT_INDEX

OPTION_VOL_EQUITY_SINGLE

OPTION_VOL_EQUITY_INDEX

OPTION_VOL_ELECTRICITY

OPTION_VOL_COMMODITY_OTHER

Method Details

unmargined

margined

oneMarginAgreementManyNettingSets

subNettingSets

multiplier

supervisoryDuration

optionDelta

cdoTrancheDelta

maturityFactor