Package 'xVA'

Calculates the CVA Capital Charge

Description

Calculates the CVA capital charge based on the standardized approach

Usage

calcCVACapital(
  trades,
  EAD,
  reg_data,
  superv,
  effective_maturity,
  cva_sensitivities
)

Arguments

trades	The full list of the Trade Objects
EAD	Exposure-at-Default
reg_data	A list containing data related to the regulatory calculations
superv	A list containing supervisory data including correlations, risk weights etc
effective_maturity	The effective maturity of the trades of the netting set
cva_sensitivities	The effective maturity of the trades of the netting set

Value

The CVA capital charge of the trade set

Author(s)

Tasos Grivas <[email protected]>

---

Calculates the Default Capital Charge

Description

Calculates the default capital charge using the advanced IRB methodology and the stressed R

Usage

calcDefCapital(trades, EAD, reg_data, effective_maturity)

Arguments

trades	The full list of the Trade Objects
EAD	The Exposure-At-Default of the trades as per the selected regulatory framework
reg_data	A list containing data related to the regulatory calculations (for example the regulatory probability-of-default, the regulatory loss-given-default etc)
effective_maturity	The effective maturity of the trades of the netting set

Value

The default capital charge

Author(s)

Tasos Grivas <[email protected]>

---

Calculates the Exposure-At-Default (EAD)

Description

Calculates the Exposure-At-Default (EAD) based on the given regulatory framework. It supports the CEM, IMM and (simplified) SA-CCR frameworks

Usage

calcEADRegulatory(
  trades,
  framework,
  sa_ccr_simplified = "",
  CSA,
  collateral,
  EEE,
  time_points
)

Arguments

trades	The full list of the Trade Objects
framework	Specifies the regulatory framework used in the calculations. It can take the values of 'IMM', 'CEM', 'SA-CCR'
sa_ccr_simplified	(Optional) Specifies whether the standard SACCR or its simplified version or the OEM will be implemented. It can take the values of ”, 'simplified', 'OEM'
CSA	The margin agreement with the counterparty
collateral	The amount of collaterals currently exchanged with the counterparty
EEE	A vector containing the effective expected exposure against the counterparty
time_points	The timepoints that the analysis is performed on

Value

The Exposure-At-Default

Author(s)

Tasos Grivas <[email protected]>

---

Calculates the Effective Maturity

Description

Calculates the effective maturity based on the specified regulatory framework

Usage

calcEffectiveMaturity(trades, time_points, framework, simulated_exposure)

Arguments

trades	The full list of the Trade Objects
time_points	The timepoints that the analysis is performed on
framework	Specifies the regulatory framework used in the calculations. It can take the values of 'IMM', 'CEM', 'SA-CCR'
simulated_exposure	The exposure profile list containing the EE, EEE etc

Value

The effective maturity of the trade set

Author(s)

Tasos Grivas <[email protected]>

---

Calculates the Capital Valuation Adjustment (KVA)

Description

Calculates the capital valuation adjustment by computing the default capital charge and the CVA capital charge and applying the required return-on-capital

Usage

calcKVA(
  CSA,
  collateral,
  trades,
  reg_data,
  time_points,
  EAD,
  effective_maturity,
  ignore_def_charge = TRUE
)

Arguments

CSA	The margin agreement with the counterparty
collateral	The current amount of collaterals currently exchanged with the counterparty
trades	The full list of the Trade Objects
reg_data	A list containing data related to the regulatory calculations (for example the 'framework' member variable can be 'IMM','SACCR','CEM')
time_points	The timepoints that the analysis is performed on
EAD	The Exposure-at-default calculated based on the prescribed framework as appearing in the 'reg_data'
effective_maturity	The effective maturity of the trades performed with a specific counterparty
ignore_def_charge	if set to true the default capital charge is set to zero

Value

The capital valuation adjustment (KVA)

Author(s)

Tasos Grivas <[email protected]>

---

Calculates the Net/Gross ratio (NGR)

Description

Calculates the Net/Gross ratio used under the CEM regulatory framework

Usage

CalcNGR(MtM_Vector)

Arguments

MtM_Vector

A vector containing the trades to be netted

Value

The Net-Gross ratio (NGR)

Author(s)

Tasos Grivas <[email protected]>

---

Calculates the Probablity of Default

Description

Calculates the probablity of the default on specific time points by using the spread of the corresponding credit curve and the loss given default

Usage

CalcPD(spread, LGD, time_points)

Arguments

spread	The spread based on the credit curve
LGD	The loss-given-default
time_points	The timepoints that the analysis is performed on

Value

A vector containing the probablity of default on the specified timepoints

Author(s)

Tasos Grivas <[email protected]>

---

Calculated the Simulated Exposure Profile

Description

Calculates the simulated exposure profile (EE, NEE, PFE, EEE) by use of the Hull-White model. Two sets of results are provided: one after taking into account the marging agreement and one assuming that there is no marging agreement present

Usage

CalcSimulatedExposure(
  discount_factors,
  time_points,
  spot_curve,
  CSA,
  trades,
  sim_data,
  framework
)

Arguments

discount_factors	The discount curve derived from the spot curve
time_points	The timepoints that the analysis is performed on
spot_curve	The curve derived from interpolating the market spot rates
CSA	The margin agreement
trades	The list of the trade objects
sim_data	A list containing simulation-related data (model parameters and number of simulation)
framework	regulatory framework can be 'IMM','SACCR','CEM'

Value

A list containing the exposure profile (both collateralized and uncollateralized)

Author(s)

Tasos Grivas <[email protected]>

---

Calculates the Valuation Adjustment

Description

Calculates the Valuation Adjustment based on the exposure, the probability-of-default and the loss-given-default

Usage

CalcVA(exposure, discount_factors, PD, LGD)

Arguments

exposure	A vector containing the exposure values on which the credit risk adjustment will be calculated
discount_factors	The Discount Curve
PD	The probability-of-Default
LGD	The Loss-Given-Default

Value

The Valuation Adjustment Value

Author(s)

Tasos Grivas <[email protected]>

---

Checks if specified currency is low risk

Description

Checks if the specified currency is eligible to receive reduced regulatory risk weights

Usage

IS_ELIGIBLE_CCY(ccy)

Arguments

ccy	The currency to be checked

Value

TRUE if the currency is is eligible to receive reduced regulatory risk weights

Author(s)

Tasos Grivas <[email protected]>

References

https://www.bis.org/basel_framework/chapter/MAR/50.htm?inforce=20230101&published=20200708

Examples

TRUE == IS_ELIGIBLE_CCY('EUR')

---

Checks if Credit rating is Investment Grade

Description

Checks if the credit rating is investment grade or not (if not rating not recognised will be unrated)

Usage

IS_IG(credit_rating)

Arguments

credit_rating

The Credit Rating to be checked

Value

TRUE if Rating is Investment Grade

Author(s)

Tasos Grivas <[email protected]>

References

https://en.wikipedia.org/wiki/Credit_rating

Examples

TRUE == IS_IG('AAA')

---

Supervisory Data Loading

Description

Loads the supervisory data (factors, correlation and option volatility) for each Asset Class and SubClass

Usage

LoadSupervisoryCVAData()

Value

A list with the required data

Author(s)

Tasos Grivas <[email protected]>

References

MAR50 - Credit Value Adjustment Framework https://www.bis.org/basel_framework/chapter/MAR/50.htm?inforce=20230101&published=20200708

---

Calculates the xVA values

Description

Calculates the xVA values (CVA, DVA, FVA, FBA, MVA, KVA)

Usage

xVACalculator(
  trades,
  CSA,
  collateral,
  sim_data,
  reg_data,
  credit_curve_PO,
  credit_curve_cpty,
  funding_curve,
  spot_rates,
  cpty_LGD,
  PO_LGD,
  no_simulations
)

Arguments

trades	The full list of the Trade Objects
CSA	The margin agreement with the counterparty
collateral	The amount of collateral currently exchanged with the counterparty
sim_data	A list containing data related to the calculation of simulated exposures (for example the model parameters and the number of simulations)
reg_data	A list containing data related to the regulatory calculations (for example the 'ccr_framework' member variable can be 'IMM','SACCR','CEM')
credit_curve_PO	The credit curve of the processing organization
credit_curve_cpty	The credit curve of the processing organization
funding_curve	A curve containing the credit spread for the funding of the collateral
spot_rates	The spot rates curve
cpty_LGD	The loss-given-default of the counterparty
PO_LGD	The loss-given-default of the processing organization
no_simulations	if true, no simulated exposure will be generated and the regulatory framework should be SA-CCR

Value

A list containing the xVA values and the cva capital charge

Author(s)

Tasos Grivas <[email protected]>

References

Gregory J., The xVA Challenge, 2015, Wiley

---

xVA calculation example

Description

Calculates the xVA values for a simple example containing two IR swaps.

Usage

xVACalculatorExample()

Value

A list with the values of various valuations' adjustments

Author(s)

Tasos Grivas <[email protected]>

Examples

## run the example

xVACalculatorExample()

---