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asrf

Asymptotic Single Risk Factor (ASRF) capital

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Syntax

[capital,VaR] = asrf(PD,LGD,R)
[capital,VaR] = asrf(___,Name,Value)

Description

example

[capital,VaR] = asrf(PD,LGD,R)computes regulatory capital and value-at-risk using an ASRF model.

example

[capital,VaR] = asrf(___,Name,Value)adds optional name-value pair arguments.

Examples

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Open Live Script

Load saved portfolio data.

loadCreditPortfolioData.mat

Compute asset correlation for corporate, sovereign, and bank exposures.

R = 0.12 * (1-exp(-50*PD)) / (1-exp(-50)) +...0.24 * (1 - (1-exp(-50*PD)) / (1-exp(-50)));

Compute the asymptotic single risk factor capital. By specifying the name-value pair argument forEAD,capitalis returned in terms of currency.

capital = asrf(PD,LGD,R,'EAD',EAD);

Apply a maturity adjustment.

b = (0.11852 - 0.05478 * log(PD)).^2; matAdj = (1 + (Maturity - 2.5) .* b) ./ (1 - 1.5 * b); adjustedCapital = capital .* matAdj; portfolioCapital = sum(adjustedCapital)
portfolioCapital = 175.7865

Input Arguments

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Probability of default, specified as aNumCounterparties-by-1数值向量和避署ments from0to1, representing the default probabilities for the counterparties.

Data Types:double

Loss given default, specified as aNumCounterparties-by-1数值向量和避署ments from0to1, representing the fraction of exposure that is lost when a counterparty defaults.LGDis defined as (1 −Recovery). For example, anLGDof 0.6 implies a 40% recovery rate in the event of a default.

Data Types:double

Asset correlation, specified as aNumCounterparties-by-1numeric vector.

The asset correlations,R, have values from0to1and specify the correlation between assets in the same asset class.

Note

The correlation between an asset value and the underlying single risk factor issqrt(R). This value,sqrt(R), corresponds to theWeightsinput argument to thecreditDefaultCopulaandcreditMigrationCopulaclasses for one-factor models.

Data Types:double

Name-Value Pair Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Namemust appear inside quotes. You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN.

Example:capital = asrf(PD,LGD,R,'EAD',EAD)

Exposure at default, specified as the comma-separated pair consisting of'EAD'and aNumCounterparties-by-1numeric vector of credit exposures.

IfEADis not specified, the defaultEADis1, meaning thatcapitalandVaRresults are reported as a percentage of the counterparty's exposure. IfEADis specified, thencapitalandVaRare returned in units of currency.

Data Types:double

Value at risk level used when calculating the capital requirement, specified as the comma-separated pair consisting of'VaRLevel'and a decimal value between0and1.

Data Types:double

Output Arguments

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Capital for each element in the portfolio, returned as aNumCounterparties-by-1vector. If the optional inputEADis specified, thencapitalis in units of currency. Otherwise,capitalis reported as a percentage of each exposure.

Value-at-risk for each exposure, returned as aNumCounterparties-by-1vector. If the optional inputEADis specified, thenVaRis in units of currency. Otherwise,VaRis reported as a percentage of each exposure.

More About

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ASRF Model Capital

In the ASRF model, capital is defined as the loss in excess of the expected loss (EL) at a high confidence level.

The formula for capital is

capital = VaR - EL

Algorithms

The capital requirement formula for exposures is defined as

V a R = E A D * L G D * Φ ( Φ − 1 ( P D ) − R Φ − 1 ( 1 − V a R L e v e l ) 1 − R ) c a p i t a l = V a R − E A D * L G D * P D

where

ɸis the normal CDF.

ɸ-1is the inverse normal CDF.

Ris asset correlation.

EADis exposure at default.

PDis probability of default.

LGDis loss given default.

References

[1] Gordy, M.B. "A risk-factor model foundation for ratings-based bank capital rule."Journal of Financial Intermediation.Vol. 12, pp. 199-232, 2003.

See Also

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Topics

Introduced in R2017b

Risk Management Toolbox Documentation

万博1manbetx

Effective Model Risk Management with MATLAB

Effective Model Risk Management with MATLAB

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