intraMode {AssetCorr} R Documentation

## Parametric Approach of Botha and van Vuuren (2010)- Mode

### Description

The intra asset correlation will be estimated by fitting the mode of the default rate time series to the theoretical mode of the default rates and backing out the remaining correlation parameter numerically. Additionally, bootstrap and jackknife corrections are implemented.

### Usage

intraMode(d, n, B = 0, DB=c(0,0), JC = FALSE,CI_Boot, type="bca", plot=FALSE)

### Arguments

 d a vector, containing the default time series of the sector. n a vector, containing the number of obligors at the beginning of the period over time. B an integer, indicating how many bootstrap repetitions should be used for the single bootstrap corrected estimate. DB a combined vector, indicating how many bootstrap repetitions should be used for the inner (first entry) and outer loop (second entry) to correct the bias using the double bootstrap. JC a logical variable, indicating if the jackknife corrected estimate should be calculated. CI_Boot a number, indicating the desired confidence interval if the single bootstrap correction is specified. By default, the interval is calculated as the bootstrap corrected and accelerated confidence interval (Bca). type a string, indicating the desired method to calculate the bootstrap confidence intervals. For more details see boot.ci. Studendized confidence intervals are not supported. plot a logical variable, indicating whether a plot of the single bootstrap density should be generated.

### Details

As stated by Botha and van Vuuren (2010) one can estimate the intra correlation by matching the theoretical and empirical mode. According to Vasicek (1991) the default rates are only unimodal if the intra correlation is smaller than 0.5. Therefore, this estimator cannot be used for higher intra correlations. The theoretical mode is given by Vasicek (1991):

Mode_Vasicek=Phi(sqrt(1-rho)/(1-2*rho)*Phi^-1(PD))

If DB is specified, the single bootstrap corrected estimate will be calculated by using the bootstrap values of the outer loop (oValues).

### Value

The returned value is a list, containing the following components (depending on the selected arguments):

 Original Estimate of the original method Bootstrap Bootstrap corrected estimate Double_Bootstrap Double bootstrap corrected estimate Jackknife Jackknife corrected estimate CI_Boot Selected two-sided bootstrap confidence interval bValues Estimates from the bootstrap resampling iValues Estimates from the double bootstrap resampling- inner loop oValues Estimates from the double bootstrap resampling- outer loop

### References

Botha M, van Vuuren G (2010). “Implied asset correlation in retail loan portfolios.” Journal of Risk Management in Financial Institutions, 3(2), 156–173.

Chang J, Hall P (2015). “Double-bootstrap methods that use a single double-bootstrap simulation.” Biometrika, 102(1), 203–214.

Efron B, Tibshirani RJ (1994). An introduction to the bootstrap. CRC press.

Gordy MB (2000). “A comparative anatomy of credit risk models.” Journal of Banking & Finance, 24(1), 119–149.

Vasicek O (1991). “Limiting loan loss probability distribution.” Finance, Economics and Mathematics, 147–148.

### Examples

set.seed(111)
d=defaultTimeseries(1000,0.3,20,0.01)
n=rep(1000,20)

IntraCorr=intraMode(d,n)

#Jackknife correction
IntraCorr=intraMode(d,n, JC=TRUE)

#Bootstrap correction with confidence intervals
IntraCorr=intraMode(d,n, B=1000, CI_Boot=0.95 )

#Bootstrap correction with confidence intervals and plot
IntraCorr=intraMode(d,n, B=1000, CI_Boot=0.95, plot=TRUE )

#Double Bootstrap correction with 10 repetitions in the inner loop and 50 in the outer loop
IntraCorr=intraMode(D1,N1, DB=c(10,50))

[Package AssetCorr version 1.0.4 Index]