intraMode: Parametric Approach of...
In AssetCorr: Estimating Asset Correlations from Default Data

Description Usage Arguments Details Value References See Also Examples

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.

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

`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.

As stated by \insertCitebotha2010implied;textualAssetCorr one can estimate the intra correlation by matching the theoretical and empirical mode. According to \insertCitevasicek1991;textualAssetCorr 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 \insertCitevasicek1991;textualAssetCorr:

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).

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

\insertRef

botha2010impliedAssetCorr

\insertRef

chang2015doubleAssetCorr

\insertRef

efron1994introductionAssetCorr

\insertRef

gordy2000comparativeAssetCorr

\insertRef

vasicek1991AssetCorr

intraFMM, intraJDP1, intraJDP2 intraCMM, intraMLE, intraAMLE, intraBeta

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))