interCov {AssetCorr}

Covariance Matching Estimator

Description

The inter correlation parameter can be estimated by matching the empirical covariance of two default time series with the theoretical. The estimated parameter is the inter correlation of the systematic factors.

Usage

interCov(d1, n1, d2, n2, rho1, rho2, B = 0, DB=c(0,0), JC = FALSE,
CI_Boot, type="bca", plot=FALSE)

Arguments

d1

a vector, containing the default time series of sector 1.

n1

a vector, containing the number of obligors at the beginning of the period in sector 1.

d2

a vector, containing the default times eries of sector 2.

n2

a vector, containing the number of obligors at the beginning of the period in sector 2.

rho1

estimated intra asset correlation of sector 1.

rho2

estimated intra asset correlation of sector 2.

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 level 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 confidence intervals. For more details see boot.ci.

plot

a logical variable, indicating whether a plot of the single bootstrap density should be generated.

Details

This function estimates the inter correlation of the systematic factors. In general, the inter correlation can be estimated for the asset variables or the systematic factors. To ensure the traceability of the estimation, the intra correlation estimates will be used as plug-in estimates. Hence only one parameter (inter correlation) must be estimated. The inter correlation of the systematic factors can be transformed to the correlation of the asset variables as follows:

rho_Asset= rho_Systematic*sqrt(rho_1*rho_2)

The estimated inter correlation of the systematic factors lies between -1 and 1.

If DB is specified, the single bootstrap corrected estimate will be calculated 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 single bootstrap resampling

iValues

Estimates from the double bootstrap resampling- inner loop

oValues

Estimates from the double bootstrap resampling- outer loop

References

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

Bluhm C, Overbeck L (2003). “Systematic risk in homogeneous credit portfolios.” Credit risk. Physica-Verlag, Heidelberg, 35–48.

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

See Also

interJDP, interCMM, interMLE, interCopula

Examples

set.seed(10)
d1=defaultTimeseries(1000,0.1,10,0.01)
d2=defaultTimeseries(1000,0.2,10,0.01)
n1=n2=rep(1000,10)

InterCorr=interCov(d1,n1,d2,n2,0.1,0.2)



InterCorr=interCov(d1,n1,d2,n2,0.1,0.2, JC=TRUE)
InterCorr=interCov(d1,n1,d2,n2,0.1,0.2, B=1000, CI_Boot=0.95)

InterCorr=interCov(d1,n1,d2,n2,0.1,0.2, DB=c(50,50))