intraAMM {AssetCorr}

Asymptotic Method of Moments Estimator

Description

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

Usage

intraAMM(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 Vasicek (1991) and Vasicek (2002), the asset variables follow a bivariate normal distribution. Since this distribution can be parametrized by the first two moments, namely the expected value and the variance, the remaining correlation parameter can be backed out numerically. The expected value will be approximated by the mean of the default rate and the variance is defined as the sample variance of the default rate. For theoretical background, see Gordy (2000). 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

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.

Vasicek O (2002). “The distribution of loan portfolio value.” Risk, 15(12), 160–162.

See Also

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

Examples

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

IntraCorr=intraAMM(d,n)

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


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

#Bootstrap correction with confidence intervals and plot
IntraCorr=intraAMM(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=intraAMM(d,n, DB=c(10,50))