inst/doc/AssetCorr_vignette.R

In AssetCorr: Estimating Asset Correlations from Default Data

## ----setup, include=FALSE-----------------------------------------------------
library(knitr)

## -----------------------------------------------------------------------------
library(AssetCorr)
set.seed(111)

#number of obligors: 1000
#intra asset correlation: 0.3
#length of the default time series: 20
#probability of default: 0.01

D1=defaultTimeseries(1000,0.3,20,0.01)
N1=rep(1000,20)

## -----------------------------------------------------------------------------
intraAMM(D1,N1)

## -----------------------------------------------------------------------------
Output<-intraAMM(D1,N1, B=1000, CI_Boot = 0.95, plot=TRUE)

Output$Original
Output$Bootstrap
Output$CI_Boot

## -----------------------------------------------------------------------------
Output<-intraAMM(D1,N1, DB=c(100,100))

Output$Original
Output$Bootstrap
Output$Double_Bootstrap


## -----------------------------------------------------------------------------
intraAMM(D1,N1, JC=TRUE)


## -----------------------------------------------------------------------------
Output<-intraALL(D1,N1, B=500, plot=TRUE,Adjust = 0.0001, Estimator = c("AMM","FMM","CMM","JDP1","JDP2","AMLE") )
Output


## -----------------------------------------------------------------------------
library(mvtnorm)
set.seed(2)
#number of obligors: 1000
#intra asset correlation 1: 0.3
#intra asset correlation 2: 0.1
#inter correlation of the systematic factors: 0.5
#length of the default time series: 20
#probability of default: 0.01

Psi=rmvnorm(20,sigma=matrix(c(1,0.5,0.5,1),2))
PDcond1=pnorm((qnorm(0.01)-sqrt(0.3)*Psi[,1])/sqrt(1-0.3))
PDcond2=pnorm((qnorm(0.01)-sqrt(0.1)*Psi[,2])/sqrt(1-0.1))

D1=rbinom(20,1000,PDcond1)
D2=rbinom(20,1000,PDcond2)
N1=N2=rep(1000,20)

## -----------------------------------------------------------------------------
rho1=intraAMM(D1,N1)$Original
rho2=intraAMM(D2,N2)$Original

interCov(D1,N1,D2,N2,rho1,rho2)

## -----------------------------------------------------------------------------
#Single bootstrap Correction
rho1=intraAMM(D1,N1)$Original
rho2=intraAMM(D2,N2)$Original

Output<- interCov(D1,N1,D2,N2,rho1,rho2, B=1000, CI_Boot = 0.95, plot=TRUE)

Output$Original
Output$Bootstrap
Output$CI_Boot

#Double bootstrap correction

Output<- interCov(D1,N1,D2,N2,rho1,rho2, DB=c(100,100))

Output$Original
Output$Bootstrap
Output$Double_Bootstrap

#Furthermore, a Jackknife correction would be possible

## -----------------------------------------------------------------------------
#A general overview

Output<-interALL(D1,N1,D2,N2,rho1,rho2 ,B=100, plot=TRUE)
Output



## -----------------------------------------------------------------------------
#A general overview

library(mvtnorm)
set.seed(111)
NoO=1000 #Number of obligors in each sector
Years=20
AC=0.3
PD=0.01

#Calculate the conditional PDs:
Psi=rmvnorm(Years,sigma=matrix(c(1,0.5,0.5,0.5,1,0.5,0.5,0.5,1),3))
PDcond1=pnorm((qnorm(PD)-sqrt(AC)*Psi[,1])/sqrt(1-AC))
PDcond2=pnorm((qnorm(PD)-sqrt(AC/2)*Psi[,2])/sqrt(1-AC/2))
PDcond3=pnorm((qnorm(PD)-sqrt(AC*2)*Psi[,3])/sqrt(1-AC*2))


#Draw the default time series, depending on the conditional PDs
DTS=cbind(rbinom(Years,NoO,PDcond1),rbinom(Years,NoO,PDcond2),rbinom(Years,NoO,PDcond3))
N=matrix(NoO,nrow = Years,ncol = 3)

Output<-analyze_AssetCorr(DTS,N, B=100, Intra = c("AMM","FMM","CMM","JDP1"), Inter=c("Copula","Cov","JDP"))

#Furthermore, the analyze_AssetCorr function also proves single/double bootstrap 
#and Jackknife corrections. Additionally, the confidence intervals
#can be estimated and visualized.