cal.probitnorm {QRMlib}R Documentation

Calibrate Probitnormal Mixture of Bernoullis

Description

calibrates a probitnormal mixture distribution on unit interval to give an exchangeable Bernoulli mixture model with prescribed default and joint default probabilities

Usage

cal.probitnorm(pi1=0.1837, pi2=0.0413)

Arguments

pi1 default probability
pi2 joint default probability

Details

see page 354 in QRM

Value

parameters mu and sigma for probitnormal mixing distribution as well as the implied asset correlation rho.asset

See Also

cal.beta, cal.claytonmix, dprobitnorm, rbinomial.mixture

Examples

pi.B <- 0.2; pi2.B <- 0.05 
probitnorm.pars <- cal.probitnorm(pi.B,pi2.B) 
probitnorm.pars 
beta.pars <- cal.beta(pi.B,pi2.B) 
beta.pars 
claytonmix.pars <- cal.claytonmix(pi.B,pi2.B) 
claytonmix.pars 
q <- (1:1000)/1001; 
q <- q[q<0.25]; 
p.probitnorm <- pprobitnorm(q,probitnorm.pars[1],
               probitnorm.pars[2]); 
p.beta <- pbeta(q, beta.pars[1], beta.pars[2]); 
p.claytonmix <- pclaytonmix(q,claytonmix.pars[1],
                  claytonmix.pars[2]); 
scale <- range((1-p.probitnorm),(1-p.beta),(1-p.claytonmix)); 
plot(q, (1 - p.probitnorm), type = "l", log = "y", xlab = "q", 
           ylab = "P(Q>q)",ylim=scale); 
lines(q, (1 - p.beta), col = 2); 
lines(q, (1 - p.claytonmix), col = 3); 
legend("topright", c("Probit-normal", "Beta", "Clayton-Mixture"), 
          lty=rep(1,3),col = (1:3)) 

[Package QRMlib version 1.4.4 Index]