| cal.probitnorm {QRMlib} | R Documentation |
calibrates a probitnormal mixture distribution on unit interval to give an exchangeable Bernoulli mixture model with prescribed default and joint default probabilities
cal.probitnorm(pi1=0.1837, pi2=0.0413)
pi1 |
default probability |
pi2 |
joint default probability |
see page 354 in QRM
parameters mu and sigma for probitnormal mixing distribution as well as the implied asset correlation rho.asset
cal.beta,
cal.claytonmix,
dprobitnorm,
rbinomial.mixture
pi.B <- 0.2; pi2.B <- 0.05;
probitnorm.pars <- cal.probitnorm(pi.B,pi2.B);
probitnorm.pars;
## Not run:
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);
abline(h = 0.01);
legend(0.05, 1e-4, c("Probit-normal", "Beta",
"Clayton-Mixture"), lty=rep(1,3),col = (1:3));
## End(Not run)