cal.claytonmix {QRMlib} | R Documentation |
calibrates a mixture distribution on unit interval to give an exchangeable Bernoulli mixture model with prescribed default and joint default probabilities. The mixture distribution is the one implied by a Clayton copula model of default.
cal.claytonmix(pi1=0.1837, pi2=0.0413)
pi1 |
default probability |
pi2 |
joint default probability |
see page 362 in QRM
parameters pi and theta for Clayton copula default model
cal.beta
,
cal.probitnorm
,
rclaytonmix
,
rbinomial.mixture
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))