cal.claytonmix {QRMlib}R Documentation

Calibrate Mixture of Bernoullis Equivalent to Clayton Copula Model

Description

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.

Usage

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

Arguments

pi1 default probability
pi2 joint default probability

Details

see page 362 in QRM

Value

parameters pi and theta for Clayton copula default model

See Also

cal.beta, cal.probitnorm, rclaytonmix, 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]