In systemicrisk: A Toolbox for Systemic Risk

An example using the fitness model

This document describe a toy example for the use of the package systemicrisk.

library(systemicrisk)

Suppose we observe the following vector of total liabilities and todal assets.

l <- c(714,745,246, 51,847)
a <- c(872, 412, 65, 46,1208)

The following sets up a model for 5 banks:

mod <- Model.additivelink.exponential.fitness(n=5,alpha=-2.5,beta=0.3,gamma=1.0,
                 lambdaprior=Model.fitness.genlambdaparprior(ratescale=500))

Choosing thinning to ensure sample is equivalent to number of

thin <- choosethin(l=l,a=a,model=mod,silent=TRUE)
thin

Running the sampler to produce 1000 samples.

res <- sample_HierarchicalModel(l=l,a=a,model=mod,nsamples=1e3,thin=thin,silent=TRUE)

Some examples of the matrics generated are below.

res$L[[1]]
res$L[[2]]

The sampler produces samples from the conditional distribution of matrix and parameter values given the observed data. To see the posterior distribution of the liabilities of Bank 1 towards Bank 2:

plot(ecdf(sapply(res$L,function(x)x[1,2])))

Diagnostic of the R-output

All the caveats of MCMC algorithms apply. In particular the samples are dependent.

Some automatic diagnostic can be generated via the function diagnose.

diagnose(res)

Trace plots of individual liabilities also shoud show rapid mixing - as seems to be the case for the liabilities of Bank 1 towards Bank 2.

plot(sapply(res$L,function(x)x[1,2]),type="b")

Trace plot of the fitness of bank 1.

plot(res$theta[1,],type="b")

Also, the autocorrelation function should decline quickly. Again, considering the liabilities between bank 1 and bank 2:

acf(sapply(res$L,function(x)x[1,2]))

In this case it decays quickly below the white-noise threshold (the horizontal dashed lines).

systemicrisk documentation built on May 2, 2019, 9:26 a.m.