RTransProb (version 0.3.3)

duration.CI: Bootstrapped confidence intervals - Duration

Description

estimate confidence intervals for the transition probabilities using a bootstrapping procedure for duration method

Usage

duration.CI(genMat,portWgts,nHorizon,sim)

Arguments

genMat

generator matrix

portWgts

list containing weights of each rating class

nHorizon

horizon

sim

number of simulations

Value

Returns the default probabilites values for the n ratings at the 2.5, 5, 25, 50, 75, 95, 97.5 percentiles.

Details

The general idea of bootstrapping is to use resampling methods to estimate features of the sampling distribution of an estimator, especially in situations where asymptotic approximations may provide poor results. In the case of a parametric bootstrap method one samples from the estimated distribution derived using maximum likelihood estimation. In summary,

1. Estimate the distribution from the observed sample using maximum likelihood

2. Draw samples from the estimated distribution

3. Calculate the parameter of interest from each of the samples

4. Construct an empirical distribution for the parameter of interest

5. Select percentiles from the empirical distribution

One can contrast this method with a nonparametric bootstrap in which one samples with replacement from the empirical cumulative distribution function of the observed sample.

A parametric bootstrapping method is employed for the time-homogeneous continuous-time Markov model. The elements of the infinitesimal generator matrix, provide most of the information one needs to perform the parametric bootstrap. The outline of the bootstrapping is provided below.

For each obligor in a given assigned credit grade:

1. Start by drawing a (sojourn) time from the exponential distribution with parameter, \(-\hat{\lambda}_{kk}\)

2. If the time is greater than or equal to the time left to horizon then stop

3. If the time is less than the time left to horizon

   • Draw from the multinomial distribution associated with the possible transition states using the vector of probabilities

   • Determine the state to which the obligor moves, for example, \(i\)

   • Repeat the process in 1. now using the diagonal element, \(-\hat{\lambda}_{ii}\)

   • Continue until the sampled time exceeds the time to horizon

References

Hanson, S. and Schuermann, T. 2005 Confidence Intervals for Probabilities of Default, Federal Reserve Bank of New York

Jafry, Y. and Schuermann, T. 2003 Metrics for Comparing Credit Migration Matrices, Wharton Financial Institutions Working Paper 03-08.

Loffler, G., P. N. Posch. 2007 Credit Risk Modeling Using Excel and VBA. West Sussex, England, Wiley Finance

Trueck, Stefan, (February 16, 2009) Simulating Dependent Credit Migrations. Available at SSRN: https://ssrn.com/abstract=1344897

Examples

# NOT RUN {
startDate  <- "2000-01-01"
endDate    <- "2005-01-01"
method       <- "duration" 
snapshots <- 4
interval  <-  0
Example1  <-getPIT(data,startDate, endDate,method, snapshots, interval)

lstInit <- Example1$lstInitVec[lapply(Example1$lstInitVec,length)>0]
lstCnt <-  Example1$lstCntMat[lapply(Example1$lstCntMat,length)>0]
ExampleTTC1<-duration.TTC(Example1$lstCntMat,Example1$lstInitVec)


genMat   <- ExampleTTC1$WGM
portWgts <- ExampleTTC1$SWFY[,1]
nHorizon <- length(ExampleTTC1$UUPTM[[1]])
sim      <- 100

tolerance_Duration <- duration.CI(genMat,portWgts,nHorizon,sim)
# }
# NOT RUN {
# }