RTransProb (version 0.1.0)

duration.TTC: Duration - Data Weighting and "TTC" Calculation

Description

Calculating Through-the-Cycle generator matrix and transition counts using duration method

Usage

duration.TTC(lstCnt,lstInit,gYear,snapshots,nStates,transtype,TotalDateRange)

Arguments

lstCnt

annual off-diagonal transition counts (matrix)

lstInit

Initial counts for each state (start vector)

gYear

count of annual date vector.

snapshots

integer indicating the number of credit-rating snapshots per year to be considered for the estimation. Valid values are 1, 4, or 12. The default value is 1, i.e., one snapshot per year. This parameter is only used in the 'cohort' algorithm.

nStates

number of rating categories.

transtype

averaging method. The valid values

• transRaw

• genAverage

• transAverageGen

• transAverage

• individualAnnualTrans

TotalDateRange

annual date vector.

Value

transRaw

transition matrix created from generator matrix created using the average annual transition counts and average annual.

genAverage

average annual generator matrix.

transAverageGen

transition matrix from average annual generator matrix.

transAnnual

individual annual transition matrices.

Details

Given data representing x years of monthly off-diagonal transition counts, this function combines those data to obtain average monthly counts, in such a way as to preserve the information while implementing a weighting scheme that would allow for the weighting of the historical experiences.

Let \(T(m,y)\) and \(F(m,y)\) represent the off-diagonal transition matrix and 'firm-years' vector, for month = \(m\) and year = \(y\), respectively. Then, $$T(m,y) = \{T_{ij}(m,y)\}_{i,j\,=\,1,\ldots,K}$$ $$F(m,y) = \{F_{i}(m,y)\}_{i\,=\,1,\ldots,K}$$

Many credit risk models require a long-run average PD estimate. This has been interpreted as meaning the data from multiple years should be combined and in a method capable of supporting some form of weighting of samples. The three methods of weighting considered for data generated via the duration method are:

1. Scale the number of transitions and firm counts/years using the a single year count to preserve dynamics, then average transitions and firms counts/years separately to create a generator matrix.

2. Estimate the single-year quantities (annual generator matrices), then average across years

3. Average annual transition matrices

The Markov property allows for direct weighting as each year can be regarded as distinct.

Examples

# NOT RUN {
TotalDateRange <- seq(as.Date("2000-01-01"), as.Date("2002-01-01"), "years")

snapshots <- 1    #This uses a 1 year transition matrices
interval <- 1     #This gives a 1 year transition matrix

lstCnt <-rep(list(list()), length(TotalDateRange)-1)
lstInit <-rep(list(list()), length(TotalDateRange)-1)
kk <- 1
k <- 1

#Create transition and inital countsused as inputs to the function
for (l in 1:(length(TotalDateRange)-1)){

  istartDate = POSIXTomatlab(as.POSIXlt(as.Date(TotalDateRange[l],format = "%Y-%m-%d")))
  iendDate = POSIXTomatlab(as.POSIXlt(as.Date(TotalDateRange[l+1],format = "%Y-%m-%d")))
  DateRange        <- as.Date(matlabToPOSIX(cfdates(istartDate,iendDate,snapshots)))

  for(i in 1:(length(DateRange)-1)){

    sDate  <- DateRange[i]       # i.e "3/31/1990"
    eDate    <- DateRange[i+1]     # i.e "6/30/1990"

    t<-TransitionProb(data,sDate, eDate, 'duration', snapshots, interval)

    lstCnt[[k]][[kk]] <- t$sampleTotals$totalsMat
    lstInit[[k]][[kk]]  <- t$sampleTotals$totalsVec

    if(kk>=snapshots){
      kk <- 1
      k <- k+1
    } else {
      kk <- kk+1
    }

  }

}



transtype <- "genAverage"
gYear <- utils::head(TotalDateRange,-1)
nStates <- nrow(as.data.frame(lstInit[[1]][1]))

AverageGeneratorMatrices<-duration.TTC(lstCnt,lstInit,gYear,snapshots,nStates,transtype,
TotalDateRange)

# }