Profit / Loss Distribution histogram

Description

cm.hist plots a histogram for the simulated profit / loss distribution.

Usage

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cm.hist(M, lgd, ead, N, n, r, rho, rating,
        col = "steelblue4", main = "Profit / Loss Distribution",
        xlab = "profit / loss", ylab = "frequency")

Arguments

M

one year empirical migration matrix, where the last row gives the default class.

lgd

loss given default

ead

exposure at default

N

number of companies

n

number of simulated random numbers

r

riskless interest rate

rho

correlation matrix

rating

rating of companies

col

a colour to be used to fill the bars, the default is 'steelblue4'.

main

an overall title for the plot, the default is 'Profit / Loss Distribution'.

xlab

a title for the x axis, the default is 'profit / loss'.

ylab

a title for the y axis, the defualt is 'frequency'.

Details

This function gives a histogram of the simulated profits and losses. The 'breaks' of the histogram are obtained through the minimum and the maximum of the simulated values and the number of simulated random numbers. This is

\mbox{breaks} = (\max (\mbox{SimGV}) - \min (\mbox{SimGV})) / 2n

Value

A histogram of the the simulated profit and loss distribution.

Author(s)

Andreas Wittmann andreas\_wittmann@gmx.de

References

Glasserman, Paul, Monte Carlo Methods in Financial Engineering, Springer 2004

See Also

cm.matrix, cm.gain, hist

Examples

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  N <- 3
  n <- 50000
  r <- 0.03
  ead <- c(4000000, 1000000, 10000000)
  lgd <- 0.45
  rating <- c("BBB", "AA", "B")
  firmnames <- c("firm 1", "firm 2", "firm 3")
  
  # correlation matrix
  rho <- matrix(c(  1, 0.4, 0.6,
                  0.4,   1, 0.5,
                  0.6, 0.5,   1), 3, 3, dimnames = list(firmnames, firmnames),
                  byrow = TRUE)

  # one year empirical migration matrix from standard&poors website
  rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
  M <- matrix(c(90.81,  8.33,  0.68,  0.06,  0.08,  0.02,  0.01,   0.01,
                 0.70, 90.65,  7.79,  0.64,  0.06,  0.13,  0.02,   0.01,
                 0.09,  2.27, 91.05,  5.52,  0.74,  0.26,  0.01,   0.06,
                 0.02,  0.33,  5.95, 85.93,  5.30,  1.17,  1.12,   0.18,
                 0.03,  0.14,  0.67,  7.73, 80.53,  8.84,  1.00,   1.06,
                 0.01,  0.11,  0.24,  0.43,  6.48, 83.46,  4.07,   5.20,
                 0.21,     0,  0.22,  1.30,  2.38, 11.24, 64.86,  19.79,
                    0,     0,     0,     0,     0,     0,     0, 100
              )/100, 8, 8, dimnames = list(rc, rc), byrow = TRUE)
              
  cm.hist(M, lgd, ead, N, n, r, rho, rating,
          col = "steelblue4", main = "Profit / Loss Distribution",
          xlab = "profit / loss", ylab = "frequency")