CreditMetrics (version 0.0-2)

cm.val: Valuation for the credit positions of each scenario

Description

cm.val performs a valuation for the credit positions of each scenario. This is an allocation in rating classes identification of the credit position values.

Usage

cm.val(M, lgd, ead, N, n, r, rho, rating)

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

Value

Simulated values of the firms for each rating of each scenario.

Details

According to the value $V_t$ the company is located in an other rating class. This location is performed with the migration matrix by determining the thresholds. In order to implement a valuation at time t, the credit spreads must be computed. With these the nominal is risk adjusted calculated. For a portfolio with many credits correlations are included by simulating correlated company yield returns. So the simulated ratings for each firm at time t = 1 can be computed.

References

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

See Also

cm.matrix, eigen, cm.state, cm.quantile, cm.rnorm.cor

Examples

  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.val(M, lgd, ead, N, n, r, rho, rating)