CreditMetrics (version 0.0-2)

cm.CVaR: Computation of the Credit Value at Risk (CVaR)

Description

cm.CVaR computes the credit value at risk for the simulated profits and losses.

Usage

cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, 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

alpha

confidence level

rating

rating of companies

Value

Return value is the credit value at risk at confidence level $\alpha$.

Details

With function cm.gain one gets the profit and loss distribution of the credit positions. By building the quantile at confidence level $\alpha$ the credit value at risk can be reached.

References

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

See Also

cm.matrix, cm.gain, quantile

Examples

  N <- 3
  n <- 50000
  r <- 0.03
  ead <- c(4000000, 1000000, 10000000)	
  rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
  lgd <- 0.45
  rating <- c("BBB", "AA", "B")	
  firmnames <- c("firm 1", "firm 2", "firm 3")
  alpha <- 0.99
  
  # 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.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)