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

In CreditMetrics: Functions for calculating the CreditMetrics risk model

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

Details

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

Value

Return value is the credit value at risk at confidence level α.

Author(s)

Andreas Wittmann andreas\[e-mail]

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)

Example output

     1% 
4063750 

CreditMetrics documentation built on May 2, 2019, 8:55 a.m.