CreditMetrics (version 0.0-2)

cm.ref: Computation of reference value

Description

cm.ref computes the value of a credit in one year for each rating, this is the return value constVal. Further the portfolio value at time t = 1 is computed, this is constPV.

Usage

cm.ref(M, lgd, ead, r, rating)

Arguments

M

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

lgd

loss given default

ead

exposure at default

r

riskless interest rate

rating

rating of companies

Value

• a list containing following components:
• constVal
  credit value in one year
• constPV
  portfolio of all credit values in one year

Details

This function computes the value of the credit in one year, this is $$V_t = EAD_t e^{-(r_t + CS_t) t}$$ where t = 1.

References

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

See Also

cm.matrix, cm.cs

Examples

r <- 0.03
  ead <- c(4000000, 1000000, 10000000)
  rating <- c("BBB", "AA", "B")
  lgd <- 0.45

  # 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.ref(M, lgd, ead, r, rating)