CreditMetrics (version 0.0-2)

cm.state: Computation of state space

Description

cm.state computes a state space, this is at time t = 1 the credit positions of all companies for all migrations is calculated. This state space is needed for the later valuation for the credit positions of each scenario.

Usage

cm.state(M, lgd, ead, N, r)

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

r

riskless interest rate

Value

• Return value is the matrix V for time t = 1 of each rating in the migration matrix including the credit values for all companies. The last column in the matrix V is the value for the default event of each company.

Details

This function computes the value of the credits of each firm in one year, this is $$V_t = EAD_t e^{-(r_t + CS_t) t}$$ where t = 1. Also the value for the default class is calculated, that is $$V_t = EAD (1 - LGD)$$

References

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

See Also

cm.matrix, cm.cs, matrix

Examples

N <- 3
  r <- 0.03
  ead <- c(4000000, 1000000, 10000000)
  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.state(M, lgd, ead, N, r)