# 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

1 | ```
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 |

### 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.

### Value

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

### Author(s)

Andreas Wittmann andreas\_wittmann@gmx.de

### References

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

### See Also

`cm.matrix`

, `eigen`

, `cm.state`

, `cm.quantile`

,
`cm.rnorm.cor`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | ```
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)
``` |

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