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The example is a portfolio of two obligors X and Y, with a small number of credit states to make the calculations tractable. Using the joint migration matrix above, we have a probability for each cell, and all sum to 1. Mapping credit spreads with ratings serves to value exposures. The spreads by risk class are given in Table 49.2, using only three states, inclusive of the default state (risk class 3).

The assumptions for the calculations of the value distribution of the portfolio as of end of year 1(Eoy1)are:

• All facilities are zero-coupons with 2-year maturity and an identical terminal final flow of 100. The 2-year maturity allows us to conduct value calculations at both the current date and the horizon date, 1 year in the future.

• The loss under default is 100% of exposure.

• The risk-free rate is 6% and the yield curve is flat.

• Credit spreads represent the difference between the flat risk-free curve and the risky yieldtomaturity.

• Credit spreads are also identical for the first year and for the second year.

For the two zero-coupons, the current values discount a final flow of 100 at the risky yield to maturity YTM, including the credit spread. The corresponding values are given in Table 49.3, with a total portfolio value of X + Y of 173.619.