Correlation in Practice
This chapter looks at the variety of ways the correlated default time model can be applied in practice and the advantages and disadvantages associated with each approach. The final section also looks at other ways in which the default time model could be applied.
21.1 TRANCHE CORRELATION
21.1.1 Valuation and Key Features
We first illustrate some features of tranche correlation. The ‘fair premium’ for a tranche is the premium that makes the net value of the tranche (calculated today) equal to zero: equation (20.12) is equal to zero if p is the fair premium. The fair premium changes as the life of the deal and the spreads, etc., on the underlying names change - it is unrelated to a fixed agreed premium on the tranche. Restating the above, the expected loss on the tranche (at any moment) is equal to the (then) valuation of the fair premium stream.
Table 21.1 and Figures 21.1-Figures 21.3 show the calculated fair premium on a 5-year 125 name reference pool with iTraxx tranching for the various tranches. The results are typical but change in detail according to the maturity of the deal, tranche attachment and detachment points, and spreads and recoveries on the underlying names.
The following features are typical:
1. The fair premium for the most junior tranche [0, x] (x = 3 in this example) decreases monotonically as correlation increases.
Think for a moment how the default time correlation works. At zero correlation the defaults of individual names ...