Explanation:
Option (B) is false. The default01 sensitivity is highly dependent on the correlation level. Changing the correlation alters the loss distribution, which in turn shifts the default01 sensitivity curves for different tranches. Therefore, default01 is not invariant to correlation levels.
Option (A) is true as tranche values decrease monotonically with an increase in default probability, meaning default01 is always positive. Option (C) is true because at very high default rates, tranches are completely wiped out, so a marginal change in default rate has no further impact (default01 converges to zero). Option (D) is true because the equity tranche absorbs the first losses, so its peak sensitivity is at a default probability of zero. The mezzanine and senior tranches are hit at progressively higher default rates based on their attachment points.
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315.1. According to Malz, "The default01 measures the impact of an increase of one (1) basis point in the default probability. It is analogous to the DV01 and the spread01 and is calculated numerically in a similar way. To compute the default01, we increase and decrease default probability 10bps and revalue each tranche at these new [default probability] values ... Each default01 is expressed as a positive number and expresses the decline in value or increase in loss resulting from a 1-basis point rise in default probability."¹⁶
Each of the following is true about default01 EXCEPT, which is false?
A
For all tranches, in all cases, default01 is positive regardless of the initial value of default probability correlation since equity and bond values decrease monotonically as the default probability rises
B
Because default01 "models correlation as constant according to an implicit ceteris paribus," default01 is invariant (insensitive) to different correlation levels
C
The default01 sensitivity converges to zero for all the tranches for very high default rates
D
The peak default01 is at a default probability of zero for the equity tranche (its attachment point) and occurs at a lower default rate for the mezzanine than for the senior tranche because it has a lower attachment point