Unformatted text preview: 1.89M−1.236M = 0.654M lel over for the junior tranche, for a loss of 18.25%. • If senior tranche’s interest is less senior than junior tranche’s capital, then – Senior tranche gets its capital back, 1.2M – 1.89M−1.2M = 0.7M lel over for the junior tranche, for a loss of 12.5% Example, con:nued • In any case, the senior tranche’s capital is untouched if there are four or fewer defaults. • The number of defaults also greatly inﬂuences how well or badly the junior tranche performs. Independent defaults • If defaults are independent, the probability of k=4 or fewer defaults is ⎛ 10 ⎞ n 10 − n
0.1 0.9
= 0.910 + 10 ⋅ 0.1 ⋅ 0.9 9 + 45 ⋅ 0.12 ⋅ 0.9 8
∑⎜ n ⎟
⎠
n=0 ⎝
k 10!
10!
⋅ 0.13 ⋅ 0.9 7 +
⋅ 0.14 ⋅ 0.9 6
3!⋅ 7!
4 !⋅ 6!
≈ 0.348678 + 0.387420 + 0.193710 + 0.057396 + 0.011160
+ ≈ 0.998 • The probability that the senior tranche loses...
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 Spring '08
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