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day1pnl


Total Posts: 5
Joined: Jun 2017
 
Posted: 2017-10-07 20:14
Nice example gentinex.

Genti-traxx S1 tranche indications


Ref = 1/3
FTD 0.33 / 0.55 vs 1.18x
2TD 0.11 / 0.33 vs 0.82x

All tranches quoted in protection upfront
Widest names: A, B.


Just to expand it a bit further. Let's suppose in addition to P(A) = 1/3 and P(B) = 1/3 that the "true" correlation is 50% and that any single name default triggers a cds pay of full notional (zero recovery for simplicity).

With the correlation assumption we now have
P(exactly 2 defaults) = P(A) * P(B) + corr x sqrt[P(A) * (1-P(A)) * P(B) * (1-P(B))] = 1/9 + 50% * (2/9) = 2/9
P(exactly 1 defaults) = P(A) + P(B) - 2 * P(exactly 2 defaults) = 1/3 + 1/3 - 2 * (2/9) = 2/9
P(exactly 0 defaults) = 5/9

So a 2nd-to-default on those two names will have a "correlation vega" of +$0.22 per correlation point per $100 notional traded (as seen from protection buyer). Not sure if I now interpret this correctly, but the single name delta would be dP(exactly 2 defaults)/dP(A) = P(B) + 50% * (1/6) = 5/12 ~ 0.41 so that protection buyer is long protection of approximately +$0.41 per probability point. That is, to hedge directional risk, trader should sell $41 worth of protection on each name for every $100 2nd-to-default traded (which seems like a little bit of an an oversell.. hm..).

Anyways.. On the other hand if the credit B, say, defaults overnight, he would have to fork out $41 in payments on the single name cds. The 2nd-to-default basket, however, would only lose subordination and will simply now become a cds on name A. Recalling that the names are correlated, the probability of the 2nd-to-default contract defaulting (or, equivalently the single name A) goes to

P(A|B) = P(B) + corr x sqrt[P(A) / P(B) * (1-P(A)) * (1-P(B))] = 1/3 + 50% * (2/3) = 2/3

So before the first event he was oversold, and after it actually a bit short I suppose..
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