day1pnl


Total Posts: 30 
Joined: Jun 2017 


Nice example gentinex.
Gentitraxx 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) * (1P(A)) * P(B) * (1P(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 2ndtodefault 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 2ndtodefault 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 2ndtodefault 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 2ndtodefault contract defaulting (or, equivalently the single name A) goes to
P(AB) = P(B) + corr x sqrt[P(A) / P(B) * (1P(A)) * (1P(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.. 


