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#### David Yip

##### New Member
Hi all
When asset correlation increases, the probability of any one reference entity defaulting is lower and hence the premium is lower?
Or should it be correlations increases, prob of multiple defaut also increases and hence premium increases?

Hope to hearing from u soon
Thanks

#### ShaktiRathore

##### Well-Known Member
Subscriber
in a basket CDS, with high correlation the probability of all CDS's defaulting simultaneously increases, while with low correlation the probability of all CDS's defaulting simultaneously decreases. Consider a sample space S with possible events that can take place. Now with high correlation basket let event be E1 as all CDS defaulting simultaneously and prob. of event=p(E1) where E1 represents almost same type of n CDS in basket.
With low correlation if there are n CDS than let E1,E2,...En be the events that any of the CDS can default than any one defaulting=p(E1)+p(E2)+p(E3)+......p(En) assuming that E1,E2....En are n independent CDS's.
From above its seen that p(E1)<p(E1)+p(E2)+p(E3)+......p(En)
=> prob. of default occurring in high correlation basket< prob. of default occuring in low correlation basket

thanks

##### New Member
Hi Shakti,
If we compare the probabilities of all defaulting in the condition that correlation = 1, it will be equal to p(A) for all in the basket ,while for correlation= 0, it is equal to [p(A)*p(B).......*p(N)] which is certainly less than p(A) alone. In such condition, for corr = 1 case the premium should be higher.
Thanks

#### ShaktiRathore

##### Well-Known Member
Subscriber
Consider the 1st to default CDS basket, here the chances of any one CDS defaulting is higher in a low correlation CDS than a high correlation CDS. Because the factors affecting CDS are quite different in low correlation CDS than chances of happening of any factor out of n factors is much more than in a high correlation CDS where only some particular factors affect n CDS so chances of happening of these some factors which can cause default is less. So simple logic is that chances of happening of any one factor out of a large number of factors is more than chances of happening of one factor out of some few factors. So risk for 1st to default low correlation CDS is much more than 1st to default high correlation CDS. So spread is more subsequently.

thanks

##### New Member
Consider the 1st to default CDS basket, here the chances of any one CDS defaulting is higher in a low correlation CDS than a high correlation CDS. Because the factors affecting CDS are quite different in low correlation CDS than chances of happening of any factor out of n factors is much more than in a high correlation CDS where only some particular factors affect n CDS so chances of happening of these some factors which can cause default is less. So simple logic is that chances of happening of any one factor out of a large number of factors is more than chances of happening of one factor out of some few factors. So risk for 1st to default low correlation CDS is much more than 1st to default high correlation CDS. So spread is more subsequently.

thanks

@ shakti, my logic was more from the "all defaulting" condition. It seems logical. So, essentially we are agreeing on that

1) risk of default of all 20 assets (in a basket of 20) is more in a high correlation compared to all defaulting in a low correlation; and
2) risk of 1 defaulting in a basket of 20 assets in a low correlation is more than that of 1 default in a high correlation

#### David Yip

##### New Member
Thx shakti and addityafrm, I got the same conclusion as well after exploring more!!!

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