First-to-Default Credit Swap: what is the payoff when a joint default occurs

Question

I keep reading about the impact of default correlation on the pricing of a First-to-Default (FtD) credit default swap (CDS). What no one explains is how a joint default event impacts the actual payoff of the FtD CDS. If we assume that it is impossible that more than one names can default at exactly the same time then I cannot see how default correlation matters. If on the other hand the probability of joint default is not zero, then it can only impact the valuation if upon a joint default of two or more names the payoff somehow changes (perhaps the term sheet specifies that the worst credit is redeemed). But in none of the books, papers and other treatises has anyone deemed appropriate to explain what actually happens when a joint default occurs. Now is the time for someone to do this...

Answer 1

I am not a lawyer.

I do have some old $n$th to default term sheets just lying around. Reading them, I interpret their language to work very similarly to the cheapest-to-delver language in single-name CDS. To emphasize again this is just my understanding of some complex legalese and I could well be missing something.

Recall that with the single-name CDS, after the credit event, the protection buyer can either physically deliver one of the obligations pari passu with the reference obligation; or pay cash amount determined at the auction. Natually, the protection buyer will choose whichever is the cheapest for him.

My interpretation of the term sheets is that if the $n$th and the $n+1$st credit events happen similtaneously, then the protection buyer can either physically deliver one of the obligations pari passu with either the $n$th or the $n+1$st reference obligation; or pay cash amount determined at either $n$th or the $n+1$st auction. Again, we can expect the the protection buyer to choose the cheapest. The protection buyer chooses which event to serve notice on, and which physical defaulted obligation, or cash to deliver.

Further, if only the $n$th event occurs, then the protection buyer can still choose to wait for the $n+1$st (or $n+2$nd etc) event to occur, and then serve notice on the protection seller for the $n+1$st event (or $n+2$nd etc). I don't see that the buyer is obligated to serve notice on the $n$th event and is not allowed to wait for a more favorable event.

However, sorry, I'm not sure how this connects to default correlation.

Suppose, as an extreme example, that you buy first to default ptotection on UMS sovereign and PEMEX and CFELEC (quasi's). Suppose than one of the quasis defaults Monday and another quasi defaults Wednesday, and finally the sovereign defaults Friday. You'd choose which notice to deliver based on your belief who has lower recovery, which would probably be one of the quasis. But if the sovereign never defaults, only the quasis do, then you'd still collect on the defaulted quasi of your choice (paying premium until the day of the event you choose to serve notice for).