I have a question about nth to default CDS that I'm not clear. Say for 2nd to default CDS, after 1 default, how do we pay the premium fee? Do we adjust the total notional to exclude that name? Or we still pay based on the notional from the beginning?I looked for various reference, they don't say it clearly which seems pretty obvious.Thanks for your information...

adjust to exclude defaulting name

Purchasing a 2nd to default basket on N names.After first default the price should be the same as purchasing a 1st to default on the remaining N-1 names.

Thanks for your answers.madmax's answer is contrary to what I thought. And Monte Carlo results using adjusted notional are off Hull White's Analytical Copula model. For RedAlert, what I'm trying to understand is the pricing mechanism you originally paid when you bought this 2nd to default (Monte Carlo) ...PS: If nth to default did happen, the protection payoff should be (1 - Ri)*N, Rn is the recovery rate for ith name (with nth to default) , and N is the total notional for all those names in basket (whether defaults or not). Am I right?

I had exactly the same problem yesterday when I started the Monte Carlo pricing.You need to understand how a basket CDS works. While I am not an expert myself, here's an except from Douglas Lucas and Alberto Thomas of UBS that I came across in their article "Nth to default swaps and notes: all about default correlation". It considers a third to default swap with a notional of USD 10 million. Mind you, this notional is the notional of the basket CDS as a whole and is not specific to a particular entity in the basket. "Upon the default of the the third credit in our example, the protection seller pays default losses associated with the reference credit to the protection buyer and the swap termintaes. In physical settlement, the protection buyer of USD 10 million notional swap delivers USD 10 million par of a deliverable obligation of the defaulted name to the protection seller. The protection seller pays USD 10 million to the protection buyer. The protection seller is then free to retain or sell the obligation as it sees fit. In cash settlement, the market price of USD 10 million par of the deliverable obligation of the defaulted name is determined through a specified process of dealer polling. The protection seller pays the protection buyer the difference between USD 10 million and the determined market value of the deliverable obligation. Note that the severity of default losses associated with the first and second defaults among the reference credits does not make a difference to the payout under a 3rd to default swap.After paying default losses on the nth to default credit, th eprotection seller has no responsibility for subsequent defaults of reference entities." So according to what I gather, the notional is fixed and does not change with the initial n-1 defaults in an nth to default. Upon default, if the terms are of physical settlement, the protection buyer fetches from market, bonds of the defaulted entity for the face value equal to notional and the protection seller either keeps them or sell them and considers that the recovery.So in a monte carlo instance, expected recovery rate of the nth to default entity would matter and rest n-1 would not matter. Suppose one wants to un-wind the deal during its life, say a 3rd-to-default for which 1 default has already happen, to mark it to market, it'd be needed to remodel the basket with one less entity and treat it as 2nd-to-default.Please correct me if my understanding is flawed, excuse the verbosity.

there are two types of ntd, one that pays out only on the nth default and one that pays on each default