# Credit quotations with which ISDA models?

I understand that single name liquid CDSs are (roughly speaking) quoted through either upfront+coupon, spread or price, and that for the pricing, the ISDA standard model is used : among other hypotheses the default intensity $\lambda$ is supposed constant.

• How are quoted cds indexes ? Are only tranches of cds indexes quoted ?
• I saw a (maturity, tranche) quotation, what does it mean ? That's, which market model is used ? I heard the same standard model than the one for single names is used : what does that mean ?
• As far as I understand no correlation is involved for cds indexes, does the "cds index ISDA standard model" assume that all default time are independant with the same constant default intensity ?
• As far as I understand, for CDOs (standard or bespoke), the correlation comes into play : how are they quoted, and through which market model ?
• options on cds index tranches : od they exist ? how are they quoted ? which market model is used ?