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They cannot be coputed directly. It is a static model. You can estimate the Greeks by shifting the market-data inputs, but there are no analytic formulas. Since most firms calculate Greeks by shifting data, regardless of the availability of analytic formulas, this is not a bad possibility. The difficult part is determining which sensitivities you may want to hedge against.
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What is the base correlation in a credit derivative pricing model?
While compound correlation is the correlation found by calibrating the Gaussian copula model to the price of a CDO tranche (for example 3-6%), base correlation is found by calibrating to the price of a first loss tranche, i.e. to the sum of all tranches up to an attachment point (for example 0-6%, the sum of 0-3% and 3-6%). The curve of correlations obtained by calibrating to first loss tranches turns out to be much smoother and more stable than that obtained by calibrating to plain tranches.
What is a copula in a church?
I think you mean cupola which is latin for 'small cup' and is a cup-like structure that crests belltowers, dome, etc. Usually found on churches because of a law that should make the church a highest building in a town. In order to get the extra height, a cupola is usually built.
