  We explore the possibilities of importance sampling in the Monte Carlo
pricing of a structured credit derivative referred to as Collateralized Debt
Obligation (CDO). Modeling a CDO contract is challenging, since it depends on a
pool of (typically about 100) assets, Monte Carlo simulations are often the
only feasible approach to pricing. Variance reduction techniques are therefore
of great importance. This paper presents an exact analytic solution using
Laplace-transform and MC importance sampling results for an easily tractable
intensity-based model of the CDO, namely the compound Poissonian. Furthermore
analytic formulae are derived for the reweighting efficiency. The computational
gain is appealing, nevertheless, even in this basic scheme, a phase transition
can be found, rendering some parameter regimes out of reach. A
model-independent transform approach is also presented for CDO pricing.
