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We consider $N$ Bernoulli random variables, which are independent conditionalon a common random factor determining their probability distribution. We showthat certain expected functionals of the proportion $L_N$ of variables in agiven state converge at rate $1/N$ as $N\rightarrow \infty$. Based on theseresults, we propose a multi-level simulation algorithm using a family ofsequences with increasing length, to obtain estimators for these expectedfunctionals with a mean-square error of $\epsilon^2$ and computationalcomplexity of order $\epsilon^{-2}$, independent of $N$. In particular, thisoptimal complexity order also holds for the infinite-dimensional limit.Numerical examples are presented for tranche spreads of basket creditderivatives.

Multilevel simulation of functionals of Bernoulli random variables with application to basket credit derivatives