Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives
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We consider N Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion L N of variables in a given state converge at rate 1/N as N → ∞. Based on these results, we propose a multi-level simulation algorithm using a family of sequences with increasing length, to obtain estimators for these expected functionals with a mean-square error of ϵ 2 and computational complexity of order ϵ −2, independent of N. In particular, this optimal complexity order also holds for the infinite-dimensional limit. Numerical examples are presented for tranche spreads of basket credit derivatives.
KeywordsMultilevel Monte Carlo simulation Large deviations principle Exchangeability Basket credit derivatives
AMS 2000 Subject Classifications65C05 60F10 91G60 91G40
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