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Methodology and Computing in Applied Probability

, Volume 17, Issue 3, pp 579–604 | Cite as

Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives

  • K. Bujok
  • B. M. Hambly
  • C. Reisinger
Article

Abstract

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.

Keywords

Multilevel Monte Carlo simulation Large deviations principle Exchangeability Basket credit derivatives 

AMS 2000 Subject Classifications

65C05 60F10 91G60 91G40 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematical InstituteOxford UniversityOxfordUK

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