caa a22 4500 605519587 CHVBK 20210128100731.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s11009-013-9380-5 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9380-5 Multilevel Simulation of Functionals of Bernoulli Random Variables with Application to Basket Credit Derivatives [Elektronische Daten] [K. Bujok, B. Hambly, C. Reisinger] 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. Springer Science+Business Media New York, 2013 Multilevel Monte Carlo simulation nationallicence Large deviations principle nationallicence Exchangeability nationallicence Basket credit derivatives nationallicence Bujok K. Mathematical Institute, Oxford University, 24-29 St Giles, Oxford, OX1 3LB, UK aut Hambly B. Mathematical Institute, Oxford University, 24-29 St Giles, Oxford, OX1 3LB, UK aut Reisinger C. Mathematical Institute, Oxford University, 24-29 St Giles, Oxford, OX1 3LB, UK aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 579-604 1387-5841 17:3<579 2015 17 11009 https://doi.org/10.1007/s11009-013-9380-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9380-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bujok K. Mathematical Institute, Oxford University, 24-29 St Giles, Oxford, OX1 3LB, UK aut NATIONALLICENCE 700 1- Hambly B. Mathematical Institute, Oxford University, 24-29 St Giles, Oxford, OX1 3LB, UK aut NATIONALLICENCE 700 1- Reisinger C. Mathematical Institute, Oxford University, 24-29 St Giles, Oxford, OX1 3LB, UK aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/3(2015-09-01), 579-604 1387-5841 17:3<579 2015 17 11009