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

K. Bujok (), B. M. Hambly () and C. Reisinger ()
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K. Bujok: Oxford University
B. M. Hambly: Oxford University
C. Reisinger: Oxford University

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 3, 579-604

Abstract: 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; 65C05; 60F10; 91G60; 91G40 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (11)

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DOI: 10.1007/s11009-013-9380-5

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