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

## Author Info

• Karolina Bujok
• Ben Hambly
• Christoph Reisinger
Registered author(s):

## 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 $N\rightarrow \infty$. 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 $\epsilon^2$ and computational complexity of order $\epsilon^{-2}$, 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.

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File URL: http://arxiv.org/pdf/1211.0707

## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1211.0707.

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 Length: Date of creation: Nov 2012 Date of revision: Handle: RePEc:arx:papers:1211.0707 Contact details of provider: Web page: http://arxiv.org/

## References

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1. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2011. "Large Portfolio Asymptotics for Loss From Default," Papers 1109.1272, arXiv.org, revised Feb 2015.
2. Denis Belomestny & John Schoenmakers & Fabian Dickmann, 2013. "Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 17(4), pages 717-742, October.
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