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

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  • Karolina Bujok
  • Ben Hambly
  • Christoph Reisinger

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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  • Karolina Bujok & Ben Hambly & Christoph Reisinger, 2012. "Multilevel simulation of functionals of Bernoulli random variables with application to basket credit derivatives," Papers 1211.0707, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1211.0707
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    References listed on IDEAS

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    1. 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.
    2. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2007. "Large Deviations In Multifactor Portfolio Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 17(3), pages 345-379, July.
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    4. 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.
    5. Nick Bush & Ben M. Hambly & Helen Haworth & Lei Jin & Christoph Reisinger, 2011. "Stochastic evolution equations in portfolio credit modelling with applications to exotic credit products," Papers 1103.4947, arXiv.org, revised Apr 2011.
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