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

2012/11/04 by Karolina Bujok, Ben Hambly, Bujok, Karolina +3 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Computational Finance (q-fin.CP) #FOS: Economics and business #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1211.0707

openalex publication_date 2012/11/04 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We consider N Bernoulli random variables, which are independent conditional\non a common random factor determining their probability distribution. We show\nthat certain expected functionals of the proportion L_N of variables in a\ngiven state converge at rate 1/N as N\→ \∞. Based on these\nresults, we propose a multi-level simulation algorithm using a family of\nsequences with increasing length, to obtain estimators for these expected\nfunctionals with a mean-square error of \ε² and computational\ncomplexity of order \ε^-2, independent of N. In particular, this\noptimal complexity order also holds for the infinite-dimensional limit.\nNumerical examples are presented for tranche spreads of basket credit\nderivatives.\n

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