BETTER CONFIDENCE INTERVALS FOR IMPORTANCE SAMPLING

Halis Sak (), Wolfgang Hörmann () and Josef Leydold ()
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Halis Sak: Department of Statistics and Mathematics, WU (Vienna University of Economics and Business), Augasse 2–6, A-1090 Wien, Austria
Wolfgang Hörmann: Department of Industrial Engineering, Boğaziçi University, 34342 Bebek-İstanbul, Turkey
Josef Leydold: Department of Statistics and Mathematics, WU (Vienna University of Economics and Business), Augasse 2–6, A-1090 Wien, Austria

International Journal of Theoretical and Applied Finance (IJTAF), 2010, vol. 13, issue 08, 1279-1291

Abstract: It is well known that for highly skewed distributions the standard method of using the t statistic for the confidence interval of the mean does not give robust results. This is an important problem for importance sampling (IS) as its final distribution is often skewed due to a heavy tailed weight distribution. In this paper, we first explain Hall's transformation and its variants to correct the confidence interval of the mean and then evaluate the performance of these methods for two numerical examples from finance which have closed-form solutions. Finally, we assess the performance of these methods for credit risk examples. Our numerical results suggest that Hall's transformation or one of its variants can be safely used in correcting the two-sided confidence intervals of financial simulations.

Keywords: Confidence intervals; skewness removal; Hall's transformation; importance sampling; quantitative risk management (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219024910006200

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