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Methods for Computing Numerical Standard Errors: Review and Application to Value-at-Risk Estimation

David Ardia EMAIL logo , Keven Bluteau and Lennart F. Hoogerheide

Abstract

Numerical standard error (NSE) is an estimate of the standard deviation of a simulation result if the simulation experiment were to be repeated many times. We review standard methods for computing NSE and perform a Monte Carlo experiments to compare their performance in the case of high/extreme autocorrelation. In particular, we propose an application to risk management where we assess the precision of the value-at-risk measure when the underlying risk model is estimated by simulation-based methods. Overall, heteroscedasticity and autocorrelation estimators with prewhitening perform best in the presence of large/extreme autocorrelation.

Acknowledgements

All analyses have been performed in the R statistical language (Core Team 2015) with the package nse (Ardia and Bluteau 2017) available at https://github.com/keblu/nse. We thank the Fonds de Recherche du Québec – Société et Culture and Industrielle–Alliance for their financial support. All errors and omissions are the sole responsibility of the authors.

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Published Online: 2018-07-21

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