VaR stress tests for highly non‐linear portfolios

John H.J. Einmahl (Tilburg University, Tilburg, The Netherlands)
Walter N. Foppen (Rabobank International, Utrecht, The Netherlands)
Olivier W. Laseroms (Interpolis Re, Tilburg, The Netherlands)
Casper G. de Vries (Erasmus University, Rotterdam, The Netherlands)

Journal of Risk Finance

ISSN: 1526-5943

Publication date: 1 December 2005



It is the purpose of this article to improve existing methods for risk management, in particular stress testing, for derivative portfolios. The method is explained and compared with other methods, using hypothetical portfolios.


Closed form option pricing formulas are used for valuation. To assess the risk, future price movements are modeled by an empirical distribution in conjunction with a semi‐parametrically estimated tail. This approach captures the non‐linearity of the portfolio risk and it is possible to estimate the extreme risk adequately.


It is found that this method gives excellent results and that it clearly outperforms the standard approach based on a quadratic approximation and the normal distribution. Especially for very high confidence levels, the improvement is dramatic.

Practical implications

In applications of this type the present method is highly preferable to the classical Delta‐Gamma cum normal distribution approach.


This paper uses a “statistics of extremes” approach to stress testing. With this approach it is possible to estimate the far tail of a derivative portfolio adequately.



Einmahl, J., Foppen, W., Laseroms, O. and de Vries, C. (2005), "VaR stress tests for highly non‐linear portfolios", Journal of Risk Finance, Vol. 6 No. 5, pp. 382-387.

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Copyright © 2005, Emerald Group Publishing Limited

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