Analytical risk contributions for non-linear portfolios

The value-at-risk of portfolios needs to account for non-linear effects in the loss distribution’s dependence on risk factors. Using the classical Cornish-Fisher expansion, Helmut Lutz and Carsten Wehn derive analytical formulas for risk contributions to the VAR by applying the Euler principle that aid capital allocation across sub-portfolios, and save computing time and data volume in comparison with a traditional Monte Carlo approach

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Estimating and controlling exposure to different kinds of risk is an important task for every financial institution. It is market practice to measure risks in terms of value-at-risk, that is, as a quantile of the portfolio’s loss distribution over a given time horizon. Once the calculation of VAR has been done at a group or portfolio level, the question of distributing the corresponding risk capital adequately back to portfolios and their risk factors is of crucial importance for managing the

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