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

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