Facoltà di scienze economiche

Applying and testing VaR estimation methods for non-linear portfolios

Fierli, Francesco

In the first part of this work, some of the most known VaR estimation methods are described. In such a description we try to focus mainly on the application problems of each approach, which are modified to take into account non-linear positions. In particular, some generalizations of the standard historical simulation and of the filtered historical simulation methods are shown. The second part is... More

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    Summary
    In the first part of this work, some of the most known VaR estimation methods are described. In such a description we try to focus mainly on the application problems of each approach, which are modified to take into account non-linear positions. In particular, some generalizations of the standard historical simulation and of the filtered historical simulation methods are shown. The second part is devoted to measuring the performances of the different estimation methods by testing them on the last two years data (including the recent NAS-DAQ crash). The observed variables are the number of times that the loss exceed VaR and the mean of the ratio between the losses which exceed VaR and the VaR itself. For linear portfolios all the methods give quite accurate results, while for portfolios containing options the best performances are given by the non-parametric and the semi-parametric methods. The main contribution of this paper is to show how the generalized historical simulation methods perfom better than the standard ones during high volatily periods.