Accounting for risk of non linear portfolios: a novel Fourier approach
AbstractThe presence of non linear instruments is responsible for the emergence of non Gaussian features in the price changes distribution of realistic portfolios, even for Normally distributed risk factors. This is especially true for the benchmark Delta Gamma Normal model, which in general exhibits exponentially damped power law tails. We show how the knowledge of the model characteristic function leads to Fourier representations for two standard risk measures, the Value at Risk and the Expected Shortfall, and for their sensitivities with respect to the model parameters. We detail the numerical implementation of our formulae and we emphasizes the reliability and efficiency of our results in comparison with Monte Carlo simulation.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1002.4817.
Date of creation: Feb 2010
Date of revision: May 2010
Publication status: Published in Eur. Phys. J. B 76 157-165 (2010)
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