This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). Making use of Malliavin calculus, we recast the traditional Euler contributions from an expectation conditional to an event of zero probability to a ratio of conditional expectations , where both the numerator and the denominator's conditioning events have  positive probability. For several different modelswe show empirically that the estimator using this novel representation has no perceivable bias and variance smaller than a standard estimator used in practice .
This paper is concerned with the process of risk allocation for a generic multivariate model when the risk measure is chosen as the Value-at-Risk (VaR). We recast the traditional Euler contributions from an expectation conditional on an event of zero probability to a ratio involving conditional expectations whose conditioning events have stricktly positive probability. We derive an analytical form of the proposed representation of VaR contributions for various parametric models. Our numerical experiments show that the estimator using this novel representation outperforms the standard Monte Carlo estimator in terms of bias and variance . Moreover, unlike the existing estimators, the proposed estimator is free from hyperparameters .
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Making use of Malliavin calculus, we
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on
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of conditional expectations , where both the numerator and the denominator's
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stricktly
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For several different modelswe show empirically
We derive an analytical form of the proposed representation of VaR contributions for various parametric models. Our numerical experiments show
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has no perceivable
outperforms the standard Monte Carlo estimator in terms of
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smaller than a standard estimator used in practice
. Moreover, unlike the existing estimators, the proposed estimator is free from hyperparameters