Reduction of Value-at-Risk bounds via independence and variance information

VaR Bounds for Joint Portfolios with Dependence Constraints

“…This paper continues the streamline of easily computable and practical bounds on VaR which has been initiated in [6] and further extended in [26]. Based on a novel extension of classical Hoe ding-Fréchet bounds, we provide an upper VaR bound for a joint risk portfolio with xed marginal distributions and positive dependence information assumed on a subset of the domain of its distribution function.…”

“…E ects of this dependence information on the reduction of the VaR bounds are described in [6] and in [2]. Some higher order marginal information has been investigated in [13], [23], [14], and in [26]. The reduction of VaR bounds by inclusion of additional second or higher order moment information was described in [3] and in [4].…”

A Practical Approach to Quantitative Model Risk Assessment

“…Puccetti, Rüschendorf, and Manko (2016) considered the value-at-risk upper bounds in the case where positive dependence information is assumed in the tails or some central part of the distribution function. In Puccetti et al (2017), independence among (some) subgroups of the marginal components is assumed, a fact that leads to a considerable improvement in the value-at-risk bounds as compared with the case where only the marginals are known (see Theorems 4 and 5).…”

“…Bertsimas, Lauprete, and Samarov (2004) derived value-at-risk bounds when only the mean and a maximum variance of the portfolio loss can be trusted (see Theorem 7). Moreover, Puccetti et al (2017) derived bounds when information on the maximum variance of the portfolio loss is assumed in addition to the knowledge of the marginals and the independence among some subgroups of the marginals (see Theorem 8).…”

“…One can easily check such a relation statistically and by intuition. In the following theorems we present VaR bounds derived in Puccetti et al (2017) in scenarios where all or some of the subgroups of the portfolio are assumed independent.…”