Multivariate extreme value analysis quantifies the probability and magnitude of joint extreme events. Classical multivariate models, such as max-stable or multivariate generalised Pareto distributions, generally have a high computational cost of fitting, which limits their application. To overcome this, models based on the asymptotically dependent multivariate Pareto distribution have recently incorporated graphical models to induce sparsity and reduce the dimension of the parameter space. While this approach is computationally efficient, the assumption of asymptotic dependence is inappropriate for many applications. The conditional multivariate extreme value model (CMEVM) is a popular model for which the asymptotic dependence assumption is not required. Unfortunately, inference for this model is semi-parametric, and consequently, it has poor predictive performance in high dimensions. An extension of the CMEVM that allows both the incorporation and selection of sparse dependence structures, and fully parametric prediction is proposed. The approach fills a current gap in statistical methodology by extending graphical models to asymptotically independent multivariate extreme value models. To support inference in high dimensions, a stepwise inference procedure that is computationally efficient and loses no information or predictive power is proposed. Simulation studies show the model is highly flexible, and an application to discharges in the upper Danube River basin provides promising results.

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