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Title: Joint-VaR: A new conditional risk measure Authors:  Leopoldo Catania - Aarhus BBS (Denmark)
Alessandra Luati - University of Bologna (Italy)
Elisabetta Mensali - University of Bologna (Italy) [presenting]
Abstract: The Joint Value at Risk (JVaR) is defined as the quantile of an asset return distribution, given an upper tail event affecting its log-volatility. The purpose of JVaR is to measure financial risk under a volatility stress scenario. A distinguishing feature of the proposed risk measure is that conditioning events are latent. The relations with the VaR and the CoVaR, that is, the VaR conditional to some observed event, are made explicit. The properties of JVaR are studied based on a stochastic volatility representation of the underlying process. We prove that JVaR is leverage consistent, i.e. it is an increasing function of the dependence parameter in the stochastic representation. The difference between the JVaR and its reference state, represented by the VaR, provides a natural tool for monitoring risk. A feasible class of semiparametric M-estimators is introduced by exploiting the elicitability of quantiles and the stochastic ordering theory. Consistency and asymptotic normality of the proposed JVaR M-estimator are derived in two steps based on the pair (VaR, JVaR), and its finite-sample properties are illustrated in a simulation study. Empirical results with S\&P500 data show that accounting for extreme volatility levels is relevant to characterize the evolution of risk better.