On an Extension of Value at Risk and Its Applications

application/pdfIn the quantitative risk management, the estimation of risks plays an important step,and for this purpose, various kind of risk measures have been introduced so far. Value at Risk (VaR), which is defined normally on single random variable, is one of well employed risk measures. In this report, a new definition of copula-based conditional Value at Risk (CCVaR) is introduced, which is defined on multivariate random variables with copulas and real-valued. It is recognized that copula functions provide flexible tools to model possible nonlinear relations among several risk factors; the combination of VaR and copula gives a natural procedure to estimate risk of multivariate risk factors in a sense. We show several properties of this new copula-based risk measure. Empirical studies are also implemented, which verifies the usefulness of our CCVaR. Main contents of the present article are a summary of the part of the thesis by Andres Mauricio Molina Barreto (2020).departmental bulletin pape