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Title: Virtual historical simulation for estimating the conditional VaR of large portfolios Authors:  Jean-Michel Zakoian - CREST (France) [presenting]
Christian Francq - CREST and University Lille III (France)
Abstract: In order to estimate the conditional risk of a portfolio's return, two strategies can be advocated. A multivariate strategy requires estimating a dynamic model for the vector of risk factors, which is often challenging, when at all possible, for large portfolios. A univariate approach based on a dynamic model for the portfolio's return seems more attractive. However, when the combination of the individual returns is time varying, the portfolio's return series is typically non stationary which may invalidate statistical inference. An alternative approach consists in reconstituting a virtual portfolio, whose returns are built using the current composition of the portfolio and for which a stationary dynamic model can be estimated. The asymptotic properties of this method, that we call Virtual Historical Simulation (VHS), are established. Numerical illustrations on simulated and real data are provided.