Virtual Historical Simulation for estimating the conditional VaR of large portfolios

Christian Francq and Jean-Michel Zakoļan
Keywords: Accuracy of VaR estimation, Dynamic Portfolio, Estimation risk, Filtered Historical Simulation, Virtual returns.
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. This paper establishes the asymptotic properties of this method, that we call Virtual Historical Simulation. Numerical illustrations on simulated and real data are provided.
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Archive with the R codes and data sets for the numerical illustrations of the paper R (extract the zip file and see the file readme.txt for an explanation of the R codes)