Virtual Historical Simulation for estimating the conditional VaR of large portfolios

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.JEL Classification: C13, C22 and C58.

Generalized dynamic factor models and volatilities: Consistency, rates, and prediction intervals

“…The literature on Glivenko-Cantelli and quantile consistency under ergodicity and mixing is abundant, and we will not proceed with imposing any specific mixing conditions here which anyway hardly can be checked from the data. The reader may like to refer to Theorem 3.1 in Francq and Zakoian (2019) for details.…”

Pathwise grid valuation of fixed-income portfolios with applications to risk management

“…To solve this problem, they propose a generic simulation-based algorithm to calculate the VaR for nonlinear portfolios. Francq and Zakoian (2020) propose a new method called Virtual Historical Simulation to estimate the ES of large-scale portfolios. This method avoids facing challenges such as estimating a dynamic model for the vector of risk factors.…”