Virtual Historical Simulation for estimating the conditional VaR of large portfolios

TL;DR

This paper introduces Virtual Historical Simulation, a method for estimating the conditional VaR of large portfolios by constructing a stationary 'virtual portfolio' to simplify dynamic risk modeling.

Contribution

It establishes the asymptotic properties of Virtual Historical Simulation, offering a new approach for risk estimation in large, non-stationary portfolios.

Findings

Method is theoretically validated with asymptotic properties.

Numerical results demonstrate effectiveness on simulated data.

Application to real data shows practical utility.

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.