Design of an algorithm for an adaptive Value at Risk measurement through the implementation of robust methods in relation to asset cross-correlation

Abstract

This study proposes an algorithmic approach for selecting among different Value at Risk (VaR) estimation methods. The proposed metaheuristic, denominated as “Commitment Machine” (CM), has a strong focus on assets cross-correlation and allows to measure adaptively the VaR, dynamically evaluating which is the most performing method through the minimization of a loss function. The CM algorithm compares five different VaR estimation techniques: the traditional historical simulation method, the filtered historical simulation (FHS) method, the Monte Carlo method with correlated assets, the Monte Carlo method with correlated assets which uses a GARCH model to simulate asset volatility and a Bayesian Vector autoregressive model. The heterogeneity of the compared methodologies and the proposed dynamic selection criteria allow us to be confident in the goodness of the estimated risk measure. The CM approach is able to consider the correlations between portfolio assets and the non-stationarity of the analysed time-series in the different models. The paper describes the techniques adopted by the CM, the logic behind model selection and it provides a market application case of the proposed metaheuristic, by simulating an equally weighted multi-asset portfolio.