Filtered Historical Simulation in VAR Models

Historical simulation is becoming a widely used methodology for modeling financial risks of the Capital market. It is one of the standard methodologies for Value at Risk models. Major exchanges, such as Chicago Mercantile Exchange, started to adapt historical simulation methodology as marginal models instead of stress testing models and the parametric models. Among different approaches of the historical simulations, the filtered historical approach is one of the most common approaches. The approach aims to reflect the stylized facts of the behavior of the markets, such as the correlation of the realized volatility and the underlying. In this work, we will revisit the statistical evidence of the relationship of volatility and the underlying. We will assess the impact of the scaling on model outputs. This research offers two new aspects, a different approach of defining the scaling, and an illustration of the effect of the scaling under different market conditions.