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Value-at-Risk Models
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In this chapter, we build first a univariate and then a multivariate filtered historical simulation
(FHS) model for financial risk management. Both the univariate and multivariate methods
simulate future returns from a model using historical return innovations. While the former
relies on portfolio returns filtered by a dynamic variance model, the latter uses individual or
base asset return innovations from dynamic variance and correlation models. The univariate
model is suitable for passive risk management or risk measurement whereas the multivariate
model is useful for active risk management such as optimal portfolio allocation. Both models
are constructed in such a way as to capture the stylized facts in daily asset returns and to be
simple to estimate. The FHS approach enables the risk manager to easily compute Value-at-
Risk and other risk measures including Expected Shortfall for various investment horizons that
are conditional on current market conditions. The chapter also lists various alternatives to the
suggested FHS approach.