8. Simulating the Term Structure of Risk
This chapter introduces simulation methods for computing VaR and ES when the horizon of interest is longer than one day. The simulation based methods introduced here allow the risk manager to use dynamic risk models to compute VaR and ES at any horizon of interest and therefore to compute the entire term structure of risk. We will introduce two techniques: Monte Carlo simulation, which relies on artificial random numbers, and Filtered Historical Simulation, which uses historical random shocks. First, we will consider simulating forward univariate risk models. Second, we simulate forward in time multivariate risk models with constant correlations across assets. Third, we simulate multivariate risk models ...

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