8 - Simulating the Term Structure of Risk

Abstract

The purpose of this chapter is to introduce Monte Carlo simulation and filtered historical simulation techniques, which can be used to compute the term structure of risk in the univariate risk models. Multivariate filtered historical simulation is done easily when one assumes constant correlations. In addition, when correlations across assets are assumed to be constant then filtered historical simulation (FHS) is relatively easy because one can draw from historical asset shocks, using the entire vector of historical shocks. The historical correlation is preserved in the simulated shocks. When correlations are dynamic then one requires ensuring that the correlation dynamics are simulated forward but in FHS one can use the historical shocks. The advantages of the multivariate FHS approach tally with those of the univariate case: it captures current market conditions by means of dynamic variance and correlation models. It makes no assumption on the conditional multivariate shock distributions. It also allows for the computation of any risk measure for any investment horizon of interest.