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Extra resources for Return to RiskMetrics: The Evolution of a Standard
Monte Carlo methods are highly accurate, but are also computationally expensive. The second method is based on a parametric analysis that relies on the assumption that pricing functions are linear in the risk factors. Parametric methods provide very fast answers that are only as accurate as the underlying linearity assumption. An alternative to an explicit model for return distributions is the use of historical frequencies of returns. , volatilities and correlations) need to be estimated. This means that the historical data dictate the shape of the multivariate distribution of returns.
Hull and White (1998) present a volatility updating scheme; instead of using the actual historical changes in risk factors, they use historical 1 See Appendix A for a discussion of non-normal distributions. 25 CHAPTER 3. MODELS BASED ON EMPIRICAL DISTRIBUTIONS 26 changes that have been adjusted to reflect the ratio of the current volatility to the volatility at the time of the observation. 1 Historical simulation One can make use of the empirical distribution of returns and obtain risk statistics through the use of historical simulation.
Given the importance of including expert views on stress events and accounting for potential changes in every risk factor, we need to come up with user-defined scenarios for every single variable affecting the value of the portfolio. To facilitate the generation of these comprehensive user-defined scenarios, we have developed a framework in which we can express expert views by defining changes for a subset of risk factors (core factors), and then make predictions for the rest of the factors (peripheral factors) based on the user-defined variables.