Beyond VaR: parametric and simulation-based risk management tools

Financial institutions worldwide have devoted much effort to developing enterprise-wide systems that integrate financial information across their organizations to measure their institution's risk. Probabilistic measures such as value-at-risk (VaR), are now widely accepted by both financial institutions and regulators for assigning risk capital and monitoring risk. Since development efforts have been driven largely by regulatory and internal requirements to report risk numbers, tools needed to understand and manage risk across the enterprise have generally lagged behind those designed to measure it. The paper presents an extended simulation based risk management toolkit developed on top of the analytical tools presented by R. Litterman (1996; 1997). Simulation based tools provide additional insights when the portfolio contains nonlinearities, when the market distributions are not normal or when there are multiple horizons. In particular, these tools should prove very useful not only for market risk, but also for credit risk, where the exposure and loss distributions are generally skewed and far from normal. We also demonstrate that simulation based tools can be used, sometimes even more efficiently, with other risk measures in addition to VaR. Indeed, they also uncover limitations of VaR as a coherent risk measure, as demonstrated by P. Artzner et al. (1998). We focus in particular on constructing useful visualizations of risk, as provided by triangular decompositions and trade risk profiles, and calculating relevant risk measures such as marginal VaR and VaR contributions.