Philippe Muller: Computation of Risk Measures using Importance Sampling

Estimation of Value-at-Risk and expected shortfall using standard Monte Carlo can result in high computational cost. We make a review of importance sampling, a common method to make estimations more efficient. A direct approach to compute risk measures from simulations drawn from an importance sampling density is described in detail. We explain how to select an efficient importance sampling distribution for loss probability estimations in the case of normally distributed risk factor changes. Some algorithms for efficient risk measure computations are presented explicitly. By considering numerical examples, we analyse the effect of regularly updating the importance sampling density during the simulation process.

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