An Empirical Evaluation of Value at Risk by Scenario Simulation

Abstract

It has become standard practice for banks and financial institutions to calculate value at risk and similar measures of portfolio risk exposure on a regular basis. Typically, Monte Carlo simulation of fairly complex models is required. This creates a potentially enormous computational burden, especially when assets in multiple currencies are involved, that limits both the accuracy and the frequency that is feasible for the analysis. Using principal components to reduce the dimensionality of the set of underlying risk factors helps, but the need to revalue a large number of assets in each simulation run is still a major impediment. One recent suggestion has been to restrict each risk factor to take only a small number of distinct values, leading to a small (or, at last, manageable) number of possible “scenarios,” each corresponding to a portfolio value that only needs to be computed once. Monte Carlo simulation is then done by sampling among these scenarios, leading to a great reduction in the number of portfolio revaluations required. In this article, Abken explains these techniques in detail and examines their relative performance on a portfolio involving interest rate derivatives. Unfortunately, he finds that scenario simulation only converges slowly to the correct limiting values, and convexity of the derivative values significantly impairs the performance of scenario simulation relative to standard Monte Carlo.