Non-Uniform Nested Simulation Algorithms in Portfolio Risk Measurement

Abstract

In this paper we deal with the computational burden for estimating quantile based risk measures such as Valueat- Risk using Monte Carlo simulation. The estimator is a conditional expectation type estimator where two stage simulation are needed to compute the risk measure : an outer simulation for risk factors and inner simulation are used to reprice the portfolio conditioned on the risk factors. We propose a new set of algorithm based on a non uniform distribution of the computational budget between risk factors scenarios. The algorithms give more importance to scenario that are more likely to have a direct impact on the value of the estimator. At the end, we demonstrate using simple experimental settings that our set of algorithm outperforms the uniform one and results in a lower variance and bias with the same initial settings and resources.