Estimating future value-at-risk from value samples, and applications to future initial margin

Abstract

Predicting future value-at-risk is an important problem in finance. It arises in the modeling of future initial margin requirements for counterparty credit risk and future market value-at-risk. We are also interested in derived quantities such as both dynamic initial margin and margin value adjustment in the counterparty risk context and risk-weighted assets and capital value adjustment for market risk. This paper describes several methods that can be used to predict future value-at-risk. We begin with the nested Monte Carlo empirical quantile method as a benchmark, but it is too computationally intensive for routine use. We review several known methods and discuss their novel applications to the problem at hand. The techniques that are considered include computing percentiles from distributions (normal and Johnson) that were matched to estimates of moments and percentiles, quantile regressions methods and others with more specific assumptions or requirements. We also consider how limited inner simulations can be used to improve the performance of these techniques. The paper also provides illustrations, results and visualizations of intermediate and final results for the various approaches and methods.