Stress testing techniques and value-at-risk measures: A unified approach

Abstract

We investigate a methodology to set up consistent scenarios for stress testing analysis in financial risk control and management. The method, based on the Black and Litterman bayesian approach to portfolio optimization, enables to mix historic and implied or private information, accounting for the co-movement among the markets. By tuning the mean values chosen for the scenarios and the degree of precision attached to them we are able to devise a whole range of mean loss and maximum probable loss, or Value-at-Risk measures. In particular, by setting a very precise scenario the mean and maximum probable loss converge toward similar values, while for very imprecise scenarios the mean loss figure is found to converge to zero, and the maximum probable loss collapses to the standard Value-at-Risk figure computed using historical information. As for options, we show that tuning the precision of the scenarios allows for the effects of changes in volatility on the option value, under each different scenarios. Finally, for more complex positions, such as those involving credit risk exposures, or more generally exposures to different markets, we suggest a tree methodology to report the scenarios and to pinpoint the key sources of risk.