Stochastics for the worst case: distributions and risk measures for minimal returns

Distributions for returns are used to compute the capital charge for portfolios in investment banks. The mainstream definition of returns is based on closing prices and neglects the important effects of intraday trading activity on the losses . In this paper we introduce ''minimal returns'', a definition of returns that accounts for intraday trading and gives a worst-case approach on losses. We suggest an appropriate distribution for minimal returns that can be used to compute Value at Risk and coherent risk measures, as suggested by Artzner et al. (1997).