Backtesting within the trading book

Gerhard Stahl, Carsten S.Wehn* and Andreas Zapp

Journal of Risk

Abstract: ABSTRACT The regulatory requirements for backtesting the forecast quality of models for market risk consider the trading book as a whole, whereas in fact the trading book is the product of a process that aggregates nested portfolios. This structure mirrors in detail the trading activities related to different risk categories, trading desks or locations. In this paper, we analyze the portfolio tree’s data matrix of risk forecasts and associated realized gains or losses by applying statistical methods to assess the common distribution of the different random variables and the respective aggregation scheme. This structural feature has not so far been considered in the literature on backtesting. It is of particular practical relevance not only for on-site inspections but also to enable financial institutions to identify sub-portfolios with suspect forecast quality. In addition, we deploy contamination model-like methods to assess the adequacy of risk forecasts at the different portfolio levels. The methods we develop are applied to real-life data.

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