UCLouvain Finance Seminar: Thorsten Schmidt

On the efficient estimation of risk

Thorsten Schmidt, University of Freiburg

The estimation of risk measures recently gained  a lot of attention, partly because of the backtesting issues of expected shortfall related to elicitability. In this work we shed a new and fundamental light on optimal estimation procedures of risk measures in terms of bias. We show that once the parameters of a model need to be estimated, one has to take additional care when estimating risks.  The typical plug-in approach, for example, introduces a bias which leads to a systematic \emph{underestimation} of risk.

In this regard, we introduce a novel notion of \emph{unbiasedness} to the estimation of risk which is motivated by economic principles. In general,  the proposed concept does not coincide with the well-known statistical notion of unbiasedness. We show that an appropriate bias correction is available for many well-known estimators.  In particular, we consider value-at-risk and expected shortfall (tail value-at-risk). In the special case of normal distributions, closed-formed solutions for unbiased estimators can be obtained.

We present a number of motivating examples which show the outperformance of unbiased estimators in many circumstances. The unbiasedness has a direct impact on backtesting and therefore adds a further viewpoint to established statistical properties.