Unbiased Estimation of Risk

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 talk, the speaker will discuss the optimal estimation procedures in terms of bias and relate them to backtesting. The typical risk estimation procedure consist of two separate steps: in the first step the speaker estimate the distribution of the future P&Ls; in the second step the distribution is considered as a true distribution and the targeted risk-measure is computed. In the parametric case, this is achieved by using the formula for the risk-measure in the model and inserting the estimated parameters. The speaker will outline selected estimation methods and show that most of them underestimate the risk. The speaker will introduce a novel notion of unbiasedness which is motivated from economic principles and show that the bias correction is possible for many well-established estimation procedures. Surprisingly, in the normal framework, one can even obtain new closed-form solutions for unbiased estimators for Value-at-Risk or Expected Shortfall that outperforms the classical ones.