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Unbiased Estimation of Risk
| Content Provider | Scilit |
|---|---|
| Author | Pitera, Marcin |
| Copyright Year | 2016 |
| Description | Journal: SSRN Electronic Journal 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 underestimation of risk. In this regard, we introduce a novel notion of 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. |
| Related Links | http://arxiv.org/pdf/1603.02615 https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=2890034 |
| ISSN | 10914358 |
| e-ISSN | 15565068 |
| DOI | 10.2139/ssrn.2890034 |
| Journal | SSRN Electronic Journal |
| Language | English |
| Publisher | Elsevier BV |
| Publisher Date | 2016-12-25 |
| Access Restriction | Open |
| Subject Keyword | Journal: SSRN Electronic Journal Statistics and Probability Tail Value-at-risk Expected Shortfall Estimation of Risk Measures Unbiased Estimation of Risk Measures |
| Content Type | Text |
| Resource Type | Article |
| Subject | Public Health, Environmental and Occupational Health Psychiatry and Mental Health |
