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Foundation ERM Session 8: Extreme Events and Extreme Value Theory (EVT)
This presentation is based on a part of an academic course on Enterprise Risk Management (ERM) titled ‘Extreme Events and Extreme Value Theory (EVT)’ and covers topics such as: what do we mean by extreme events and why are they relevant in a financial context, Extreme Value Theory (EVT) and a case study on wind storm losses using EVT
Slides
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Session 8: Extreme Events and Extreme Value Theory (EVT)
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Session 8: Extreme Events and Extreme Value Theory (EVT)
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Extreme events
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Analysing fat-tailed behaviour
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Anchoring versus experience
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Example QQ-plot (versus Normal)
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Many (most?) investment return series are ‘fat-tailed’
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More periods give more scope for extreme events
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Skew(ness), kurtosis and Cornish-Fisher
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Flaws in Cornish Fisher (and hence skew/kurtosis)
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Joint fat-tailed behaviour
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What causes fat-tailed behaviour?
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Time-varying volatility
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Explains some market index fat tails, esp. on upside
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A longer term phenomenon too
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Crowded trades and selection effects
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Session 8: Extreme Events and Extreme Value Theory (EVT)
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Extreme Value Theory (EVT)
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In case study we will focus on
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Extreme value theory (EVT) results
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Block maxima results
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Generalised extreme value (GEV) distribution
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Limiting behaviour
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Main result for threshold exceedances
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Potential weaknesses
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Using EVT to Estimate VaRs
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Maximum likelihood (ML) estimation of tails
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Estimate the quantile that starts the tail
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Combined estimate
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Choosing the threshold
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Judging the start of the tail
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Session 8: Extreme Events and Extreme Value Theory (EVT)
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Estimated loss quantiles in SEK m
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Other analyses included in case study
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Application to ERM
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Important Information
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