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Stress Testing and Back-testing for UCITS [9]

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Bullet points include: Often we are particularly interested in a specific quantile point, i.e. level of ‘unlikelihood’, rather than in the entire distributional form. E.g. VaR at 99.5% confidence level involves a 99.5% (or 0.5%) quantile point. We can focus on just one quantile by defining a hit (‘violation’) sequence, It(k) = 1 if outcome at time t is beyond quantile point k, = 0 otherwise. We want acceptable unconditional coverage, i.e. actual probability of occurrence when averaged through time to match expected probability of occurrence. Test using, say, Kupiec’s test statistic or a z-statistic, comparing observed number of hits versus expected number, rejecting model fit if the two deviate too far from each other in a statistical sense

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