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Extreme Events and Portfolio Construction [16]

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Bullet points include: Suppose interested in risk measures relating to losses, xj. EVT aims to supply two closely related results: Less relevant to risk management: Distribution of ‘block maxima’ (or ‘block minima’), i.e. maximum value of xi in blocks of m observations of x, tends to a Generalised Extreme Value (GEV) distribution. More relevant to risk management: Distribution of ‘threshold exceedances’ (i.e. ‘peaks-over-thresholds’) tends to a generalised Pareto distribution (GPD) . Here u is a predetermined high threshold and we focus on realisations of xj that exceed u, i.e.:

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