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Extreme events - A Summary [7]

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Bullet points include: Very widely observed phenomenon. Fits our intuition – sometimes markets seem more turbulent than at other times. Distributional mixtures of Normal distributions. E.g. draw X1 with probability p from N1, draw X2 with probability (1-p) from N2. Quite different behaviour to linear combination mixtures, i.e. a.X1 + b.X2. If N1 and N2 have same mean but different standard deviations then distributional mixture fat-tailed (if p NE 0 or 1) but not linear combination mixture. Time-varying volatility creates an analogous effect. Because we are in effect drawing from different distributions at different times

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