8 Tail estimation

Given a set of price changes (or log-retums) X1, … Xn for some asset, it is important to estimate the tail behavior. If the price changes Xt are identically distributed6 with X and P(X>r)~Cr−α, then the dispersion C and the tail index α determine the central limit behavior, as well as the extreme value behavior, of the price change distribution. Mandelbrot (1963) pioneered a graphical estimation method for C and α. If y=P(X>r) ≈ r−α then logylogC-Ρlogrsi376_e. Ordering the data so that X(1)X(2)X(n)si377_e we should have approximately that ...

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