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 . Ordering the data so that
we should have approximately that ...
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