## 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 $logy≈logC-Ρlogr$. Ordering the data so that $X(1)≥X(2)≥…≥X(n)$ we should have approximately that ...

Get Handbook of Heavy Tailed Distributions in Finance now with the O’Reilly learning platform.

O’Reilly members experience live online training, plus books, videos, and digital content from nearly 200 publishers.