Chapter 16 - Extreme Value Theory

Question 1

Fat tails that are observed in financial data are the result of two factors:

Answer 1

Returns are heteroscedastic –> volatility varies over time in a stochastic way

Innovations in heteroscedastic models are best modelled using a fat tailed distribution

Question 2

Underlying distributions

Answer 2

Will Go Fishing
Weibull Gumbell Frechet
SP: L0

BUT (Beta, Uniform, Triangular)

CW GLEN
Chi-Square, Weibull
Gamma, Lognormal, Exponential, Normal

Try Let Fish Bite Properly
T dist
LogGamma
F dist
Burr
Pareto

Question 3

EVT - rough criteria to predict which family it belongs to:

Answer 3

Weibull: distributions that have upper limits

Gumbell: distributions with finite moments of all orders

Frechet: Heavy tail distributions, with higher moments that can be finite

Question 4

Generalised Extreme Value (GEV) describes distribution of maximum values, to get we divide data into blocks, and calculate maximum for each block. Can be used to analyse a set of observed data in two different ways:

Answer 4

Return level: Select max observation in each block, fewer blocks give more information about extreme values, but increases variance

Return period: Count the # of observations in each block that exceed some set level