5.9 calibrate_evt_gpd

Function File: [chi sigma u] = calibrate_evt_gpd(v)

Calibrate sorted losses of historic or MC portfolio values to a generalized pareto distribution and returns chi, sigma and u as parameters for further VAR and ES calculation.
Implementation according to Risk Management and Financial Institutions by John C. Hull, 4th edition, Wiley 2015, section 13.6, page 292ff.
Variables:

• v: INPUT: sorted profit and loss distribution of all required tail events (1xN vector)
• chi: OUTPUT: Generalized Pareto distribution: shape parameter (scalar)
• sigma: OUTPUT: scale parameter (scalar)
• u: OUTPUT: location parameter(scalar)