The paper aims to study the tail-related risk measures including static and dynamic risk measures by extreme value theory
(EVT) in the WTI market.
Vaienti, "Sampling local properties of attractors via extreme value theory
," Chaos, Solitons and Fractals, vol.
Extreme Value Theory
(EVT) is a branch of statistics where the goal is to describe and estimate the unlikely, dating back to the early works of Fisher and Tippett (1928) and Gnedenko (1943).
In addition, Table 3 shows that the best VaR methods for a confidence level of 5% are the GARCH(1, 1), the RiskMetrics[TM] and the dynamic Extreme Value Theory
(EVT) methods, in which the percentage of losses exceeding the VaR are very close to the 5% confidence level required.
One of the most recent methods of VaR calculation is based on the Extreme Value Theory
The GEV distribution is a family of continuous probability distributions developed within extreme value theory
to combine the Gumbel, Frechet and Weibull families.
Djakovic, Andjelic and Borocki (2011) investigates the performance of the extreme value theory
for four emerging markets, the Serbian, Croatian, Slovenian and Hungarian stock indices.
Then, we summarize basic facts from extreme value theory
which will be needed to obtain main results stated in the subsequent section.
Considering that a basic assumption from the extreme value theory
(TVE) is that the distribution of the maximums of independent and identically distributed random variables, converge to one of the particular cases of the GEV (COLES, 2001), and also based on the assumption that the GEV has all the flexibility of its three particular cases NADARAJAH & CHOI, 2007).
To understand the origin of extreme value theory
, consider the problem of "records" - very low or very high values associated with a distribution.
While up to now the Pareto distribution was commonly employed to modeling the tails of loss severities, adjustments with Extreme Value Theory
(EVT)-based distributions significantly improve tail distribution inference and analysis.
The whole idea of Extreme value theory
and Monte Carlo simulation is to forecast the possible claims at certain level of confidence or to permit capital allocation to guard against extreme conditions.