However, dealing with small probabilities is inherent to the analysis of extreme events, and mathematical tools exist (e.g., the extreme value theory
; Coles 2001) to cope with distribution tails and enable statistical inference on rare values.
Vaienti, "Extreme value theory
for singular measures," Chaos.
The second part introduces the SV model of gold price volatility, and the third part introduces VaR model combining SV model and extreme value theory
. The fourth part analyzes daily closing price data of AU99.99 of Shanghai Gold Exchange.
The GPD in the extreme value theory
has played an important role in modeling the excess distribution over a high threshold.
Selcuk, "Extreme value theory
and value-at-risk: relative performance in emerging markets," International Journal of Forecasting, vol.
Rare or extreme events, by definition, appear in the tails of the distributions; in this context, the extreme value theory
is the adequate statistical tool for analyzing the realization of extreme turmoils in financial returns.
We will follow earlier work on modelling these spikes as an error process (Contreras et al., 2003; Garcia et al., 2005; Swider and Weber, 2007) using Extreme Value Theory
(EVT) (Bystrom, 2005; Chan and Gray, 2006).
(14) We use eight different methods to estimate these risk measures (the methods are explained in detail in Appendix C): the VaR method of variance-covariance; the VaR method of exponential decay (RiskMetrics[TM]); the VaR GARCH method; the VaR t-student distribution method; the VaR extreme value theory
method (static version); the VaR extreme value theory
method (dynamic version); the VaR historical simulation method; and the VaR Monte Carlo simulation method.
(2009), the Extreme Value Theory
(EVT) shows good ability to accommodate the occurrence of extreme observations.
Extreme Value Theory
(EVT) is very useful in predicting and estimating the extreme behavior of financial products and has arisen as a new methodology to analyze the tail behavior of stock returns.
Based on the Extreme Value Theory
, Coles (2001), Pujol et al.
In order to address the problems of heavy tails, VaR measures based on the Extreme Value Theory
(EVT) have been developed which allows us to model the tails of distributions, and to estimate the probabilities of the extreme movements that can be expected in financial markets.