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.
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.