Financial models with long-tailed distributions and volatility clustering

Financial models with long-tailed distributions and volatility clustering have been introduced to overcome problems with the realism of classical financial models. These classical models of financial <a href="/facts/Time_series/fSXPR817">time series</a> typically assume <a href="/facts/Homoskedasticity/50v2qyEN">homoskedasticity</a> and <a href="/facts/Normal_distribution/UapjjPyQ">normality</a> and as such cannot explain stylized phenomena such as <a href="/facts/Skewness/rdS8luFa">skewness</a>, <a href="/facts/Heavy_tails/BHLSHPku">heavy tails</a>, and <a href="/facts/Volatility_clustering/HhAIFmcX">volatility clustering</a> of the empirical asset returns in finance. In 1963, <a href="/facts/Beno%C3%AEt_Mandelbrot/fa8tKP93">Benoit Mandelbrot</a> first used the <a href="/facts/Stable_distribution/rvtRmhlz">stable (or 
 
 
 
 α
 
 
 {\displaystyle \alpha }
 
-stable) distribution</a> to model the empirical distributions which have the skewness and heavy-tail property. Since 
 
 
 
 α
 
 
 {\displaystyle \alpha }
 
-stable distributions have infinite 
 
 
 
 p
 
 
 {\displaystyle p}
 
-th moments for all 
 
 
 
 p
 >
 α
 
 
 {\displaystyle p>\alpha }
 
, the tempered stable processes have been proposed for overcoming this limitation of the stable distribution.
On the other hand, <a href="/facts/GARCH/CyPM79ao">GARCH</a> models have been developed to explain the <a href="/facts/Volatility_clustering/HhAIFmcX">volatility clustering</a>. In the GARCH model, the innovation (or residual) distributions are assumed to be a standard normal distribution, despite the fact that this assumption is often rejected empirically. For this reason, GARCH models with non-normal innovation distribution have been developed.
Many financial models with stable and tempered stable distributions together with volatility clustering have been developed and applied to risk management, option pricing, and portfolio selection.

Financial models with long-tailed distributions and volatility clustering open-in-new

Financial models with long-tailed distributions and volatility clustering