New Frontiers for Arch Models
29 Pages Posted: 3 Nov 2008
Date Written: June 2002
In the 20 years following the publication of the ARCH model, there has been a vast quantity of research uncovering the properties of competing volatility models.Wide-ranging applications to financial data have discovered important stylized facts and illustrated both the strengths and weaknesses of the models. There are now many surveys of this literature.This paper looks forward to identify promising areas of new research. The paper lists five new frontiers. It briefly discusses three high frequency volatility models, large-scale multivariate ARCH models, and derivatives pricing models. Two further frontiers are examined in more detail application of ARCH models to the broadclass of non-negative processes, and use of Least Squares Monte Carlo to examine non-linear properties of any model that can be simulated. Using this methodology, the paper analyzes more general types of ARCH models, stochastic volatility models, long memory models and breaking volatility models. The volatility of volatility is defined,estimated and compared with option implied volatilities.
Keywords: ARCH, GARCH, volatility, non-linear process, non-negative process, option pricing, stochastic volatility, long memory, Least Squares Monte Carlo, ACD, Multiplicative Error Model, MEM
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