Autoregressive Conditional Heteroscedasticity (ARCH) Models: A Review

Abstract

Autoregressive Conditional Heteroscedasticity (ARCH) models have successfully been employed in order to predict asset return volatility. Predicting volatility is of great importance in pricing financial derivatives, selecting portfolios, measuring and managing investment risk more accurately. In this paper, a number of univariate and multivariate ARCH models, their estimating methods and the characteristics of financial time series, which are captured by volatility models, are presented. The number of possible conditional volatility formulations is vast. Therefore, a systematic presentation of the models that have been considered in the ARCH literature can be useful in guiding one's choice of a model for exploiting future volatility, with applications in financial markets.

Evaluating volatility forecasts in option pricing in the context of a simulated options market

“…ARCH models go by such exotic names as AARCH, NARCH, PARCH, PNP-ARCH and STARCH among others. A wide range of proposed ARCH models is covered in surveys such as , Bollerslev et al (1994), Bera and Higgins (1993), Gourieroux (1997) and Degiannakis and Xekalaki (2004).…”

“…Of course, as the number of candidate models increases, the probability of finding models with superior predictive ability will increase as well. Note that in our simulation study, 3 conditional variance specifications and Degiannakis and Xekalaki (2004) have presented 31 conditional variance specifications in the context of the ARCH framework. However, the investigation of the SPEC algorithm performance with a set of more flexible ARCH models, which account for recent developments in the area of asset returns volatility, is suggested for further research.…”

Efficiency of the IBEX spot–futures basis: The impact of the mini‐futures

“…There is a large and extensive literature on the appropriate model for capturing time variation in volatility dynamics (see, for example, recent reviews of GARCH modeling and forecasting by Bollerslev, Engle, & Nelson, 1994;Poon & Granger, 2003, 2005Degiannakis & Xekalaki, 2004). Such volatility modeling is all the more complicated when examining intra-day data because of multiple components within such processes (Andersen & Bollerslev, 1997, 1998.…”

Volatility and predictability of the Russian ruble exchange rate

“…Some of the most influential of these early papers were collected in Engle (1995). Numerous surveys of the burgeon ARCH literature also exist; e.g., Andersen and Bollerslev (1998), Andersen, Bollerslev, Christoffersen and Diebold (2006), Bauwens, Laurent and Rombouts (2006), Bera and Higgins (1993), Bollerslev, Chou and Kroner (1992), Bollerslev, Engle and Nelson (1994), Degiannakis and Xekalaki (2004), Diebold (2004), Diebold and Lopez (1995), Engle (2001Engle ( , 2004, Engle and Patton (2001), Pagan (1996), Palm (1996), and Shephard (1996). Moreover, ARCH models have now become standard textbook material in econometrics and finance as exemplified by, e.g., Alexander (2001Alexander ( , 2008, Brooks (2002), Campbell, Lo and MacKinlay (1997), Chan (2002), Christoffersen (2003), Enders (2004), Franses and van Dijk (2000), Gourieroux and Jasiak (2001), Hamilton (1994), Mills (1993), Poon (2005), Singleton (2006), Stock and Watson (2005), Tsay (2002), and Taylor (2004).…”