GARCH models with changes in variance: An approximation to risk measurements

Abstract

This study aims to model volatility as an approximation to an optimum measurement of stock market risk because of the importance of this concept for, among other things, the proper management of portfolios. Following the proposal of Lamoureux and Lastrapes (1990), the authors consider that the high degree of persistence detected in GARCH models arises from a poor specification of the equation of the variance due to not considering the possible deterministic changes in the unconditional variance of the financial series. To determine the point in time as well as the duration of these changes, the proposal made by Inclan and Tiao (1994) is used. As an empirical application, whether or not the consideration of the changes obtained influences the diagram of conditional heteroscedasticity presented by the spot and futures series on the IBEX-35 index is tested for the Spanish stock market. The results show that the consideration of these changes considerably decreases the degree of persistence for the IBEX-35 index while, for its futures contract, the GARCH diagram disappears.

Volatility persistence in crude oil markets

“…To overcome this problem, the authors propose a new test that explicitly consider the fourth moment properties of the disturbances and the conditional heteroskedasticity. 2 Ewing and Malik (2010) examine daily WTI crude oil prices from July 1, 1993 to June 30, 2008, by using this modified ICSS algorithm to identify structural breaks in volatility of oil prices. Consider the returns series ε t , which is defined by ε t = log P t − log P t−1 , where P t is the observed price at time t, and consider the GARCH(1,1) model…”

“…As underlined by Aragó and Fernandez-Izquierdo (2003), the degree of persistence of the variance has evident economic implications, arising from the effect that this aspect has on the predictability of their future value. Poterba and Summers (1986) argue that, for multiperiod assets such as stocks, shocks have to persist for a long time for a time-varying risk premium to be able to explain the large fluctuations observed in the stock market.…”

Simulation Framework to Determine Suitable Innovations for Volatility Persistence Estimation: The GARCH Approach

“…This could potentially lead to a significant reduction in asset losses. Moreover, it is documented that shocks with a permanent influence on the variance will have a greater effect on price than those with temporary influence (Arago and Fernandez-Izquierdo 2003). Hence, through the fit of these innovations, policymakers and other financial market participants may benefit from a better understanding of the effects of shocks to future volatility, especially from knowing whether the effects of the shocks are transient or (highly) persistent.…”

Testing for the Long Memory and Multiple Structural Breaks in Consumer ETFs

“…Lamoureux and Lastrapes (1990) and Glosten et al (1993) combined the GARCH model with dummy variables to demonstrate changes in variance. The modified GARCH model cited by Arago and Izquierdo (2003) incorporates the identified changes in unconditional variance, and are expressed as follows:…”