Generalised long-memory GARCH models for intra-daily volatility

Bordignon, Silvano; Caporin, Massimiliano; Lisi, Francesco

doi:10.1016/j.csda.2006.11.004

Cited by 36 publications

(42 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the proposed model, the introduction of a log-transformation enables the removal of the constraints for positivity of conditional variances, thus simplifying the model estimation. The conditional variance dynamic could follow alternative specifications, starting from the seminal contributions of Engle (1982) and Bollerslev (1986), to the long-memory model of Baillie et al (1996), to the more advanced specifications such as the periodic longmemory GARCH of Bordignon et al (2007Bordignon et al ( , 2009). For a survey of possible GARCH specifications see Bollerslev et al (1992, 1994), and Bollerslev (2009.…”

Section: An Econometric Model For Energy and Temperature Datamentioning

confidence: 99%

Model based Monte Carlo pricing of energy and temperature Quanto options

Caporin¹,

Preś²,

Torró³

2012

Energy Economics

Self Cite

View full text Add to dashboard Cite

Weather derivatives have become very popular tools in weather risk management in recent years. One of the elements supporting their diffusion has been the increase in volatility observed on many energy markets. Among the several available contracts, Quanto options are now becoming very popular for a simple reason: they take into account the strong correlation between energy consumption and certain weather conditions, so enabling price and weather risk to be controlled at the same time. These products are more efficient and, in many cases, significantly cheaper than simpler plain vanilla options. Unfortunately, the specific features of energy and weather time series do not enable the use of analytical formulae based on the BlackScholes pricing approach, nor other more advanced continuous time methods that extend the Black-Scholes approach, unless under strong and unrealistic assumptions. In this study, we propose a Monte Carlo pricing framework based on a bivariate time series model. Our approach takes into account the average and variance interdependence between temperature and energy price series. Furthermore, our approach includes other relevant empirical features, such as periodic patterns in average, variance, and correlations. The model structure enables a more appropriate pricing of Quanto options compared to traditional methods.

show abstract

Section: An Econometric Model For Energy and Temperature Datamentioning

confidence: 99%

Model based Monte Carlo pricing of energy and temperature Quanto options

Caporin¹,

Preś²,

Torró³

2012

Energy Economics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Bordignon et al (2007) proposed to include the generalized long memory filter P (L) into a GARCH structure in order to describe periodic long memory patterns in the conditional variance of a time series. Such kind of patterns are observed, for example, in some intra-daily financial time series.The resulting class of models was called G-GARCH.…”

Section: Periodic Long Memory Filters and Generalised-garch Modelsmentioning

confidence: 99%

“…Since the estimation of PLM-and G-GARCH models is based on likelihood methods, classical misspecifiction tests, for example Likelihood Ratio (LR) and Lagrange Multiplier (LM), may be used to select the more appropriate model. Bordignon et al (2005Bordignon et al ( , 2007 showed, by a simulation study, the practical applicability and the good performance of the Quasi-Maximum Likelihood (QML) procedure for parameters estimation. However, they also highlighted the lack of formal results concerning consistency or distributional theory, even asympotically, for estimators based on likelihood methods in long memory models.…”

Section: Introductionmentioning

confidence: 99%

“…Several models were also proposed in the statistical and econometric literature to capture the observed persistence in the conditional variance; among these FI-GARCH and FIEGARCH models (Baillie et al, 1996;Bollerslev and Mikkelsen, 1996;Andersen and Bollerslev, 1997) and the Long Memory Stochastic Volatility model (Breidt et al, 1998) are well known and very common. In order to model the empirical evidences of periodic long memory behaviour in the volatility of intra-daily financial returns, more recently, Bordignon et al(2005Bordignon et al( , 2007 introduced new GARCH-type models characterised by long memory behaviour of periodic type. These models, called Periodic Long-Memory GARCH (PLM-GARCH) and Generalised Long Memory GARCH (G-GARCH), generalise the FIGARCH and FIEGARCH models introducing suitable filters allowing to account also for periodic long memory patterns in conditional variance (associated to the zero frequency of the power spectrum).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Misspecification Tests for Periodic Long Memory GARCH Models

Caporin

Lisi

2007

SSRN Journal

Self Cite

View full text Add to dashboard Cite

Distributional theory for Quasi-Maximum Likelihood estimators in long memory conditional heteroskedastic models is not formally defined, even asympotically. Because of that, this paper analyses the performance of the Likelihood Ratio and the Lagrange Multiplier misspecification tests for Periodic Long Memory GARCH models. The real size and power of these tests are studied by means of Monte Carlo simulations with respect to the class of Generalized Long Memory GARCH models. An application to the U SD/JP Y exchange rate is also provided.

show abstract

“…The general Gegenbauer process encompasses seasonal long memory as a special case. While Bordignon, Caporin, and Lisi (2009) extended the FIGARCH and FIEGARCH models by accommodating seasonal long memory, Bordignon, Caporin, and Lisi (2007) developed the general Gegenbauer GARCH model. Although their focus is on investigating the long memory structure within a day, it may also be worth examining the general Gegenbauer process using daily realized volatility measure.…”

Section: Introductionmentioning

confidence: 99%

Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

McAleer

Peiris

2017

SSRN Journal

View full text Add to dashboard Cite

In recent years fractionally differenced processes have received a great deal of attention due to their exibility in nancial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum.Forestimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the rst step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the nite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against theRSV-GGLM model.We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory.Keywords Stochastic Volatility; Realized Volatility Measure; Long Memory; Gegenbauer Polynomial; Seasonality; Whittle Likelihood. JEL Classification AbstractIn recent years fractionally differenced processes have received a great deal of attention due to their flexibility in financial applications with long memory. In this paper, we develop a new realized stochastic volatility (RSV) model with general Gegenbauer long memory (GGLM), which encompasses a new RSV model with seasonal long memory (SLM). The RSV model uses the information from returns and realized volatility measures simultaneously. The long memory structure of both models can describe unbounded peaks apart from the origin in the power spectrum. For estimating the RSV-GGLM model, we suggest estimating the location parameters for the peaks of the power spectrum in the first step, and the remaining parameters based on the Whittle likelihood in the second step. We conduct Monte Carlo experiments for investigating the finite sample properties of the estimators, with a quasi-likelihood ratio test of RSV-SLM model against theRSV-GGLM model. We apply the RSV-GGLM and RSV-SLM model to three stock market indices. The estimation and forecasting results indicate the adequacy of considering general long memory.

show abstract

Generalised long-memory GARCH models for intra-daily volatility

Cited by 36 publications

References 17 publications

Model based Monte Carlo pricing of energy and temperature Quanto options

Model based Monte Carlo pricing of energy and temperature Quanto options

Misspecification Tests for Periodic Long Memory GARCH Models

Realized Stochastic Volatility Models with Generalized Gegenbauer Long Memory

Contact Info

Product

Resources

About