GARCH-like Models with Dynamic Crash Probabilities : A Parametric Approach for Modelling Extreme Events

Paul Koether

ISBN 10: 3639014405 / ISBN 13: 9783639014402

Editore: VDM Verlag Dr. Müller, VDM Verlag Dr. Müller E.K., 2008

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Neuware - We work in the setting of time series of financial returns.Our starting point are the GARCH models, which are very common in practice.We introduce the possibility of having crashes in such GARCH models.A crash will be modeled by drawing innovations from a distribution with much mass on extremely negative events, while in normal times the innovations will be drawn from a normal distribution.The probability of a crash is modeled to be time dependent, depending on the past of the observed time series and/or exogenous variables. The aim is a splitting of risk into normal risk coming mainly from the GARCH dynamic and extreme event risk coming from the modeled crashes.For the ARCH case we formulate (quasi) maximum likelihood estimators and can derive conditions for consistency and asymptotic normality of the parameter estimates.On the practical side we look for the outcome of estimating models with genuine GARCH dynamic and compare the result toclassical GARCH models. We apply the models to Value at Risk estimation and see that in comparison to the classical modelsmany of ours seem to work better although we chose the crash distributions quite heuristically.

Codice articolo 9783639014402

Dati bibliografici

• Titolo: GARCH-like Models with Dynamic Crash Probabilities : A Parametric Approach for Modelling Extreme Events
• Editore: VDM Verlag Dr. Müller, VDM Verlag Dr. Müller E.K.
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3639014405
• ISBN 13: 9783639014402
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

We work in the setting of time series of financial returns. Our starting point are the GARCH models, which are very common in practice. We introduce the possibility of having crashes in such GARCH models. A crash will be modeled by drawing innovations from a distribution with much mass on extremely negative events, while in normal times the innovations will be drawn from a normal distribution. The probability of a crash is modeled to be time dependent, depending on the past of the observed time series and/or exogenous variables. The aim is a splitting of risk into normal risk coming mainly from the GARCH dynamic and extreme event risk coming from the modeled crashes. For the ARCH case we formulate (quasi) maximum likelihood estimators and can derive conditions for consistency and asymptotic normality of the parameter estimates. On the practical side we look for the outcome of estimating models with genuine GARCH dynamic and compare the result to classical GARCH models. We apply the models to Value at Risk estimation and see that in comparison to the classical models many of ours seem to work better although we chose the crash distributions quite heuristically.