英语摘要

The extremal index for GARCH(1, 1) processes

Clusters; Extreme value theory; Extremal index; Finance; GARCH; Bivariate regular variation;

eralised autoregressive conditional heteroskedastic (GARCH) processes have wide application in financial modelling. To characterise the extreme values of this process the extremal index is required. Existing results, which derive the analytical expression for the extremal index for the squared GARCH(1, 1) process, cannot be used to obtain the extremal index for the GARCH(1, 1) process. For the squared GARCH(1, 1) process with symmetric innovations with continuous density function and satisfying a finite moment condition, we derive an alternative analytical expression for the extremal index and new results for the limiting distribution of the size of clusters of extremes. Using these results we obtain an analytical expression for the extremal index of the GARCH(1, 1) process and an

Stochastic GARCH dynamics describing correlations

between stocks

GARCH; Price dynamics; Long-range correlations The ARCH and GARCH processes have been successfully used for modelling price dynamics such as stock returns or foreign exchange rates. Analysing the long range correlations between stocks, we propose a model, based on the GARCH process, which is able to describe the main characteristics of the stock price correlations, including the mean, variance, probability density distribution and the noise spectrum. Efficient Gibbs sampling for Markov switching GARCH

models

Bayesian inference; GARCH; Markov-switching; Multiple-try Metropolis; Efficient simulation techniques for Bayesian inference on Markov-switching (MS) GARCH models are developed. Different multi-move sampling techniques for Markov switching state space models are discussed with particular attention to MS-GARCH models. The multi-move sampling strategy is based on the Forward Filtering Backward Sampling (FFBS) approach applied to auxiliary MS-GARCH models. A unified framework for

MS-GARCH approximation is developed and this not only encompasses the considered specifications, but provides an avenue to generate new variants of MS-GARCH auxiliary models. The use of multi-point samplers, such as the multiple-try Metropolis and the multiple-trial metropolized independent sampler, in combination with FFBS, is considered in order to reduce the correlation between

Financial fluctuations in the Tunisian repressed market context: a Markov-switching–GARCH approach

cyclical financial fluctuations; Markov switching–GARCH model; investor

sentiment; synchronization; concordance index; E32; C32; Small open economies are not immune to financial shocks. Fluctuations arising there interest more and more decision makers as they influence their policies’ effectiveness. A common belief is that opening the capital account is the primary source of financial instability. In this article we show that even if a capital account is not previously opened in Tunisia, the investor sentiment plays the role of the transmission channel of financial fluctuations. On monthly data (2000:01–2010:03) we filter financial business cycles via the Hodrick–Prescott procedure. Also we establish their turning points in Tunisian, Moroccan and French markets using the Bry–Boschan algorithm. Thus we build the investor sentiment index in Tunisia. Then we use it for the estimation of the financial volatility

Measuring tail thickness under GARCH and an application to extreme exchange rate changes

Fat tails; Tail index; Stationary marginal distribution; GARCH; Hill estimator; Foreign

exchange Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including generalized autoregressive conditional heteroskedastic (GARCH) models and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail thickness due to small sample bias. Thus, high quantile estimation may lead to a substantial underestimation of tail risk.

Forecasting interest rates volatilities by GARCH (1,1) and

stochastic volatility models

GARCH; Markov chain Monte Carlo; stochastic volatility; swap rates;

In this paper, we compare the forecast ability of GARCH(1,1) and stochastic volatility models for interest rates. The stochastic volatility is estimated using Markov chain Monte Carlo methods. The comparison is based on daily data from 1994 to 1996 for the ten year swap rates for Deutsch Mark, Japanese Yen, and Pound Sterling. Various forecast horizons are considered. It turns out that forecasts based on stochastic volatility models are in most cases superiour to those obtained by GARCH(1,1) models.