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A stochastic volatility model where volatility was driven solely by a latent variable called news was estimated for three stock indices. A Markov chain Monte Carlo algorithm was used for estimating Bayesian parameters and filtering volatilities. Volatility persistence being close to one was consistent with both volatility clustering and mean reversion. Filtering showed highly volatile markets, reflecting frequent pertinent news. Diagnostics showed no model failure, although specification improvements were always possible. The model corroborated stylized findings in volatility modeling and has potential value for market participants in asset pricing and risk management, as well as for policymakers in the design of macroeconomic policies conducive to less volatile financial markets.
"This paper proposes the EGARCH [Exponential Generalized Autoregressive Conditional Heteroskedasticity] model with jumps and heavy-tailed errors, and studies the empirical performance of different models including the stochastic volatility models with leverage, jumps and heavy-tailed errors for daily stock returns. In the framework of a Bayesian inference, the Markov chain Monte Carlo estimation methods for these models are illustrated with a simulation study. The model comparison based on the marginal likelihood estimation is provided with data on the U.S. stock index."--Author's abstract.
The first essay describes a very general stochastic volatility (SV) model specification with leverage, heavy tails, skew and switching regimes, using realized volatility (RV) as an auxiliary time series to improve inference on latent volatility. The information content of the range and of implied volatility using the VIX index is also analyzed. Database is the S&P 500 index. Asymmetry in the observation error is modeled by the generalized hyperbolic skew Student-t distribution, whose heavy and light tail enable substantial skewness. Resulting number of regimes and dynamics differ dependent on the auxiliary volatility proxy and are investigated in-sample for the financial crash period 2008/09 in more detail. An out-of-sample study comparing predictive ability of various model variants for a calm and a volatile period yields insights about the gains on forecasting performance from different volatility proxies. Results indicate that including RV or the VIX pays off mostly in more volatile market conditions, whereas in calmer environments SV specifications using no auxiliary series outperform. The range as volatility proxy provides a superior in-sample fit, but its predictive performance is found to be weak. The second essay presents a high frequency stochastic volatility model. Price duration and associated absolute price change in event time are modeled contemporaneously to fully capture volatility on the tick level, combining the SV and stochastic conditional duration (SCD) model. Estimation is with IBM stock intraday data 2001/10 (decimalization completed), taking a minimum midprice threshold of a half tick. Persistent information flow is extracted, featuring a positively correlated innovation term and negative cross effects in the AR(1) persistence matrix. Additionally, regime switching in both duration and absolute price change is introduced to increase nonlinear capabilities of the model. Thereby, a separate price jump.
Empirical Studies on Volatility in International Stock Markets describes the existing techniques for the measurement and estimation of volatility in international stock markets with emphasis on the SV model and its empirical application. Eugenie Hol develops various extensions of the SV model, which allow for additional variables in both the mean and the variance equation. In addition, the forecasting performance of SV models is compared not only to that of the well-established GARCH model but also to implied volatility and so-called realised volatility models which are based on intraday volatility measures. The intended readers are financial professionals who seek to obtain more accurate volatility forecasts and wish to gain insight about state-of-the-art volatility modelling techniques and their empirical value, and academic researchers and students who are interested in financial market volatility and want to obtain an updated overview of the various methods available in this area.