Modeling the Dynamics of Stock Prices Using Realized Variation Measures

Recently, the availability of high-frequency financial data has opened new research directions for modeling the volatility of asset returns. In particular, building on the theory of quadratic variation, the high-frequency returns can be used to construct non-parametric and consistent measures of the variation of the price process at a lower frequency, such as the daily realized covariance, as defined by the sum of the outer product of intradaily returns, or the realized Bipower variation measuring only the continuous sample path variation. As such the measures provide new and useful information on the dynamics of stock prices, while the volatility can be treated as an observed rather than a latent variable to which standard time series procedures can be applied. In fact, it turned out empirically, that the models developed so far for the realized volatility outperform the conventional stochastic volatility or GARCH-type models in terms of forecasting performance. This thesis therefore makes also use of the realized variation measures for modeling the individual as well as the cross-sectional dynamics of stock returns. We extend the existing literature in several respects. We first show that the residuals of the most commonly used realized volatility models exhibit volatility clustering and non-Gaussianity. Given this observation, the usually imposed assumption of identically and independently Gaussian distributed innovations seems to be inadequate leading potentially to inefficiencies in the estimation of such realized volatility models and to distortions in their predictive ability, in turn impairing risk management. We therefore propose two model extensions that explicitly account for the time-variation in the volatility of the realized volatility as well as for the non-Gaussianity, and show that their incorporation leads to substantial improvements in in-sample and out-of-sample performance. Second, we develop an empirically highly accurate simultaneous equation model for the returns, the realized continuous sample path and the jump variation measures. In doing so we explicitly disentangle the dynamics and interrelationships of the variation coming from the continuous sample path evolvement and the variation coming from the jumps in the prices, which is novel to the literature. Interestingly, we find that the often observed lagged leverage effect primarily acts through the continuous volatility component (as measured by the Bipower variation) and that there exists a similar mechanism in the contemporaneous leverage effect. Moreover, the stunning accuracy of our model along with the availability of its likelihood function and analytic derivatives makes it an ideal candidate as an auxiliary model for the estimation of continuous-time stochastic volatility models using indirect inference methods. Third, we exploit the realized covariance measure and its information for modeling the joint dynamics of stock prices. Our approach is novel as we no longer assume that the true covariance is observable - as is the case in the existing discrete-time realized (co)variance models - and as we do not specify a purely latent covariance process. Instead we propose a multivariate discrete-time generalized hyperbolic stochastic volatility model, in which the mean of the unobserved "true" covariance depends on the lagged realized covariances. In doing so we acknowledge the fact that in practice, once market microstructure effects have been accounted for, the realized covariance is certainly an unbiased but importantly a noisy estimator of the quadratic covariation

Local Assortativity in Weighted and Directed Complex Networks

Assortativity, i.e. the tendency of a vertex to bond with another based on their similarity, such as degree, is an important network characteristic that is well-known to be relevant for the network's robustness against attacks. Commonly it is analyzed on the global level, i.e. for the whole network. However, the local structure of assortativity is also of interest as it allows to assess which of the network's vertices and edges are the most endangering or the most protective ones. Hence, it is quite important to analyze the contribution of individual vertices and edges to the network's global assortativity. For unweighted networks M. Piraveenan, M. Prokopenko, and A. Y. Zomaya (2008, 2010) and Guo-Qing Zhang, Su-Qi Cheng, and Guo- Qiang Zhang (2012) suggest two allegedly different approaches to measure local assortativity. In this paper we show their equivalence and propose generalized local assortativity measures that are also applicable to weighted (un)directed networks. They allow to analyze the assortative behavior of edges and vertices as well as of entire network components. We illustrate the usefulness of our measures based on theoretical and real-world weighted networks and propose new local assortativity profiles, which provide, inter alia, information about the pattern of local assortativity with respect to edge weight.Comment: 25 pages, 7 figures, 5 table

Localized Realized Volatility Modelling

With the recent availability of high-frequency Financial data the long range dependence of volatility regained researchers' interest and has lead to the consideration of long memory models for realized volatility. The long range diagnosis of volatility, however, is usually stated for long sample periods, while for small sample sizes, such as e.g. one year, the volatility dynamics appears to be better described by short-memory processes. The ensemble of these seemingly contradictory phenomena point towards short memory models of volatility with nonstationarities, such as structural breaks or regime switches, that spuriously generate a long memory pattern (see e.g. Diebold and Inoue, 2001; Mikosch and Starica, 2004b). In this paper we adopt this view on the dependence structure of volatility and propose a localized procedure for modeling realized volatility. That is at each point in time we determine a past interval over which volatility is approximated by a local linear process. Using S&P500 data we find that our local approach outperforms long memory type models in terms of predictability.Localized Autoregressive Modeling, Realized Volatility, Adaptive Procedure

The volatility of realized volatility

Using unobservable conditional variance as measure, latent-variable approaches, such as GARCH and stochastic-volatility models, have traditionally been dominating the empirical finance literature. In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. By constructing "observable" or realized volatility series from intraday transaction data, the use of standard time series models, such as ARFIMA models, have become a promising strategy for modeling and predicting (daily) volatility. In this paper, we show that the residuals of the commonly used time-series models for realized volatility exhibit non-Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance when modeling and forecasting realized volatility. In an empirical application for S&P500 index futures we show that allowing for time-varying volatility of realized volatility leads to a substantial improvement of the model's fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting. Klassifikation: C22, C51, C52, C5

The Volatility of Realized Volatility

Using unobservable conditional variance as measure, latent–variable approaches, such as GARCH and stochastic–volatility models, have traditionally been dominating the empirical finance literature. In recent years, with the availability of high–frequency financial market data modeling realized volatility has become a new and innovative research direction. By constructing “observable” or realized volatility series from intraday transaction data, the use of standard time series models, such as ARFIMA models, have become a promising strategy for modeling and predicting (daily) volatility. In this paper, we show that the residuals of the commonly used time–series models for realized volatility exhibit non–Gaussianity and volatility clustering. We propose extensions to explicitly account for these properties and assess their relevance when modeling and forecasting realized volatility. In an empirical application for S&P500 index futures we show that allowing for time–varying volatility of realized volatility leads to a substantial improvement of the model’s fit as well as predictive performance. Furthermore, the distributional assumption for residuals plays a crucial role in density forecasting.Finance, Realized Volatility, Realized Quarticity, GARCH, Normal Inverse Gaussian Distribution, Density Forecasting

Nonlinearity in cap-and-trade systems: the EUA price and its fundamentals

In this paper we examine the nonlinear relation between the EUA price and its fundamentals, such as energy prices, macroeconomic risk factors and weather conditions. By estimating a Markov regime-switching model, we and that the relation between the EUA price and its fundamentals varies over time. In particular, we are able to identify a low and a high volatility regime, both showing a strong impact of the fundamentals on the EUA price. The high volatility regime is predominant during the recession of 2008 and 2009 - a time period in which the actual emissions sharply decreased due to the economic crisis

Volatility estimation based on high-frequency data

With the availability of high-frequency data ex post daily (or lower frequency) nonparametric volatility measures have been developed, that are more precise than conventionally used volatility estimators, such as squared or absolute daily returns. The consistency of these estimators hinges on increasingly finer sampled high-frequency returns. In practice, however, the prices recorded at the very high frequency are contaminated by market microstructure noise. We provide a theoretical review and comparison of high-frequency based volatility estimators and the impact of different types of noise. In doing so we pay special focus on volatility estimators that explore different facets of high-frequency data, such as the price range, return quantiles or durations between specific levels of price changes.The various volatility estimators are applied to transaction and quotes data of the S&P500 E-mini and of one stock of Microsoft using different sampling frequencies and schemes. We further discuss potential sources of the market microstructure noise and test for its type and magnitude. Moreover, due to the volume of high-frequency financial data we focus also on computational aspects, such as data storage and retrieval

A Canonical Correlation Approach for Selecting the Number of Dynamic Factors

In this article, we propose a selection procedure that allows us to consistently estimate the number of dynamic factors in a dynamic factor model. The procedure is based on a canonical correlation analysis of the static factors which has the advantage of being invariant to a rescaling of the factors. Monte Carlo simulations suggest that the proposed selection rule outperforms existing ones, in particular, if the contribution of the common factors to the overall variance is moderate or low. The new selection procedure is applied to the US macroeconomic data panel used in Stock and Watson [NBER working paper 11467 (2005)]