Modeling the Dynamics of Stock Prices Using Realized Variation Measures

Abstract

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. <br /> 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.<br /> 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.<br /> 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.