Essays on Realized Volatility and Jumps

Abstract: Financial markets sometimes generate significant discontinuities, so called jumps, triggered by large informational shocks and extreme events. In the last decade, there is an increasing interest in financial economics towards modeling these jumps which may have significant consequences for risk management, and portfolio allocation. This thesis extends the literature within these areas in several ways by using high frequency data in combination with so called realized and power variation measures to identify and analyze jumps. The thesis consists of five chapters. The first reviews some theory of realized volatility and summarizes the thesis. The second chapter investigates the economic importance of this jump component within an asset allocation problem. We find that a risk averse investor with quadratic utility is willing to sacrifice a significant percentage return in order to account for jumps when modeling and forecasting the covariance matrix of returns. In the third chapter, co-authored with Mia Holmfeldt, we propose a framework to improve the predictability of total return variance. Within a GARCH-jump framework we obtain one-step-ahead predictions of the total return variance by modeling the continuous part of total variance and the jump separately. A significant increase in the predictability is reported when the duration and the size of the jumps are considered. Ignoring such jump characteristics will result in misleading quantile predictions with unsatisfying risk management as a result. Today there is strong support for changes in the market co-movements in periods of financial distress or extreme events. In chapter four we investigate this by examining the correlation between the stock and bond market on jump days. We find significant changes in both the realized and bi-power version of the correlation coefficient. To investigate the dependence further we apply a volatility decomposition in a vector autoregression and construct a transmission index. We report a transmission effect for both the smooth volatility and the jump component. A time changing version of the index reveal strong support for changes in the dependence on jump days and during periods associated with key economic events. In the last chapter we further explore this issue by studying the dependence structure in multivariate high frequency stock and bond data. Using copula techniques, we find a pronounced time-variation in the dependence with a significant increase on jump days. Furthermore we find support for jumps being transmitted across asset classes given that one of the market jumps. Small stock market jumps are more of idiosyncratic type and is not influencing the dependence structure to the same extent as jumps in the bond market.