<p>The main goal of this work is to explore the effects of time-varying extreme jump tail dependencies in asset markets. Consequently, a lot of attention has been devoted to understand the extremal tail dependencies between of assets. As pointed by Hansen (2013), the estimation of tail risks dependence is a challenging task and their implications in several sectors of the economy are of great importance. One of the principal challenges is to provide a measure systemic risks that is, in principle, statistically tractable and has an economic meaning. Therefore, there is a need of a standardize dependence measures or at least to provide a methodology that can capture the complexity behind global distress in the economy. These measures should be able to explain not only the dynamics of the most recent financial crisis but also the prior events of distress in the world economy, which is the motivation of this paper. In order to explore the tail dependencies I exploit the information embedded in option prices and intra-daily high frequency data. </p><p>The first chapter, a co-authored work with Andrew Patton, proposes a new class of dynamic copula models for daily asset returns that exploits information from high frequency (intra-daily) data. We augment the generalized autoregressive score (GAS) model of Creal, et al. (2013) with high frequency measures such as realized correlation to obtain a "GRAS" model. We find that the inclusion of realized measures significantly improves the in-sample fit of dynamic copula models across a range of U.S. equity returns. Moreover, we find that out-of-sample density forecasts from our GRAS models are superior to those from simpler models. Finally, we consider a simple portfolio choice problem to illustrate the economic gains from exploiting high frequency data for modeling dynamic dependence.</p><p>In the second chapter using information from option prices I construct two new measures of dependence between assets and industries, the Jump Tail Implied Correlation and the Tail Correlation Risk Premia. The main contribution in this chapter is the construction of a systemic risk factor from daily financial measures using a quantile-regression-based methodology. In this direction, I fill the existing gap between downturns in the financial sector and the real economy. I find that this new index performs well to forecast in-sample and out-of-sample quarterly macroeconomic shocks. In addition, I analyze whether the tail risk of the correlation may be priced. I find that for the S&P500 and its sectors there is an ex ante premium to hedge against systemic risks and changes in the aggregate market correlation. Moreover, I provide evidence that the tails of the implied correlation have remarkable predictive power for future stock market returns.</p> / Dissertation

Empirical likelihood, which was pioneered by Thomas and Grunkemeier (1975) and Owen (1988), is a powerful nonparametric method of statistical inference that has been widely used in the statistical literature. In this thesis, we investigate the merits of empirical likelihood for various problems arising in ratio estimation. First, motivated by the smooth empirical likelihood (SEL) approach proposed by Zhou & Jing (2003), we develop empirical likelihood estimators for diagnostic test likelihood ratios (DLRs), and derive the asymptotic distributions for suitable likelihood ratio statistics under certain regularity conditions. To skirt the bandwidth selection problem that arises in smooth estimation, we propose an empirical likelihood estimator for the same DLRs that is based on non-smooth estimating equations (NEL). Via simulation studies, we compare the statistical properties of these empirical likelihood estimators (SEL, NEL) to certain natural competitors, and identify situations in which SEL and NEL provide superior estimation capabilities. Next, we focus on deriving an empirical likelihood estimator of a baseline cumulative hazard ratio with respect to covariate adjustments under two nonproportional hazard model assumptions. Under typical regularity conditions, we show that suitable empirical likelihood ratio statistics each converge in distribution to a 2 random variable. Through simulation studies, we investigate the advantages of this empirical likelihood approach compared to use of the usual normal approximation. Two examples from previously published clinical studies illustrate the use of the empirical likelihood methods we have described. Empirical likelihood has obvious appeal in deriving point and interval estimators for time-to-event data. However, when we use this method and its asymptotic critical value to construct simultaneous confidence bands for survival or cumulative hazard functions, it typically necessitates very large sample sizes to achieve reliable coverage accuracy. We propose using a bootstrap method to recalibrate the critical value of the sampling distribution of the sample log-likelihood ratios. Via simulation studies, we compare our EL-based bootstrap estimator for the survival function with EL-HW and EL-EP bands proposed by Hollander et al. (1997) and apply this method to obtain a simultaneous confidence band for the cumulative hazard ratios in the two clinical studies that we mentioned above. While copulas have been a popular statistical tool for modeling dependent data in recent years, selecting a parametric copula is a nontrivial task that may lead to model misspecification because different copula families involve different correlation structures. This observation motivates us to use empirical likelihood to estimate a copula nonparametrically. With this EL-based estimator of a copula, we derive a goodness-of-fit test for assessing a specific parametric copula model. By means of simulations, we demonstrate the merits of our EL-based testing procedure. We demonstrate this method using the data from Wieand et al. (1989). In the final chapter of the thesis, we provide a brief introduction to several areas for future research involving the empirical likelihood approach.

Empirical likelihood, which was pioneered by Thomas and Grunkemeier (1975) and Owen (1988), is a powerful nonparametric method of statistical inference that has been widely used in the statistical literature. In this thesis, we investigate the merits of empirical likelihood for various problems arising in ratio estimation. First, motivated by the smooth empirical likelihood (SEL) approach proposed by Zhou & Jing (2003), we develop empirical likelihood estimators for diagnostic test likelihood ratios (DLRs), and derive the asymptotic distributions for suitable likelihood ratio statistics under certain regularity conditions. To skirt the bandwidth selection problem that arises in smooth estimation, we propose an empirical likelihood estimator for the same DLRs that is based on non-smooth estimating equations (NEL). Via simulation studies, we compare the statistical properties of these empirical likelihood estimators (SEL, NEL) to certain natural competitors, and identify situations in which SEL and NEL provide superior estimation capabilities. Next, we focus on deriving an empirical likelihood estimator of a baseline cumulative hazard ratio with respect to covariate adjustments under two nonproportional hazard model assumptions. Under typical regularity conditions, we show that suitable empirical likelihood ratio statistics each converge in distribution to a 2 random variable. Through simulation studies, we investigate the advantages of this empirical likelihood approach compared to use of the usual normal approximation. Two examples from previously published clinical studies illustrate the use of the empirical likelihood methods we have described. Empirical likelihood has obvious appeal in deriving point and interval estimators for time-to-event data. However, when we use this method and its asymptotic critical value to construct simultaneous confidence bands for survival or cumulative hazard functions, it typically necessitates very large sample sizes to achieve reliable coverage accuracy. We propose using a bootstrap method to recalibrate the critical value of the sampling distribution of the sample log-likelihood ratios. Via simulation studies, we compare our EL-based bootstrap estimator for the survival function with EL-HW and EL-EP bands proposed by Hollander et al. (1997) and apply this method to obtain a simultaneous confidence band for the cumulative hazard ratios in the two clinical studies that we mentioned above. While copulas have been a popular statistical tool for modeling dependent data in recent years, selecting a parametric copula is a nontrivial task that may lead to model misspecification because different copula families involve different correlation structures. This observation motivates us to use empirical likelihood to estimate a copula nonparametrically. With this EL-based estimator of a copula, we derive a goodness-of-fit test for assessing a specific parametric copula model. By means of simulations, we demonstrate the merits of our EL-based testing procedure. We demonstrate this method using the data from Wieand et al. (1989). In the final chapter of the thesis, we provide a brief introduction to several areas for future research involving the empirical likelihood approach.