A Collection of Portfolio Management Issues

This thesis consists of three chapters of interest to a portfolio manager. The first paper examines how the profitability of trading rules depends on volatility. In particular, a question of interest is whether one rule dominates all others regardless of the level of volatility, or whether it is more profitable to vary the choice of trading rule corresponding to volatility. Certain rules, such as the KST indicator using overbought/oversold levels, appear to excel under highly volatile conditions, while exponential moving average rules perform better with low volatility. In the second paper, a Value-at-Risk (VaR) model capable of producing accurate and robust forecasts is presented. In particular, the model presented here provides an extension to the VARLINEX model of Knight, Satchell, and Wang (2003) (hereafter KSW (2003)). The end result is a model capable of accurately forecasting VaR during the recent stock market crash (2008-09), as well as before and after the crash. The new model outperforms a benchmark model that had been successful prior to the crash, as well as the original VARLINEX model (KSW (2003)). The third paper explicitly spells out the link between independence tests and goodness-of-fit tests that are based on copula functions. However, the primary contribution is the development of a new copula-based goodness of fit test, which involves incorporating a weighting function in one of the test statistics proposed in Genest, Remillard, and Beaudoin (2009). Guidance is given in terms of how to choose an appropriate weighting function, and an application to Value-at-Risk forecasting is included

Fitting high-dimensional Copulae to Data

This paper make an overview of the copula theory from a practical side. We consider different methods of copula estimation and different Goodness-of-Fit tests for model selection. In the GoF section we apply Kolmogorov-Smirnov and Cramer-von-Mises type tests and calculate power of these tests under different assumptions. Novating in this paper is that all the procedures are done in dimensions higher than two, and in comparison to other papers we consider not only simple Archimedean and Gaussian copulae but also Hierarchical Archimedean Copulae. Afterwards we provide an empirical part to support the theory.copula, multivariate distribution, Archimedean copula, GoF

Essays in theoretical and applied econometrics

This thesis investigates three topics in theoretical and applied econometrics: Bartlett-type correction of the Distance Metric (DM) test, a Generalized Method of Moments (GMM) study of the effect of the North American Free Trade Agreement (NAFTA) on Quebec manufacturing industries, and a goodness-of-fit test for copulas. The first topic derives an Edgeworth approximation of the distribution of the DM test statistic and obtains a Bartlett-type correction factor, then it uses examples of covariance structures to illustrate the theoretical results and applies the theoretical results to study the covariance structure of earnings. The second topic calculates Canadian tariff rates over the period 1991-2007 for manufacturing industries, classified using the North American Industry Classification System (NAICS), proposes a simulation-based moment selection procedure to improve the properties of the system GMM estimator, and analyzes the effect of NAFTA on earnings of Quebec manufacturing industries. The third topic proposes a new rank-based goodness-of-fit test for copulas, conducts a power study to show that the new test has reasonable properties, and presents an applicatio

Non linear dependences in finance

La thèse est composée de trois parties. La partie I introduit les outils mathématiques et statistiques appropriés pour l'étude des dépendances, ainsi que des tests statistiques d'adéquation pour des distributions de probabilité empiriques. Je propose deux extensions des tests usuels lorsque de la dépendance est présente dans les données, et lorsque la distribution des observations a des queues larges. Le contenu financier de la thèse commence à la partie II. J'y présente mes travaux concernant les dépendances transversales entre les séries chronologiques de rendements journaliers d'actions, c'est à dire les forces instantanées qui relient plusieurs actions entre elles et les fait se comporter collectivement plutôt qu'individuellement. Une calibration d un nouveau modèle à facteurs est présentée ici, avec une comparaison à des mesures sur des données réelles. Finalement, la partie III étudie les dépendances temporelles dans des séries chronologiques individuelles, en utilisant les mêmes outils et mesures de corrélations. Nous proposons ici deux contributions à l'étude du volatility clustering , de son origine et de sa description: l'une est une généralisation du mécanisme de rétro-action ARCH dans lequel les rendements sont auto-excitants, et l'autre est une description plus originale des auto-dépendances en termes de copule. Cette dernière peut être formulée sans modèle et n'est pas spécifique aux données financières. En fait, je montre ici aussi comment les concepts de récurrences, records, répliques et temps d'attente, qui caractérisent la dynamique dans les séries chronologiques, peuvent être écrits dans la cadre unifié des copules.The thesis is composed of three parts. Part I introduces the mathematical and statistical tools that are relevant for the study of dependences, as well as statistical tests of Goodness-of-fit for empirical probability distributions. I propose two extensions of usual tests when dependence is present in the sample data and when observations have a fat-tailed distribution. The financial content of the thesis starts in Part II. I present there my studies regarding the cross-sectional dependences among the time series of daily stock returns, i.e. the instantaneous forces that link several stocks together and make them behave somewhat collectively rather than purely independently. A calibration of a new factor model is presented here, together with a comparison to measurements on real data. Finally, Part III investigates the temporal dependences of single time series, using the same tools and measures of correlation. I propose two contributions to the study of the origin and description of volatility clustering : one is a generalization of the ARCH-like feedback construction where the returns are self-exciting, and the other one is a more original description of self-dependences in terms of copulas. The latter can be formulated model-free and is not specific to financial time series. In fact, I also show here how concepts like recurrences, records, aftershocks and waiting times, that characterize the dynamics in a time series can be written in the unifying framework of the copula.CHATENAY MALABRY-Ecole centrale (920192301) / SudocSudocFranceF

Reliability-based design of offshore structures for oil and gas applications

Offshore structures are complex in their structural and functional form and operate in a harsh and uncertain environment with complex interactions between ocean variables. Consequently, the ocean environment presents a high risk to these structures hence the need to develop an efficient and reliable design. Therefore, the need for a design that effectively: captures complex ocean parameter interactions, reduces the computational burden in structural response determination, quantifies the structure's ability to bounce back when faced with disruptive events, and minimizes cost under uncertainty at the desired safety levels of the asset is critical. A robust offshore structural design under uncertainty is essential for the safety of life, asset, and the environment during oil and gas exploration and production activities. This thesis presents improved methods for the effective reliability-based design of offshore structures. First, a framework is developed to capture the dependency of multivariate environmental ocean variables using vine copula and its impact on the reliability assessment of offshore structural systems. The model was tested using a cantilever beam and applied to an offshore jacket structure. The comparative results from the jacket structure and cantilever problem reveals that failure probability considering dependence between ocean variables is closer to the reference value than when variables are independent or modeled with a Gaussian copula. The outcome shows the importance of capturing nonlinearity and tail dependence between ocean variables in reliability evaluation. Secondly, the effectiveness of a hybrid metamodel, which is a combination of two commonly and independently used methods, Kriging and Polynomial Chaos Expansions (PCE), is investigated for offshore structural response determination and reliability studies. The hybrid metamodel herein, called (APCKKm-MCS) is constructed from an adaptive process with multiple enrichment of Experimental Design (ED). The hybrid approach was tested on simple non-linear functions, a truss bar, and an offshore deepwater Steel Catenary Riser (SCR). The study's outcome revealed that APCKKm-MCS produced a high predictive response capacity, reduced model evaluation, and shorter computing time during reliability evaluation than the single enrichment case (APCK-MCS) and the adaptive ordinary Kriging case (AK-MCS) considered. In addition, a novel framework is developed for the resilience quantification of offshore structures in terms of their time-varying reliability, adaptability, and maintainability. The developed framework was demonstrated using an internally corroded pipeline segment subject to disruptive events of leak, burst, and rupture. The framework captured the resilience index of the natural gas pipeline for its design life, and its sensitivity analysis revealed the influence of the pipe wall thickness and corrosion depth growth rate on the resilience of the pipeline. The framework provides a quantitative approach to determine the resilience of offshore structures and ascertain their critical influencing parameters for effective decision-making. Finally, a methodology for optimal structural design under uncertainty considering the dependency of environmental variables with the implementation of a hybrid metamodel in the inner loop of a nested optimization problem is presented and demonstrated on a steel column function and a segmented SCR. The study showed different decision outcomes for various vine tree configurations in the dependence modeling for the steel column function noting the importance of choosing the appropriate variable order in the vine tree for optimal design under uncertainty. Also, the research reveals the suitability of adaptive PCK for the inner loop reliability phase for a double-loop structural optimization due to its high predictive capacity and observed relatively low cross-validation error. The method shows the importance of effective dependence modeling of environmental ocean variables in structural cost minimization and selecting optimal structural design variables under uncertainty. From the research outcomes, considering multivariate dependence between ocean variables using vine copula and utilizing multiple enrichment hybrid metamodels in response evaluation for reliability and optimal design assessment of offshore structures could better predict their failure probability and enhance a safer structural design. In addition, the resilience quantification framework developed provides a vital decision-making tool for offshore structural systems' design and integrity management. The research into high dimensional dependence modeling of offshore structures using vine copula, comparative study of sampling strategies required for the hybrid (Kriging and PCE) metamodel construction, dependence-based structural resilience quantification, and multiobjective dependence-based structural optimization under uncertainty are among areas proposed for future investigation

Goodness-of-fit tests for multi-dimensional copulas: Expanding application to historical drought data

The question of how to choose a copula model that best fits a given dataset is a predominant limitation of the copula approach, and the present study aims to investigate the techniques of goodness-of-fit tests for multi-dimensional copulas. A goodness-of-fit test based on Rosenblatt's transformation was mathematically expanded from two dimensions to three dimensions and procedures of a bootstrap version of the test were provided. Through stochastic copula simulation, an empirical application of historical drought data at the Lintong Gauge Station shows that the goodness-of-fit tests perform well, revealing that both trivariate Gaussian and Student t copulas are acceptable for modeling the dependence structures of the observed drought duration, severity, and peak. The goodness-of-fit tests for multi-dimensional copulas can provide further support and help a lot in the potential applications of a wider range of copulas to describe the associations of correlated hydrological variables. However, for the application of copulas with the number of dimensions larger than three, more complicated computational efforts as well as exploration and parameterization of corresponding copulas are required