Empirical essays in quantitative risk management

Zhao, Yang (2016) Empirical essays in quantitative risk management. PhD thesis, University of Glasgow.

Abstract

Copula theory is particularly useful for modeling multivariate distributions as it allows us to decompose a joint distribution into marginal distributions and a copula. Copula-based models have been widely applied in finance, insurance, macroeconomics, microeconomics and many other areas in recent years. This doctoral thesis particularly pays attention to applications of copula theory in quantitative risk management.

The first chapter of this thesis provides a comprehensive review of recent developments of copula models and some important applications in the large and growing finance and economics literature. The first part of this chapter briefly introduces the definition and properties of copulas as well as several related concepts. The second part reviews estimation and inference methods, goodness-of-fit tests and model selection tests for copula models considered in the literature. The third part provides an exhaustive review of the extensive literature of copula-based models in finance and economics. Finally, an interesting topic for further research is suggested.

The remaining three chapters investigate applications of copula theory in three topics: market risk prediction, portfolio optimization and credit risk estimation.

Chapter Two investigates the dynamic and asymmetric dependence structure between equity portfolios from the US and UK. We demonstrate the statistical significance of dynamic asymmetric copula models in modeling and forecasting market risk. First, we construct ``high-minus-low" equity portfolios sorted on beta, coskewness, and cokurtosis. We find substantial evidence of dynamic and asymmetric dependence between characteristic-sorted portfolios. Second, we consider a dynamic asymmetric copula model by combining the generalized hyperbolic skewed t copula with the generalized autoregressive score (GAS) model to capture both the multivariate non-normality and the dynamic and asymmetric dependence between equity portfolios. We demonstrate the usefulness of this model by evaluating the forecasting performance of Value-at-Risk and Expected Shortfall for high-minus-low portfolios. From backtesting, we find consistent and robust evidence that our dynamic asymmetric copula model provides the most accurate forecasts, indicating the importance of incorporating the dynamic and asymmetric dependence structure in risk management.

Chapter Three investigates the dependence between equity and currency in international financial markets and explores its economic importance in portfolio allocation. First, we find striking evidence for the existence of time-varying and asymmetric dependence between equity and currency. Second, we offer a methodological contribution. A novel time-varying skewed t copula (TVAC) model is proposed to accommodate non-Gaussian features in univariate time series as well as the dynamic and asymmetric dependence in multivariate time series. The multivariate asymmetry is captured by the skewed t copula derived from the mutlivariate skewed t distribution in Bauwens and Laurent (2005) and the time-varying dependence is captured by the GAS dynamics proposed by Creal et al. (2013). This model can be easily generalized from the bivariate case to the multivariate case. Third, we show that findings of dynamic and asymmetric dependence between equity and currency have important implications for risk management and asset allocation in international financial markets. Our empirical results show the statistical significance of the TVAC model in risk management and its economic values in real-time investment.

Chapter Four studies the credit risk of UK top-tier banks. We document asymmetric and time-varying features of dependence between the credit risk of UK top tier banks using a new CDS dataset. The market-implied probability of default for individual banks is derived from observed market quotes of CDS. The default dependence between banks is modeled by a novel dynamic asymmetric copula framework. We show that all the empirical features of CDS spreads, such as heavy-tailedness, skewness, time-varying volatility, multivariate asymmetries and dynamic dependence, can be captured well by our model. Given the marginal default probability and estimated copula model, we compute the joint and conditional probability of default of UK banks by applying a fast simulation algorithm. Comparing our model with traditional copula models, we find that the traditional models may underestimate the joint credit risk most of the time, especially during a crisis. Furthermore, we perform an extensive regression analysis and find solid evidence that time-varying tail dependence between CDS spreads of UK banks contains useful information to explain and predict their joint and conditional default probabilities.

Chapter Five concludes with recommendations for further study.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Copulas, dependence structure, asymmetry, time-varying dependence, hyperbolic generalized skewed t copula, generalized autoregressive score, market risk, portfolio optimization, credit risk, joint probability of default, conditional probability of default.
• Subjects: H Social Sciences > HG Finance
• Colleges/Schools: College of Social Sciences > Adam Smith Business School > Economics
• Supervisor's Name: Cerrato, Prof. Mario and Ewald, Prof. Christian
• Date of Award: 2016
• Depositing User: Dr YANG ZHAO
• Unique ID: glathesis:2016-7179
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 30 Mar 2016 10:35
• Last Modified: 15 Apr 2016 11:41
• URI: https://theses.gla.ac.uk/id/eprint/7179