Dependence and Systemic Risks in Financial Markets: Spatial and Upper Tail Analysis

Abstract

[eng] In general, this thesis analyses the dependence between the financial stocks índices from different perspectives, taking into account the spatial dependence between financial returns, financial losses and financial risk measures. Finally, the thesis presents an innovative analysis of upper tail dependence between Spanish financial index losses against the losses of other market indices which are more or less close. Taken together, all this indicates that strong dependence is related to certain systemic risks caused by particular financial crises, but the intensity of the dependency changes from one financial crisis to another. Throughout the period analysed, the sub-prime crisis is revealed as the one with the greatest spatial dependence between financial markets. With regard to the other crises, the results depend on the analysed variable, loss or risk measure. When the focus is on the risk measures, Brexit is revealed as a source of dependency between financial markets. If we analyse losses, it is the European debt crisis that reflects a strong spatial dependency between markets.

In the first chapter the feasibility and benefits of using neighbourhood relations between stock markets based on time criteria are analysed, such as the time differences between country capitals where each financial market operates and the simultaneous opening hours between these markets. These criteria are compared with the distance in kilometres between country capitals. The objective is to find clusters between neighbouring stock indices that are associated with dependent financial markets. We apply the idea of spatial dependence between markets and use the Moran’s I statistic proposed by Moran (1950), calculated monthly for the period between January 2000 and December 2015, in order to analyse the spatial dependencies between market log-returns. The results show that the criterion based on simultaneous opening hours provides more relationships between neighbourhood markets. In addition, particularly between European markets, neighbourly relations were more intense during the 2008 financial crisis generated by the fall of Lehman Brothers. As a result of the events that occurred during this financial crisis, financial institutions were anxious to detect possible neighbour relationships between markets for systemic reasons in order to identify possible new sources of risk based on spatial dependence between indices. A Spanish version of this chapter was published in Acuña et al. (2018), with the title “Análisis de la dependencia espacial entre índices bursátiles”.

In Chapter 2 of this thesis the period analysed is extended until March 2021, incorporating Brexit and the COVID-19 pandemic in the study. This same period between January 2000 and March 2021 is also used in Chapters 3 and 4. Chapter 2 analyses two new dynamic distance criteria applied to stock markets based on exogenous criteria; the well-known World Uncertainty Index (WUI) and the proposed Google Trends Uncertainty Index (GTUI). The chapter discusses the feasibility and benefits of these dynamic distances compared to alternative hourbased criteria. Using the new distance criterion to obtain the Moran’s Index, the spatial dependence between the financial indices losses of 46 stock markets is analysed. Specifically, Chapter 2 focuses on learning more about the possible relation between systemic risk and spatial dependence. This systemic risk is related to the most important financial crises of the last 17 years: the bankruptcy of Lehman Brothers, the sub-prime mortgage crisis, the crisis of European debt, Brexit and the COVID-19 pandemic, the latter also affecting the financial markets.

The aim of Chapter 3 is to study the spatial dependence between the risk measures associated with the financial indices losses, specifically the variance (volatility) and the Value-at-Risk (VaR). The distribution associated with these risk measures has a strong right skewness, i.e., a long and heavy right tail, so it is important to analyse how this can affect the inference based on the asymptotic normality of the global and local dependency tests based on Moran’s statistic. With this aim in mind, in Chapter 3, the finite sample properties of inference based on global and local Moran’s I statistics are analysed through a simulation study that assumes that the data are generated from distributions with different shapes (symmetric, asymmetric and heavy tailed distributions). Furthermore, we propose an alternative bootstrap based inference that improves Type I and Type II errors of asymptotic inference. The spatial dependency between stock market risks has been discussed by using the definition of neighbour based on exogenous criterion derived from the Google Trends Dynamic Uncertainty Index (GTUI) proposed in Chapter 2. We show the impact of systemic risk on spatial dependency between risk measures related to the most significant financial crises since 2005: the Lehman Brothers bankruptcy, the sub-prime mortgage crisis, the European debt crisis, Brexit and the COVID-19 pandemic, the latter also affecting the market economy. The risks are measured using the monthly variance or volatility and the monthly VaR of the filtered losses associated with the analysed stock indices. Specifically, the global spatial dependence between the risk measures of 46 stock markets and the local spatial dependence for 10 world reference stock markets are analysed. . Chapter 4 focuses on the use of a proposed new kernel estimator of the copula to analyse the upper tail dependence between stock indices losses. A copula is a multivariate cumulative distribution function with marginal distributions Uniform(0, 1). This fact means that a classical kernel estimator does not work and this estimator must be corrected at bounds, which increases the difficulty of the estimation and, in practice, the bias correction limit may not provide the desired improvement. A quantile transformation of marginals is a way of improving the classical kernel approach. A first study using the standard normal quantile transformation was presentedby Omelka et al. (2009). The objective in the development of this chapter lies in showing that a Beta quantile transformation is optimal, and a kernel estimator based on this transformation is analysed. In addition, the basic properties that allow the new estimator to be used for inference on extreme value copulas are tested. The results of a simulation study show how the new nonparametric estimator improves the alternative kernel estimators of copulas. We illustrate our proposal with an analysis of financial data. The application shows the Spanish index (IBEX 35) has upper tail dependence with European neighbour markets as well as with other markets such as those in UK, USA and Hong Kong.