Analysis of Estimation and Specification of Various Econometric Models Used to Assess Financial Risk

Resumen

This thesis aims to analyze some of the available methods that aid in risk estimation based on econometric models, as well as to propose some new ones. Some of the questions that are expected to be answered include which distribution to choose to obtain better risk estimates for series with abnormal behaviours, how to determine whether the distribution in parametric conditional models is a Student’s t, and how to assess whether an asset’s risk helps predict the risk of another asset. In Chapter 1, we estimate several cryptocurrencies’ Expected Shortfall using different error distributions and GARCH-type models for conditional variance. ur goal is to examine which distributions perform better and to check which component of the specification plays a more crucial role in estimating Expected Shortfall. The performance of the estimations is conducted using a backtesting technique with a rolling-window approach. Results show that, in the case of Bitcoin, it is important to use a distribution with at least two parameters that control its shape and an extension of the GARCH model, whether it be the NGARCH or the CGARCH model. On the other hand, other smaller cryptocurrencies yield good enough risk predictions with the Student’s t distribution and a GARCH model. The fact that the main measures of financial risk are focused on the tail of the distribution of returns highlights the importance of the choice of an appropriate distribution model. Chapter 2 develops a procedure for consistently testing the specification of a Student’s t distribution for the innovations of a dynamic model. This contributes to the existing literature by providing a test for Student’s t distributions in conditional mean and variance models with a parameter-free test statistic and, thus, a known asymptotic distribution, avoiding the use of more computationally costly resampling techniques such as bootstrapping. The specific expressions needed for the computation of the test statistic are obtained by adapting the generic test of Bai (2003), which is based on the Khmaladze (1988) transformation of the model residuals. Finally, in Chapter 3, the concept of Granger causality in Expected Shortfall (ES) is introduced, along with a testing procedure to detect this type of predictive relationship between return series. Granger causality in Expected Shortfall is here defined as the predictive ability of tail values of a series over future tail values of another series on average. This definition may help in analyzing whether past values of an asset in extreme risk affect future extreme risk values of another asset. The main contribution of this chapter is a test for detecting this type of causality, based on the test for Granger causality in VaR by Hong et al. (2009). An empirical application on financial institutions from different industries (banking, insurance, and diversified financials) is presented to analyze the risk spillovers in the US financial market. The contribution of this thesis to the field of financial econometrics focuses on the market risk of financial assets, both in its modeling through the metric known as Expected Shortfall suggested in the Basel III Accords and in its utility beyond capital requirements. The results highlight the importance of a good specification of the chosen distribution model for risk estimation - especially in high-risk assets such as cryptocurrencies - and a test is proposed to verify if the conditional distribution in parametric models used for risk predictions is or is not a Student’s t distribution. Finally, a Granger causality test in Expected Shortfall is proposed, which allows for studying risk propagation in tails of return distributions. The proposed test can be used to investigate interconnections within and between markets as a complement when evaluating systemic risk. Other potential applications include improving Expected Shortfall forecasts by including causing variables as regressors in estimations, studying the inclusion of certain asset pairs in the same portfolio based on how they interact in the riskiest situations, or constructing networks of extreme risk propagation.