Fat-tailed models for risk estimation

In the post-crisis era, financial institutions seem to be more aware of the risks posed by extreme events. Even though there are attempts to adapt methodologies drawing from the vast academic literature on the topic, there is also skepticism that fat-tailed models are needed. In this paper, we address the common criticism and discuss three popular methods for extreme risk modeling based on full distribution modeling and and extreme value theory. --

Some stylized facts of returns in the foreign exchange and stock markets in Peru

Some stylized facts for foreign exchange and stock market returns are explored using statistical methods. Formal statistics for testing presence of autocorrelation, asymmetry, and other deviations from normality is applied to these financial returns. Dynamic correlations and different kernel estimations and approximations of the empirical distributions are also under scrutiny. Furthermore, dynamic analysis of mean, standard deviation, skewness and kurtosis are also performed to evaluate time-varying properties in return distributions. Main results reveal different sources and types of non-normality in the return distributions in both markets. Left fat tails, excess kurtosis, return clustering and unconditional time-varying moments show important deviations from normality. Identifiable volatility cycles in both forex and stock markets are associated to common macro financial uncertainty events.Non-Normal Distributions, Stock Market Returns, Foreign Exchange Market Returns.

Some Stylized Facts of Returns in the Foreign Exchange and Stock Markets in Peru

Some stylized facts for foreign exchange and stock market returns are explored using statistical methods. Formal statistics for testing presence of autocorrelation, asymmetry, and other deviations from normality are applied to these ?nancial returns. Dynamic correlations and di¤erent kernel estimations and approximations of the empirical distributions are also under scrutiny. Furthermore, dynamic analysis of mean, standard deviation, skewness and kurtosis are also performed to evaluate time-varying properties in return distributions. Main results reveal di¤erent sources and types of non-normality in the return distributions in both markets. Left fat tails, excess kurtosis, return clustering and unconditional time-varying moments show important deviations from normal- ity. Identi?able volatility cycles in both forex and stock markets are associated to common macro ?nancial uncertainty events.Non-Normal Distributions, Stock Market Returns, Foreign Exchage, Market Returns

A component GARCH model with time varying weights

We present a novel GARCH model that accounts for time varying, state dependent, persistence in the volatility dynamics. The proposed model generalizes the component GARCH model of Ding and Granger (1996). The volatility is modelled as a convex combination of unobserved GARCH components where the combination weights are time varying as a function of appropriately chosen state variables. In order to make inference on the model parameters, we develop a Gibbs sampling algorithm. Adopting a fully Bayesian approach allows to easily obtain medium and long term predictions of relevant risk measures such as value at risk and expected shortfall. Finally we discuss the results of an application to a series of daily returns on the S&P500.GARCH, persistence, volatility components, value-at-risk, expected shortfall

Classification of methods for risk measures VaR and CVaR calculation and estimation

A systematic classification of the existing approaches for popular risk measures VaR and CVaR calculating and estimating is fulfilled. A review of the most used methods is done. For convenience, the considered methods are reduced to common econometric designations and concepts, guidance on the use of the methods is proposed. The correctness of the considered methods is numerically confirmed.Проведено системну класифікацію існуючих підходів знаходження і оцінювання популярних мір ризику VaR і CVaR. Проведено огляд найбільш поширених методів. Для зручності користування розглянуто методи, зведені до спільних економетричних позначень і понять, наведено рекомендації щодо використання методів. Коректність розглянутих методів підтверджено в результаті числової апробації.Проведена системная классификация существующих подходов нахождения и оценивания популярных мер риска VaR и CVaR. Проведен обзор наиболее используемых методов. Для удобства пользования рассмотренные методы сведены к общим эконометрическим обозначениям и понятиям, приведены рекомендации по использованию методов. Корректность предложенных методов подтверждена в результате численной апробации

Классификация методов вычисления и оценивания мер риска VaR и CVaR

Проведено системну класифікацію існуючих підходів знаходження і оцінювання популярних мір ризику VaR і CVaR. Проведено огляд найбільш поширених методів. Для зручності користування розглянуто методи, зведені до спільних економетричних позначень і понять, наведено рекомендації щодо використання методів. Коректність розглянутих методів підтверджено в результаті числової апробації.A systematic classification of the existing approaches for popular risk measures VaR and CVaR calculating and estimating is fulfilled. A review of the most used methods is done. For convenience, the considered methods are reduced to common econometric designations and concepts, guidance on the use of the methods is proposed. The correctness of the considered methods is numerically confirmed.Проведена системная классификация существующих подходов нахождения и оценивания популярных мер риска VaR и CVaR. Проведен обзор наиболее используемых методов. Для удобства пользования рассмотренные методы сведены к общим эконометрическим обозначениям и понятиям, приведены рекомендации по использованию методов. Корректность предложенных методов подтверждена в результате численной апробации

The Impact of Sampling Frequency and Volatility Estimators on Change-Point Tests

The paper evaluates the performance of several recently proposed change-point tests applied to conditional variance dynamics and conditional distributions of asset returns. These are CUSUM-type tests for beta-mixing processes and EDF-based tests for the residuals of such nonlinear dependent processes. Hence the tests apply to the class of ARCH and SV type processes as well as data-driven volatility estimators using high-frequency data. It is shown that some of the high-frequency volatility estimators substantially improve the power of the structural breaks tests especially for detecting changes in the tail of the conditional distribution. Similarly, certain types of filtering and transformation of the returns process can improve the power of CUSUM statistics. We also explore the impact of sampling frequency on each of the test statistics. Ce papier évalue la performance de plusieurs tests de changement structurel CUSUM et EDF pour la structure dynamique de la variance conditionelle et de la distribution conditionnelle. Nous étudions l'impact 1) de la fréquence des observations, 2) de l'utilisation des données de haute fréquence pour le calcul des variances conditionnelles et 3) de transformation des séries pour améliorer la puissance des tests.Change-point tests, CUSUM, Kolmogorov-Smirnov, GARCH, quadratic variation, power variation, high-frequency data, location-scale distribution family, tests de changement structurel, CUSUM, Kolmogov-Smirnov, GARCH, variation quadratique, 'power variation', données de haute fréquence

Applications of Vine Copulas in Commodity Risk Management and Price Analysis

This dissertation consists of three studies that focus on applications of vine copulas, a relatively new class of multivariate copula approach, in commodity risk management and price analysis. The first study proposes a vine copula approach to estimate multiproduct hedge ratios that minimize the risk of refining margin erosion – the downside risk facing a typical oil refinery whose profit greatly depends on its refining margin or the difference between the prices of its refined products and the cost of crude oil. The out-of-sample hedging effectiveness of two popular classes of vine copula models – canonical (C-) and drawable (D-) vine copula models – are evaluated and compared with that of a widely used nonparametric method and three standard multivariate copula models. The empirical results reveal that the D-vine copula model seems to be a good and safe choice in managing the downside risk of the refinery. The second study explores the importance of modeling heterogeneous dependence structures between different pairs of energy commodity returns with vine copulas in improving one-step-ahead density forecasts of these returns. The value of modeling heterogeneous dependence structures is measured by comparing the performance of density forecasts based on vine copulas with density forecasts based on standard copulas that assume homogeneous dependence structures. The empirical results suggest that modeling heterogeneous dependence structures using vine copulas does not help improve quality of multivariate density forecasts of energy commodity returns. The third study applies a vine copula approach to analyze the dependence structure and tail dependence patterns among daily prices of three agricultural commodities (corn, soybean, and wheat) and two energy commodities (ethanol and crude oil) from June 2006 to June 2016. Our findings suggest that the prices of corn and crude oil are linked through the ethanol market. We also find that crude oil and agricultural commodity prices are statistically dependent during the extreme market downturns but independent during the extreme market upturns. Moreover, the results from our sub-sample analysis show that both the upper and lower tail dependence between crude oil and other commodity markets become weaker in the recent years when the ethanol market became more mature

Risk Management of Risk Under the Basel Accord: A Bayesian Approach to Forecasting Value-at-Risk of VIX Futures

It is well known that the Basel II Accord requires banks and other Authorized Deposit-taking Institutions (ADIs) to communicate their daily risk forecasts to the appropriate monetary authorities at the beginning of each trading day, using one or more risk models, whether individually or as combinations, to measure Value-at-Risk (VaR). The risk estimates of these models are used to determine capital requirements and associated capital costs of ADIs, depending in part on the number of previous violations, whereby realised losses exceed the estimated VaR. Previous papers proposed a new approach to model selection for predicting VaR, consisting of combining alternative risk models, and comparing conservative and aggressive strategies for choosing between VaR models. This paper, using Bayesian and non- Bayesian combinations of models addresses the question of risk management of risk, namely VaR of VIX futures prices, and extends the approaches given in previous papers to examine how different risk management strategies performed during the 2008-09 global financial crisis (GFC). The use of time-varying weights using Bayesian methods, allows dynamic combinations of the different models to obtain a more accurate VaR forecasts than the estimates and forecasts that might be produced by a single model of risk. One of these dynamic combinations are endogenously determined by the pass performance in terms of daily capital charges of the individual models. This can improve the strategies to minimize daily capital charges, which is a central objective of ADIs. The empirical results suggest that an aggressive strategy of choosing the Supremum of single model forecasts, as compared with Bayesian and non-Bayesian combinations of models, is preferred to other alternatives, and is robust during the GFC.Median strategy, Value-at-Risk, Daily capital charges, Violation penalties, Aggressive risk management, Conservative risk management, Basel Accord, VIX futures, Bayesian strategy, Quantiles, Forecast densities.