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Using copulas' approach and parametric models, we show that the bivariate distribution of an Asian portfolio is not stable all along the period under study. Thus, we develop several dynamical models to compute two market risk's measures: the Value at Risk and the Expected Shortfall. The methods considered are the RiskMetric methodology, the Multivariate GARCH models, the Multivariate Markov-Switching models, the empirical histogram and the dynamical copulas. We discuss the choice of the best method with respect to the policy management of banks supervisors. The copula approach seems to be a good compromise between all these models. It permits to take into account financial crises and to obtain a low capital requirement during the most important crises.
Portfolio theory and much of asset pricing, as well as many empirical applications, depend on the use of multivariate probability distributions to describe asset returns. Traditionally, this has meant the multivariate normal (or Gaussian) distribution. More recently, theoretical and empirical work in financial economics has employed the multivariate Student (and other) distributions which are members of the elliptically symmetric class. There is also a growing body of work which is based on skew-elliptical distributions. These probability models all exhibit the property that the marginal distributions differ only by location and scale parameters or are restrictive in other respects. Very often, such models are not supported by the empirical evidence that the marginal distributions of asset returns can differ markedly. Copula theory is a branch of statistics which provides powerful methods to overcome these shortcomings. This book provides a synthesis of the latest research in the area of copulae as applied to finance and related subjects such as insurance. Multivariate non-Gaussian dependence is a fact of life for many problems in financial econometrics. This book describes the state of the art in tools required to deal with these observed features of financial data. This book was originally published as a special issue of the European Journal of Finance.
This edited volume contains essential readings for financial analysts and market practitioners working at Central Banks and Sovereign Wealth Funds. It presents the reader with state-of-the-art methods that are directly implementable, and industry 'best-practices' as followed by leading institutions in their field.
The present study compares the performance of the long memory FIGARCH model, with that of the short memory GARCH specification, in the forecasting of multi-period Value-at-Risk (VaR) and Expected Shortfall (ES) across 20 stock indices worldwide. The dataset is comprised of daily data covering the period from 1989 to 2009. The research addresses the question of whether or not accounting for long memory in the conditional variance specification improves the accuracy of the VaR and ES forecasts produced, particularly for longer time horizons. Accounting for fractional integration in the conditional variance model does not appear to improve the accuracy of the VaR forecasts for the 1-dayahead,10-day-ahead and 20-day-ahead forecasting horizons relative to the short memory GARCH specification. Additionally, the results suggest that underestimation of the true VaR figure becomes less prevalent as the forecasting horizon increases. Furthermore, the GARCH model has a lower quadratic loss between actual returns and ES forecasts, for the majority of the indices considered for the 10-day and 20-day forecasting horizons. Therefore, a long memory volatility model compared to a short memory GARCH model does not appear to improve the VaR and ES forecasting accuracy, even for longer forecasting horizons. Finally, the rolling-sampled estimated FIGARCH parameters change less smoothly over time compared to the GARCH models. Hence, the parameters' time-variant characteristic cannot be entirely due to the news information arrival process of the market; a portion must be due to the FIGARCH modelling process itself.
Financial Risk Forecasting is a complete introduction to practical quantitative risk management, with a focus on market risk. Derived from the authors teaching notes and years spent training practitioners in risk management techniques, it brings together the three key disciplines of finance, statistics and modeling (programming), to provide a thorough grounding in risk management techniques. Written by renowned risk expert Jon Danielsson, the book begins with an introduction to financial markets and market prices, volatility clusters, fat tails and nonlinear dependence. It then goes on to present volatility forecasting with both univatiate and multivatiate methods, discussing the various methods used by industry, with a special focus on the GARCH family of models. The evaluation of the quality of forecasts is discussed in detail. Next, the main concepts in risk and models to forecast risk are discussed, especially volatility, value-at-risk and expected shortfall. The focus is both on risk in basic assets such as stocks and foreign exchange, but also calculations of risk in bonds and options, with analytical methods such as delta-normal VaR and duration-normal VaR and Monte Carlo simulation. The book then moves on to the evaluation of risk models with methods like backtesting, followed by a discussion on stress testing. The book concludes by focussing on the forecasting of risk in very large and uncommon events with extreme value theory and considering the underlying assumptions behind almost every risk model in practical use – that risk is exogenous – and what happens when those assumptions are violated. Every method presented brings together theoretical discussion and derivation of key equations and a discussion of issues in practical implementation. Each method is implemented in both MATLAB and R, two of the most commonly used mathematical programming languages for risk forecasting with which the reader can implement the models illustrated in the book. The book includes four appendices. The first introduces basic concepts in statistics and financial time series referred to throughout the book. The second and third introduce R and MATLAB, providing a discussion of the basic implementation of the software packages. And the final looks at the concept of maximum likelihood, especially issues in implementation and testing. The book is accompanied by a website - www.financialriskforecasting.com – which features downloadable code as used in the book.
The Handbook of Financial Time Series gives an up-to-date overview of the field and covers all relevant topics both from a statistical and an econometrical point of view. There are many fine contributions, and a preamble by Nobel Prize winner Robert F. Engle.
The estimation of risk measures is an area of highest importance in the financial industry. Risk measures play a major role in the risk-management and in the computation of regulatory capital. The Basel III document [13] has suggested to shift from Value-at-Risk (VaR) into Expected Shortfall (ES) as a risk measure and to consider stressed scenarios at a new con dence level of 97:5%. This change is motivated by the appealing theoretical properties of ES as a measure of risk and the poor properties of VaR. In particular, VaR fails to control for tail risk". In this transition, the major challenge faced by nancial institutions is the unavailability of simple tools for evaluation of ES forecasts (i.e. backtesting ES) The objective of this thesis is to compare the performance of a variety of models for VaR and ES estimation for a collection of assets of di erent nature: stock indexes, individual stocks, bonds, exchange rates, and commodities. Throughout the thesis, by a VaR or an ES model" is meant a given speci cation for conditional volatility, combined with an assumption on the probability distribution of return innovations...
In April 2010 Europe was shocked by the Greek financial turmoil. At that time, the global financial crisis, which started in the summer of 2007 and reached systemic dimensions in September 2008 with the Lehman Brothers’ crash, took a new course. An adverse feedback loop between sovereign and bank risks reflected into bubble-like spreads, as if financial markets had received a wake-up call concerning the disregarded structural vulnerability of economies at risk.These events inspired the SYRTO project to “think and rethink the economic and financial system and to conceive it as an “ensemble of Sovereigns and Banks with other Financial Intermediaries and Corporations. Systemic Risk Tomography: Signals, Measurement and Transmission Channels proposes a novel way to explore the financial system by sectioning each part of it and analyzing all relevant inter-relationships. The financial system is inspected as a biological entity to identify the main risk signals and to provide the correct measures of prevention and intervention. Explores the economic and financial system of Sovereigns, Banks, other Financial Intermediaries, and Corporations Presents the financial system as a biological entity to be explored in order to identify the main risk signals and provide the right measures of prevention and interventions Offers a new, systemic-based approach to construct a hierarchical, internally coherent framework to be used in developing an effective early warning system
This book includes 46 scientific papers presented at the conference and reflecting the latest research in the fields of data mining, machine learning and decision-making. The international scientific conference “Intellectual Systems of Decision-Making and Problems of Computational Intelligence” was held in the Kherson region, Ukraine, from May 25 to 29, 2020. The papers are divided into three sections: “Analysis and Modeling of Complex Systems and Processes,” “Theoretical and Applied Aspects of Decision-Making Systems” and “Computational Intelligence and Inductive Modeling.” The book will be of interest to scientists and developers specialized in the fields of data mining, machine learning and decision-making systems.