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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.
We develop a portfolio risk model that uses high-frequency data to forecast the loss surface, which is the set of loss distributions at future time horizons. Our model uses a fully automated, semi-parametric fitting procedure that has its basis in extreme value statistics. We take account of distributional asymmetry, heavy tails, heteroscedasticity and serial correlation. Loss distributions are time aggregated by taking products of characteristic functions. We test loss-surface-implied forecasts of value at risk and expected shortfall out of sample on a diverse set of portfolios and we compare our forecasts to industry-standard risk forecasts that are based on asset and factor covariance matrices. The empirical results make a compelling case for the application and further development of our approach.
In this book Simona Roccioletti reviews several valuable studies about risk measures and their properties; in particular she studies the new (and heavily discussed) property of "Elicitability" of a risk measure. More important, she investigates the issue related to the backtesting of Expected Shortfall. The main contribution of the work is the application of "Test 1" and "Test 2" developed by Acerbi and Szekely (2014) on different models and for five global market indexes.
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.
Empirical studies have shown that a large number of financial asset returns exhibit fat tails and are often characterized by volatility clustering and asymmetry. Also revealed as a stylized fact is Long memory or long range dependence in market volatility, with significant impact on pricing and forecasting of market volatility. The implication is that models that accomodate long memory hold the promise of improved long-run volatility forecast as well as accurate pricing of long-term contracts. On the other hand, recent focus is on whether long memory can affect the measurement of market risk in the context of Value-at-Risk (V aR). In this paper, we evaluate the Value-at-Risk (VaR) and Expected Shortfall (ESF) in financial markets under such conditions. We examine one equity portfolio, the British FTSE100 and three stocks of the German DAX index portfolio (Bayer, Siemens and Volkswagen). Classical VaR estimation methodology such as exponential moving average (EMA) as well as extension to cases where long memory is an inherent characteristics of the system are investigated. In particular, we estimate two long memory models, the Fractional Integrated Asymmetric Power-ARCH and the Hyperbolic-GARCH with different error distribution assumptions. Our results show that models that account for asymmetries in the volatility specifications as well as fractional integrated parametrization of the volatility process, perform better in predicting the one-step as well as five-step ahead VaR and ESF for short and long positions than short memory models. This suggests that for proper risk valuation of options, the degree of persistence should be investigated and appropriate models that incorporate the existence of such characteristic be taken into account.
This book provides a comprehensive and systematic approach to understanding GARCH time series models and their applications whilst presenting the most advanced results concerning the theory and practical aspects of GARCH. The probability structure of standard GARCH models is studied in detail as well as statistical inference such as identification, estimation and tests. The book also provides coverage of several extensions such as asymmetric and multivariate models and looks at financial applications. Key features: Provides up-to-date coverage of the current research in the probability, statistics and econometric theory of GARCH models. Numerous illustrations and applications to real financial series are provided. Supporting website featuring R codes, Fortran programs and data sets. Presents a large collection of problems and exercises. This authoritative, state-of-the-art reference is ideal for graduate students, researchers and practitioners in business and finance seeking to broaden their skills of understanding of econometric time series models.
Seminar paper from the year 2009 in the subject Business economics - Controlling, grade: 1,5, University of Innsbruck (Institut für Banken und Finanzen), course: Seminar SBWL Risk Management, language: English, abstract: This seminar paper is divided in the following chapters: 1. Definition of Value at Risk: What is VaR, several definitions of this figure. 2. The three common approaches for calculating Value at Risk: Historical simulation, Monte Carlo simulation, Variance-Covariance model. 3. The critical view: Problems and limitations of Value at Risk. Which approach can be meaningfully used and when not? Why is Value at Risk not the “only truth” in financial institutions? What are the strengths and weaknesses of the several approaches in calculating Value at Risk?
Portfolio risk forecasts are commonly evaluated using test statistics that are sums of random variables. We study the distributional properties of these test statistics for value at risk, expected shortfall, and volatility. For a diverse collection of 74 US equity portfolios, risk forecasts based on an extreme value theory model greatly outperform a conditional normal model with a 23-day halflife. On the other hand, we show that the common assumption of asymptotic normality in test statistics for these risk measures is not always satisfied, especially for test statistics related to volatility.
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.