Estimation Of Market Risk In Case Of Non Gaussian Assets Returns

Written by leading market risk academic, Professor Carol Alexander, Quantitative Methods in Finance forms part one of the Market Risk Analysis four volume set. Starting from the basics, this book helps readers to take the first step towards becoming a properly qualified financial risk manager and asset manager, roles that are currently in huge demand. Accessible to intelligent readers with a moderate understanding of mathematics at high school level or to anyone with a university degree in mathematics, physics or engineering, no prior knowledge of finance is necessary. Instead the emphasis is on understanding ideas rather than on mathematical rigour, meaning that this book offers a fast-track introduction to financial analysis for readers with some quantitative background, highlighting those areas of mathematics that are particularly relevant to solving problems in financial risk management and asset management. Unique to this book is a focus on both continuous and discrete time finance so that Quantitative Methods in Finance is not only about the application of mathematics to finance; it also explains, in very pedagogical terms, how the continuous time and discrete time finance disciplines meet, providing a comprehensive, highly accessible guide which will provide readers with the tools to start applying their knowledge immediately. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Principal component analysis of European equity indices; Calibration of Student t distribution by maximum likelihood; Orthogonal regression and estimation of equity factor models; Simulations of geometric Brownian motion, and of correlated Student t variables; Pricing European and American options with binomial trees, and European options with the Black-Scholes-Merton formula; Cubic spline fitting of yields curves and implied volatilities; Solution of Markowitz problem with no short sales and other constraints; Calculation of risk adjusted performance metrics including generalised Sharpe ratio, omega and kappa indices.

While mainstream financial theories and applications assume that asset returns are normally distributed, overwhelming empirical evidence shows otherwise. Yet many professionals don’t appreciate the highly statistical models that take this empirical evidence into consideration. Fat-Tailed and Skewed Asset Return Distributions examines this dilemma and offers readers a less technical look at how portfolio selection, risk management, and option pricing modeling should and can be undertaken when the assumption of a non-normal distribution for asset returns is violated. Topics covered in this comprehensive book include an extensive discussion of probability distributions, estimating probability distributions, portfolio selection, alternative risk measures, and much more. Fat-Tailed and Skewed Asset Return Distributions provides a bridge between the highly technical theory of statistical distributional analysis, stochastic processes, and econometrics of financial returns and real-world risk management and investments.

Written by leading market risk academic, Professor Carol Alexander, Practical Financial Econometrics forms part two of the Market Risk Analysis four volume set. It introduces the econometric techniques that are commonly applied to finance with a critical and selective exposition, emphasising the areas of econometrics, such as GARCH, cointegration and copulas that are required for resolving problems in market risk analysis. The book covers material for a one-semester graduate course in applied financial econometrics in a very pedagogical fashion as each time a concept is introduced an empirical example is given, and whenever possible this is illustrated with an Excel spreadsheet. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM. Empirical examples and case studies specific to this volume include: Factor analysis with orthogonal regressions and using principal component factors; Estimation of symmetric and asymmetric, normal and Student t GARCH and E-GARCH parameters; Normal, Student t, Gumbel, Clayton, normal mixture copula densities, and simulations from these copulas with application to VaR and portfolio optimization; Principal component analysis of yield curves with applications to portfolio immunization and asset/liability management; Simulation of normal mixture and Markov switching GARCH returns; Cointegration based index tracking and pairs trading, with error correction and impulse response modelling; Markov switching regression models (Eviews code); GARCH term structure forecasting with volatility targeting; Non-linear quantile regressions with applications to hedging.

This book examines non-Gaussian distributions. It addresses the causes and consequences of non-normality and time dependency in both asset returns and option prices. The book is written for non-mathematicians who want to model financial market prices so the emphasis throughout is on practice. There are abundant empirical illustrations of the models and techniques described, many of which could be equally applied to other financial time series.

Scientific Essay from the year 2012 in the subject Business economics - Investment and Finance, grade: B, King`s College London, language: English, abstract: For quite a long time now the main concern for investors as well as regulators of financial markets has been the risk of catastrophic market and the sufficiency of capital needed to counter such kind of risk when it occurs. Many institutions have undergone loses despite their gigantic nature and good forecasting and this has been associated with inappropriate forms of pricing and poor management together with the fraudulent cases, factors that have always brought the issue of managing risk and regulating these financial markets to the level of public policy as well as discussion. A basic tool that has been identified as being effective in the assessment of financial risk is the Value at Risk (VaR) process (Artzner, et al., 1997). The VaR has been figured out as being an amount that is lost on a given form of portfolio including a small probability in a certain fixed period of time counted in terms of days. VaR however poses a major challenge during its implementation and this has more to do with the specification of the kind of probability distribution having extreme returns that is made use of during the calculation of the estimates used in the VaR analysis (Mahoney, 1996; McNeil & Frey, 2000; Dowd, 2001). As has been noted, the nature of VaR estimation majorly does depend on the accurate predictions of some uncommon events or risks that are catastrophic. This is attributed to the fact that VaR is a calculation made from the lowest portfolio returns. For this reason, any form of calculation that is employed in the estimation of VaR must be able to encompass the tail events’ prediction and make this its primary goal (Chiang, et al., 2007; Engle, 2002; Engle & Kroner, 1995; Engle & Rothschild, 1990; Francis, et al., 2001). There have been statistical techniques as well as thumb rules that many researchers argue as having been very instrumental in the prediction and analysis of intra-day and in most cases day-to-day risk. These are however; not appropriate for the analysis of VaR. The predictions of VaR now fall under parametric predictions that encompass conditional volatilities and non-parametric prediction that incorporate the unconditional volatilities (Jorion, 2006; Jorion, 2007).

The following is a chapter from The VaR Implementation Handbook, which examines the latest strategies for measuring, managing, and modeling risk across a variety of applications. Packed with the insights, methods, and models that make experienced professionals competitive all over the world, this comprehensive guide features cutting-edge research and findings from some of the industry's most respected academics, practitioners, and consultants.

Market Risk Analysis is the most comprehensive, rigorous and detailed resource available on market risk analysis. Written as a series of four interlinked volumes each title is self-contained, although numerous cross-references to other volumes enable readers to obtain further background knowledge and information about financial applications. Volume I: Quantitative Methods in Finance covers the essential mathematical and financial background for subsequent volumes. Although many readers will already be familiar with this material, few competing texts contain such a complete and pedagogical exposition of all the basic quantitative concepts required for market risk analysis. There are six comprehensive chapters covering all the calculus, linear algebra, probability and statistics, numerical methods and portfolio mathematics that are necessary for market risk analysis. This is an ideal background text for a Masters course in finance. Volume II: Practical Financial Econometrics provides a detailed understanding of financial econometrics, with applications to asset pricing and fund management as well as to market risk analysis. It covers equity factor models, including a detailed analysis of the Barra model and tracking error, principal component analysis, volatility and correlation, GARCH, cointegration, copulas, Markov switching, quantile regression, discrete choice models, non-linear regression, forecasting and model evaluation. Volume III: Pricing, Hedging and Trading Financial Instruments has five very long chapters on the pricing, hedging and trading of bonds and swaps, futures and forwards, options and volatility as well detailed descriptions of mapping portfolios of these financial instruments to their risk factors. There are numerous examples, all coded in interactive Excel spreadsheets, including many pricing formulae for exotic options but excluding the calibration of stochastic volatility models, for which Matlab code is provided. The chapters on options and volatility together constitute 50% of the book, the slightly longer chapter on volatility concentrating on the dynamic properties the two volatility surfaces the implied and the local volatility surfaces that accompany an option pricing model, with particular reference to hedging. Volume IV: Value at Risk Models builds on the three previous volumes to provide by far the most comprehensive and detailed treatment of market VaR models that is currently available in any textbook. The exposition starts at an elementary level but, as in all the other volumes, the pedagogical approach accompanied by numerous interactive Excel spreadsheets allows readers to experience the application of parametric linear, historical simulation and Monte Carlo VaR models to increasingly complex portfolios. Starting with simple positions, after a few chapters we apply value-at-risk models to interest rate sensitive portfolios, large international securities portfolios, commodity futures, path dependent options and much else. This rigorous treatment includes many new results and applications to regulatory and economic capital allocation, measurement of VaR model risk and stress testing.

AbstractPurpose- The research aims to propose a scalable multivariate non-Gaussian model for VaR and volatility estimation and analyze its efficiency(in appropriately taking into account fat tails, and asymmetry for VaR estimation) as compared to traditional Gaussian approaches used for VaR estimation and portfolio construction. Financial distributions generally tend to portray asymmetry, fat tails or a mixture of distributions, which are captured by the discussed model that involves incorporating the Pareto distribution, skewed- t distributionThe study also intends to demonstrate that this results in portfolios that are having more utility. (Utility: How much excess return was generated for each unit of risk taken by the portfolio and also generating a portfolio with higher economic growth)alternative approaches including mean-variance. The utility can be leveraged by efficiently selecting(maximizing the utility defined above) the portfolio assets and their weights. This research also investigates the correlation across stock market indices of 6 Asia-Pacific countries and uses VaR and variance as the risk measures for the analysis.Findings-The authors successfully concluded that the model proposed in the paper estimates VaR more accurately than the traditional model. Also, our proposed model tends to outperform the literature model in portfolio construction by producing asset weights more efficiently.Design/Methodology/Approach- This research uses a GSEV strategy that comprises a univariate EGARCH approach for calculating stochastic volatility and the leverage effect. The Generalized Pareto distribution captures asymmetry and heavy tails in the GARCH residuals (GPD). The skewed-t copula is used to describe asymmetric tail dependence. Originality/value- The value added is to depict how the non-Gaussian model proposed by the authors includes the exponential GARCH (EGARCH) technique, Generalized Pareto distribution, skewed-t copula, and mixed distributions consideration gives VaR prediction and portfolio asset weights values more accurately than the traditional model.

The composition of portfolios is one of the most fundamental and important methods in financial engineering, used to control the risk of investments. This book provides a comprehensive overview of statistical inference for portfolios and their various applications. A variety of asset processes are introduced, including non-Gaussian stationary processes, nonlinear processes, non-stationary processes, and the book provides a framework for statistical inference using local asymptotic normality (LAN). The approach is generalized for portfolio estimation, so that many important problems can be covered. This book can primarily be used as a reference by researchers from statistics, mathematics, finance, econometrics, and genomics. It can also be used as a textbook by senior undergraduate and graduate students in these fields.