Download or read book Using Orthogonal GARCH to Forecast Covariance Matrix of Stock Returns written by Jingjing Bai and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The motivation of this paper is to study the estimation problems in large dimension systems in quantitative finance. The paper firstly presents principal component analysis to obtain the most important information in the data. Then, the orthogonal GARCH model introduced by Alexander and Chibumba (1997) and Alexander (2000) is provided to forecast five energy stocks0́9 monthly volatilities and correlations. I show that as long as the stocks are already highly correlated with one another, the orthogonal GARCH approach will reduce computational complexity, control the amount of 0́8noise0́9, and produce volatility and correlations for all the assets. All the computation procedures were accomplished in Microsoft Excel. Forecasting of volatility and correlation of stock returns is significant in the analysis of option pricing, portfolio optimization and value-at-risk models.

Download or read book Forecasting a Large Dimensional Covariance Matrix of a Portfolio of Different Asset Classes written by Lillie Lam and published by . This book was released on 2009 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In portfolio and risk management, estimating and forecasting the volatilities and correlations of asset returns plays an important role. Recently, interest in the estimation of the covariance matrix of large dimensional portfolios has increased. Using a portfolio of 63 assets covering stocks, bonds and currencies, this paper aims to examine and compare the predictive power of different popular methods adopted by i) market practitioners (such as the sample covariance, the 250-day moving average, and the exponentially weighted moving average); ii) some sophisticated estimators recently developed in the academic literature (such as the orthogonal GARCH model and the Dynamic Conditional Correlation model); and iii) their combinations. Based on five different criteria, we show that a combined forecast of the 250-day moving average, the exponentially weighted moving average and the orthogonal GARCH model consistently outperforms the other methods in predicting the covariance matrix for both one-quarter and one-year ahead horizons.

Download or read book Orthogonal GARCH and Covariance Matrix Forecasting in a Stress Scenario written by Hans N. E. Byström and published by . This book was released on 2000 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Market Risk Analysis Practical Financial Econometrics written by Carol Alexander and published by John Wiley & Sons. This book was released on 2008-05-27 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Modelling and forecasting stock return volatility and the term structure of interest rates written by Michiel de Pooter and published by Rozenberg Publishers. This book was released on 2007 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of a collection of studies on two areas in quantitative finance: asset return volatility and the term structure of interest rates. The first part of this dissertation offers contributions to the literature on how to test for sudden changes in unconditional volatility, on modelling realized volatility and on the choice of optimal sampling frequencies for intraday returns. The emphasis in the second part of this dissertation is on the term structure of interest rates.

Download or read book A Test of Covariance Matrix Forecasting Methods written by Valeriy Zakamulin and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a more accurate covariance matrix forecast can substantially improve the performance of optimized portfolios. Using out-of-sample tests, in this paper, we evaluate alternative covariance matrix forecasting methods by looking at (1) their forecast accuracy, (2) their ability to track the volatility of the minimum-variance portfolio, and (3) their ability to keep the volatility of the minimum-variance portfolio at a target level. We find large differences between the methods. Our results suggest that shrinkage of the sample covariance matrix improves neither the forecast accuracy nor the performance of minimum-variance portfolios. In contrast, switching from the sample covariance matrix forecast to a multivariate GARCH forecast reduces forecasting error and portfolio tracking error by at least half. Our findings also reveal that the exponentially weighted covariance matrix forecast performs only slightly worse than the multivariate GARCH forecast.

Download or read book Handbook of Economic Forecasting written by G. Elliott and published by Elsevier. This book was released on 2006-07-14 with total page 1071 pages. Available in PDF, EPUB and Kindle. Book excerpt: Section headings in this handbook include: 'Forecasting Methodology; 'Forecasting Models'; 'Forecasting with Different Data Structures'; and 'Applications of Forecasting Methods.'.

Download or read book Modeling the Conditional Covariance between Stock and Bond Returns written by Wessel Marquering and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: To analyze the intertemporal interaction between the stock and bond market returns, we assume that the conditional covariance matrix follows a multivariate GARCH process. We allow for asymmetric effects in conditional variances and covariances. Using daily data, we find strong evidence of conditional heteroskedasticity in the covariance between stock and bond market returns. The results indicate that not only variances, but also covariances respond asymmetrically to return shocks. Bad news in the stock and bond market is typically followed by a higher conditional covariance than good news. Cross asymmetries, that is, asymmetries followed from shocks of opposite signs, appear to be important as well. Covariances between stock and bond returns tend to be relatively low after bad news in the stock market and good news in the bond market. A financial application of our model shows that optimal portfolio shares can be substantially affected by asymmetries in covariances. Moreover, our results show sizable gains due to asymmetric volatility timing.

Download or read book Market Risk Analysis Boxset written by Carol Alexander and published by John Wiley & Sons. This book was released on 2009-02-24 with total page 1691 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Orthogonal Methods for Generating Large Positive Semi Definite Covariance Matrices written by Carol Alexander and published by . This book was released on 2000 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is a common problem in risk management today that risk measures and pricing models are being applied to a very large set of scenarios based on movements in all possible risk factors. The dimensions are so large that the computations become extremely slow and cumbersome, so it is quite common that over-simplistic assumptions will be made. In particular, in order to generate the large covariance matrices that are used in Value-at-Risk models, some very strong constraints are imposed on the movements in volatility assumption is also imposed, because it has not been possible to generate large GARCH covariance matrices with mean-reverting term structures.This paper introduces a new method for generating large positive semi-definite covariance matrices. It is based on univariate GARCH volatilities of a few, uncorrelated key risk factors to provide more realistic term structure forecasts in covariance matrices. Alternatively the method can be used with exponentially weighted moving average key risk factor volatilities, where the smoothing constant is automatically determined by the correlation in the system. In addition to implementing multivariate GARCH of arbitrarily large dimension without the need for constrained parameterizations, advantages of this method include: the ability to tailor the amount of noise in the system so that correlation estimates are more stable; and the volatility and correlation forecasting of new issues or illiquid markets in the system.

Download or read book Financial Risk Forecasting written by Jon Danielsson and published by John Wiley & Sons. This book was released on 2011-04-20 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Flexible Multivariate GARCH Modeling with an Application to International Stock Markets written by Olivier Ledoit and published by . This book was released on 2008 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk measurement, portfolio selection, and tests of asset pricing models, this is a very important problem in practice. Our model of choice is the Diagonal-Vech version of the Multivariate GARCH(1,1) model. The problem is that the estimation of the general Diagonal-Vech model model is numerically infeasible in dimensions higher than 5. The common approach is to estimate more restrictive models which are tractable but may not conform to the data. Our contribution is to propose an alternative estimation method that is numerically feasible, produces positive semi-definite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator to a number of existing ones.

Download or read book Modeling Fat Tails in Stock Returns written by Matteo Bonato and published by . This book was released on 2009 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper a new multivariate volatility model is proposed. It combines the appealing properties of the stable Paretian distribution to model the heavy tails with the GARCH model to capture the volatility clustering. We assume that multivariate asset-returns of financial stocks follow a sub-Gaussian distribution, which is a particular multivariate stable distribution. In this way the characteristic function of the fitted returns has a tractable expression and the density function can be recovered by numerical methods. A multivariate GARCH structure is then adopted to model the covariance matrix of the Gaussian vectors underlying the sub-Gaussian system. The model is applied to a bivariate series of daily U.S. stock returns. Value-at-Risk for long and short positions is computed and compared with the one obtained using the multivariate normal and the multivariate Student's t distribution. Finally, exploiting the recent developments in the vast dimensional time-varying covariances modeling, possible feasible extensions to higher dimensions are suggested and an illustrative example using the Dow Jones index components is presented.

Download or read book Volatility and Correlation written by Riccardo Rebonato and published by John Wiley & Sons. This book was released on 2005-07-08 with total page 864 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Volatility and Correlation 2nd edition: The Perfect Hedger and the Fox, Rebonato looks at derivatives pricing from the angle of volatility and correlation. With both practical and theoretical applications, this is a thorough update of the highly successful Volatility & Correlation – with over 80% new or fully reworked material and is a must have both for practitioners and for students. The new and updated material includes a critical examination of the ‘perfect-replication’ approach to derivatives pricing, with special attention given to exotic options; a thorough analysis of the role of quadratic variation in derivatives pricing and hedging; a discussion of the informational efficiency of markets in commonly-used calibration and hedging practices. Treatment of new models including Variance Gamma, displaced diffusion, stochastic volatility for interest-rate smiles and equity/FX options. The book is split into four parts. Part I deals with a Black world without smiles, sets out the author’s ‘philosophical’ approach and covers deterministic volatility. Part II looks at smiles in equity and FX worlds. It begins with a review of relevant empirical information about smiles, and provides coverage of local-stochastic-volatility, general-stochastic-volatility, jump-diffusion and Variance-Gamma processes. Part II concludes with an important chapter that discusses if and to what extent one can dispense with an explicit specification of a model, and can directly prescribe the dynamics of the smile surface. Part III focusses on interest rates when the volatility is deterministic. Part IV extends this setting in order to account for smiles in a financially motivated and computationally tractable manner. In this final part the author deals with CEV processes, with diffusive stochastic volatility and with Markov-chain processes. Praise for the First Edition: “In this book, Dr Rebonato brings his penetrating eye to bear on option pricing and hedging.... The book is a must-read for those who already know the basics of options and are looking for an edge in applying the more sophisticated approaches that have recently been developed.” —Professor Ian Cooper, London Business School “Volatility and correlation are at the very core of all option pricing and hedging. In this book, Riccardo Rebonato presents the subject in his characteristically elegant and simple fashion...A rare combination of intellectual insight and practical common sense.” —Anthony Neuberger, London Business School

Download or read book Complex Systems in Finance and Econometrics written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2010-11-03 with total page 919 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finance, Econometrics and System Dynamics presents an overview of the concepts and tools for analyzing complex systems in a wide range of fields. The text integrates complexity with deterministic equations and concepts from real world examples, and appeals to a broad audience.

Download or read book Modeling the Conditional Covariance between Stock and Bond Returns written by Peter de Goeij and published by . This book was released on 2012 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: To analyze the intertemporal interaction between the stock and bond market returns, we allow the conditional covariance matrix to vary over time according to a multivariate GARCH model similar to Bollerslev, Engle and Wooldridge (1988). We extend the model such that it allows for asymmetric effects on conditional variances and covariances. Using weekly U.S. stock and bond market data, we find strong evidence of conditional heteroskedasticity in the covariance between stock and bond market returns. The results indicate that not only variances, but also covariances respond asymmetrically to return shocks. Regardless of the bond market shocks, bad news in the stock market is typically followed by a higher conditional covariance than good news. We find that volatility timing strategies for dynamic asset allocation significantly outperform passive strategies. Even when short-sale restrictions are present and transaction costs are high, the economic value of dynamic trading strategies is larger than that of a passive strategy. Moreover, the symmetric volatility timing strategy is outperformed by its asymmetric counterpart.

Download or read book Measuring Market Risk written by Kevin Dowd and published by John Wiley & Sons. This book was released on 2007-01-11 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fully revised and restructured, Measuring Market Risk, Second Edition includes a new chapter on options risk management, as well as substantial new information on parametric risk, non-parametric measurements and liquidity risks, more practical information to help with specific calculations, and new examples including Q&A’s and case studies.