Market Risk Measures Using Finite Gaussian Mixtures


Book Description

Value at Risk (VaR) is the most popular market risk measure as it summarizes in one figure the exposure to different risk factors. It had been around for over a decade when Expected Shortfall (ES) emerged to correct its shortcomings. Both risk measures can be estimated under several models. We explore the application of a parametric model to fit the joint distribution of risk factor returns based on multivariate finite Gaussian Mixtures, derive a closed-form expression for ES under this model and estimate risk measures for a multi-asset portfolio over an extended period. We then compare results versus benchmark models (Historical Simulation and Normal) through back-testing all of them at several confidence levels. Evidence shows that the proposed model is a competitive one for the estimation of VaR and ES.




Finite Gaussian Mixtures and Market Risk Assessment


Book Description

"El Valor en Riesgo (VaR) es la métrica de riesgo de mercado más popular, al resumir en una cifra la exposición a diversos factores de riesgo. El Déficit Esperado (ES) corrige sus limitaciones y ha ganado terreno. Ambas medidas se pueden estimar bajo distintos modelos."--Resumen h. [iii].







The Measurement of Market Risk


Book Description

This book is a revised version of my doctoral dissertation submitted to the University of St. Gallen in October 1999. I would like to thank Dr. oec. Marc Wildi whose careful reading of much of the text led to many improvements. All errors remain mine. Pfiiffikon SZ, Switzerland, March 2001 Pierre-Yves Moix Preface to the dissertation "Education is man's going forward from cocksure ignorance to thoughtful uncertainty" Don Clark's Scrapbook quoted in Wonnacott and Wonnacott (1990). After several years of banking practice, I decided to give up some of my certitudes and considered this thesis project a good opportunity to study some of the quantitative tools necessary for the modelling of uncertainty. lowe very much to Prof. Dr. Karl Frauendorfer, the referee of my thesis, for the time he took to read the manuscript and for the numerous valuable suggestions he made. I am also very grateful to Prof. Dr. Klaus Spremann who kindly accepted to co-refer my thesis and who strengthened my inter est in finance during my study period. During my time at the Institute for Operations Research of the University of St. Gallen (lfU-HSG) I had the opportunity to participate in the project "RiskLab" which provides a very profitable link between finance practice and academics. I would especially like to thank Dr. Christophe Rouvinez from Credit Suisse for his comments and all the data he provided so generously.




Measuring Market Risk


Book Description

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.




Market Risk Analysis, Boxset


Book Description

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.




Financial Market Risk


Book Description

This book covers the latest theories and empirical findings of financial risk, its measurement and management, and its applications in the world of finance.




Market Risk Analysis, Quantitative Methods in Finance


Book Description

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.