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Value-at-Risk (VaR) forecasting generally relies on a parametric density function of portfolio returns that ignores higher moments or assumes them constant. In this paper, we propose a new simple approach to estimation of a portfolio VaR. We employ the Gram-Charlier expansion (GCE) augmenting the standard normal distribution with time-varying higher moments. We allow the first four moments of the GCE to depend on past information, which leads to a more accurate approximation of the tails of the distribution. The results unambiguously show that our GCE-based VaR forecasts provide accurate and robust estimates of the realised VaR, outperforming those generated by the constant-higher-moments models.
There is ample empirical evidence that the distribution of short-term security returns is non-normal. In spite of such evidence financial data analysis generally does not explicitly incorporate the higher statistical moments of skewness and kurtosis within a likelihood-based framework. In this paper Bayesian-based Markov chain Monte Carlo (MCMC) re-sampling methods are used to estimate a non-normal likelihood function. After simulation studies to assess the methodology, new looks at the Capital Asset Pricing Model and the market risk premium show that estimation of a likelihood function incorporating all four statistical moments can give valuable new insight into the underlying return data-generating process.
The thesis analyzes the effect that the sample size, the asymmetry in the distribution of returns and the leverage in their volatility have on the estimation and forecasting of market risk in financial assets. The goal is to compare the performance of a variety of models for the estimation and forecasting of Value at Risk (VaR) and Expected Shortfall (ES) for a set of assets of different nature: market indexes, individual stocks, bonds, exchange rates, and commodities. The three chapters of the thesis address issues of greatest interest for the measurement of risk in financial institutions and, therefore, for the supervision of risks in the financial system. They deal with technical issues related to the implementation of the Basel Committee's guidelines on some aspects of which very little is known in the academic world and in the specialized financial sector. In the first chapter, a numerical correction is proposed on the values usually estimatedwhen there is little statistical information, either because it is a financial asset (bond, investment fund...) recently created or issued, or because the nature or the structure of the asset or portfolio have recently changed. The second chapter analyzes the relevance of different aspects of risk modeling. The third and last chapter provides a characterization of the preferable methodology to comply with Basel requirements related to the backtesting of the Expected Shortfall.
An inside look at modern approaches to modeling equity portfolios Financial Modeling of the Equity Market is the most comprehensive, up-to-date guide to modeling equity portfolios. The book is intended for a wide range of quantitative analysts, practitioners, and students of finance. Without sacrificing mathematical rigor, it presents arguments in a concise and clear style with a wealth of real-world examples and practical simulations. This book presents all the major approaches to single-period return analysis, including modeling, estimation, and optimization issues. It covers both static and dynamic factor analysis, regime shifts, long-run modeling, and cointegration. Estimation issues, including dimensionality reduction, Bayesian estimates, the Black-Litterman model, and random coefficient models, are also covered in depth. Important advances in transaction cost measurement and modeling, robust optimization, and recent developments in optimization with higher moments are also discussed. Sergio M. Focardi (Paris, France) is a founding partner of the Paris-based consulting firm, The Intertek Group. He is a member of the editorial board of the Journal of Portfolio Management. He is also the author of numerous articles and books on financial modeling. Petter N. Kolm, PhD (New Haven, CT and New York, NY), is a graduate student in finance at the Yale School of Management and a financial consultant in New York City. Previously, he worked in the Quantitative Strategies Group of Goldman Sachs Asset Management, where he developed quantitative investment models and strategies.
Quantitative Finance with Python: A Practical Guide to Investment Management, Trading and Financial Engineering bridges the gap between the theory of mathematical finance and the practical applications of these concepts for derivative pricing and portfolio management. The book provides students with a very hands-on, rigorous introduction to foundational topics in quant finance, such as options pricing, portfolio optimization and machine learning. Simultaneously, the reader benefits from a strong emphasis on the practical applications of these concepts for institutional investors. Features Useful as both a teaching resource and as a practical tool for professional investors. Ideal textbook for first year graduate students in quantitative finance programs, such as those in master’s programs in Mathematical Finance, Quant Finance or Financial Engineering. Includes a perspective on the future of quant finance techniques, and in particular covers some introductory concepts of Machine Learning. Free-to-access repository with Python codes available at www.routledge.com/ 9781032014432 and on https://github.com/lingyixu/Quant-Finance-With-Python-Code.
This volume contains a selection of invited papers, presented to the fourth International Conference on Statistical Data Analysis Based on the L1-Norm and Related Methods, held in Neuchâtel, Switzerland, from August 4–9, 2002. The contributions represent clear evidence to the importance of the development of theory, methods and applications related to the statistical data analysis based on the L1-norm.
Event risk is the risk that a portfolio's value can be affected by large jumps in market prices. Event risk is synonymous with quot;fat tailsquot; or quot;jump riskquot;. Event risk is one component of quot;specific riskquot;, defined by bank supervisors as the component of market risk not driven by market-wide shocks. Standard Value-at-Risk (VaR) models used by banks to measure market risk do not do a good job of capturing event risk. In this paper, I discuss the issues involved in incorporating event risk into VaR. To illustrate these issues, I develop a VaR model that incorporates event risk, which I call the Jump-VaR model. The Jump-VaR model uses any standard VaR model to handle quot;ordinaryquot; price fluctuations and grafts on a simple model of price jumps. The effect is to quot;fattenquot; the tails of the distribution of portfolio returns that is used to estimate VaR, thus increasing VaR. I note that regulatory capital could rise or fall when jumps are added, since the increase in VaR would be offset by a decline in the regulatory capital multiplier on specific risk from 4 to 3. In an empirical application, I use the Jump-VaR model to compute VaR for two equity portfolios. I note that, in practice, special attention must be paid to the issues of correlated jumps and double-counting of jumps. As expected, the estimates of VaR increase when jumps are added. In some cases, the increases are substantial. As expected, VaR increases by more for the portfolio with more specific risk.
"Quantitative Portfolio Construction: Balancing Risk and Reward with Precision" is a masterfully crafted guide that merges cutting-edge quantitative strategies with the timeless principles of finance. Ideal for both novices and seasoned investors, this book illuminates the complexities of portfolio management through a systematic approach, emphasizing the critical role of data-driven decision-making. Readers will find themselves adept at harnessing mathematical models and sophisticated algorithms to enhance asset allocation and risk management, enabling the construction of portfolios that are resilient in diverse market conditions. With clarity and depth, the book traverses a wide spectrum of topics, from the foundational elements of financial markets to the nuances of algorithmic trading and behavioral finance. Each chapter meticulously builds on the last, ensuring a comprehensive understanding of modern portfolio theory, machine learning applications, and sustainable investing. The practical insights offered empower readers to leverage advanced techniques, such as backtesting and optimization, fostering confidence in their ability to craft portfolios that balance risk and reward effectively. By the conclusion, readers are not only equipped with actionable knowledge but are also inspired to embrace the evolving paradigms of quantitative finance, poised to make informed, impactful decisions in their investment endeavors.
The subject of this textbook is to act as an introduction to data science / data analysis applied to finance, using R and its most recent and freely available extension libraries. The targeted academic level is undergrad students with a major in data science and/or finance and graduate students, and of course practitioners or professionals who need a desk reference. Assumes no prior knowledge of R The content has been tested in actual university classes Makes the reader proficient in advanced methods such as machine learning, time series analysis, principal component analysis and more Gives comprehensive and detailed explanations on how to use the most recent and free resources, such as financial and statistics libraries or open database on the internet
The classification, measurement, and management of risk are central problems in the investment process. Over the past 25 years, Value at Risk (VaR) became the common universal standard in risk measurement. However, the financial crisis of 2007/2009 clearly demonstrated great discrepancies in risk estimates based on this indicator. In this report, three of the field’s leading experts objectively consider each key criticism of VaR in recent professional literature, including VaR’s underestimation of the magnitude and frequency of extreme outcomes, the difficulty of obtaining reliable VaR estimates for complex portfolios, the limited value of historical data, imperfections in the effective market hypothesis that underlies VaR, and several more. Next, the authors carefully review refinements and alternatives that have been proposed as potential replacements or complements, including Conditional VaR (Expected Shortfall), Shock VaR, modifications in the handling of parameters uncertainty, liquidity adjustment, higher moments, and more. They conclude by discussing why a sound risk management system continues to require deep understanding of complex adaptive and often irrational market mechanisms and still cannot be reduced to a mere combination of indicators, no matter how sophisticated they are.