Computational aspects of risk estimation in volatile markets: A survey

Portfolio risk estimation requires appropriate modeling of fat-tails and asymmetries in dependence in combination with a true downside risk measure. In this survey, we discuss computational aspects of a Monte-Carlo based framework for risk estimation and risk capital allocation. We review different probabilistic approaches focusing on practical aspects of statistical estimation and scenario generation. We discuss value-at-risk and conditional value-at-risk and comment on the implications of using a fat-tailed framework for the reliability of risk estimates. ∗Prof Rachev gratefully acknowledges research support by grants from Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the Deutschen Forschungsgemeinschaft and the Deutscher Akademischer Austausch Dienst.

[1]  S. Rachev,et al.  Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures , 2008 .

[2]  Stoyan V. Stoyanov,et al.  Computing VaR and AVaR of Skewed-T Distribution , 2007 .

[3]  Svetlozar T. Rachev,et al.  Tempered Infinitely Divisible Distributions and Processes , 2011 .

[4]  P. Embrechts,et al.  Chapter 8 – Modelling Dependence with Copulas and Applications to Risk Management , 2003 .

[5]  Eckhard Platen,et al.  Empirical Evidence on Student-t Log-Returns of Diversified World Stock Indices , 2007 .

[6]  Christine M. Anderson-Cook,et al.  Book review: quantitative risk management: concepts, techniques and tools, revised edition, by A.F. McNeil, R. Frey and P. Embrechts. Princeton University Press, 2015, ISBN 978-0-691-16627-8, xix + 700 pp. , 2017, Extremes.

[7]  P. Embrechts,et al.  Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls , 2002 .

[8]  Stoyan V. Stoyanov,et al.  An Empirical Examination of Daily Stock Return Distributions for U.S. Stocks , 2005, Data Analysis and Decision Support.

[9]  Sidney I. Resnick,et al.  How to make a Hill Plot , 2000 .

[10]  B. Mandlebrot.  The Variation of Certain Speculative Prices , 1963 .

[11]  採編典藏組.  Society for Industrial and Applied Mathematics(SIAM) , 2008 .

[12]  Philippe Artzner,et al.  Coherent Measures of Risk , 1999 .

[13]  J. Corcoran.  Modelling Extremal Events for Insurance and Finance , 2002 .

[14]  G. Pflug.  Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk , 2000 .

[15]  Gennady Samorodnitsky,et al.  Computing the Portfolio Conditional Value-at-Risk in the Alpha-Stable Case , 2005 .

[16]  Sergio Ortobelli,et al.  COMPUTING THE PORTFOLIO CONDITIONAL VALUE-AT-RISK IN THE α-STABLE CASE , 2008 .

[17]  Svetlozar T. Rachev,et al.  Tempered stable and tempered infinitely divisible GARCH models , 2010 .

[18]  E. Fama.  The Behavior of Stock-Market Prices , 1965 .

[19]  R. Rockafellar,et al.  Conditional Value-at-Risk for General Loss Distributions , 2001 .

[20]  S. Rachev,et al.  Multivariate Skewed Student's t Copula in the Analysis of Nonlinear and Asymmetric Dependence in the German Equity Market , 2008 .

[21]  Stoyan V. Stoyanov,et al.  Stable ETL Optimal Portfolios and Extreme Risk Management , 2009 .

[22]  Stoyan V. Stoyanov,et al.  Asymptotic Distribution of the Sample Average Value-at-Risk in the Case of Heavy-Tailed Returns , 2007 .

[23]  M. Sørensen,et al.  Hyperbolic Processes in Finance , 2003 .

[24]  S. Rachev.  Handbook of heavy tailed distributions in finance , 2003 .

[25]  F. Eugene.  FAMA, . The Behavior of Stock-Market Prices, Journal of Business, , . , 1965 .

[26]  E. Fama.  Mandelbrot and the Stable Paretian Hypothesis , 1963 .

[27]  Ludger Rüschendorf,et al.  Distributions with fixed marginals and related topics , 1999 .

[28]  Thorsten Rheinländer.  Risk Management: Value at Risk and Beyond , 2003 .

[29]  E. Platen,et al.  Subordinated Market Index Models: A Comparison , 1997 .

[30]  M. Taqqu,et al.  Financial Risk and Heavy Tails , 2003 .

[31]  Svetlozar T. Rachev,et al.  Financial market models with Lévy processes and time-varying volatility. , 2008 .

[32]  A. Sklar,et al.  Random variables, distribution functions, and copulas---a personal look backward and forward , 1996 .

[33]  Yongli Zhang,et al.  Risk Attribution and Portfolio Performance Measurement-An Overview , 2004 .

[34]  S. Rachev,et al.  Stable Paretian Models in Finance , 2000 .