Semiparametric Estimation of Value-at-risk
Author | : Jianqing Fan |
Publisher | : |
Total Pages | : 64 |
Release | : 2003 |
Genre | : Parameter estimation |
ISBN | : |
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Author | : Jianqing Fan |
Publisher | : |
Total Pages | : 64 |
Release | : 2003 |
Genre | : Parameter estimation |
ISBN | : |
Author | : Chuan-Sheng Wang |
Publisher | : |
Total Pages | : |
Release | : 2018 |
Genre | : |
ISBN | : |
Conditional Value-at-Risk (hereafter, CVaR) and Expected Shortfall (CES) play an important role in financial risk management. Parametric CVaR and CES enjoy both nice interpretation and capability of multi-dimensional modeling, however they are subject to errors from mis-specification of the noise distribution. On the other hand, nonparametric estimations are robust but suffer from the ''curse of dimensionality'' and slow convergence rate. To overcome these issues, we study semiparametric CVaR and CES estimation and inference for parametric model with nonparametric noise distribution. In this dissertation, under a general framework that allows for many widely used time series models, we propose a semiparametric CVaR estimator and a semiparametric CES estimator that both achieve the parametric convergence rate. Asymptotic properties of the estimators are provided to support the inference. Furthermore, to draw simultaneous inference for CVaR at multiple confidence levels, we establish a functional central limit theorem for CVaR process indexed by the confidence level and use it to study the conditional expected shortfall. A user-friendly bootstrap approach is introduced to facilitate non-expert practitioners to perform confidence interval construction for CVaR and CES. The methodology is illustrated through both Monte Carlo studies and an application to S&P 500 index.
Author | : Pietro Penza |
Publisher | : John Wiley & Sons |
Total Pages | : 324 |
Release | : 2001 |
Genre | : Business & Economics |
ISBN | : 9780471393139 |
"This book, Measuring Market Risk with Value at Risk by Vipul Bansal and Pietro Penza, has three advantages over earlier works on the subject. First, it takes a decidedly global approach-an essential ingredient for any comprehensive work on market risk. Second, it ties the scientifically grounded, yet intuitively appealing, VaR measure to earlier, more idiosyncratic measures of market risk that are used in specific market environs (e.g., duration in fixed income). Finally, it encompasses all of the accepted approaches to calculating a VaR measure and presents them in a clearly explained fashion with supporting illustrations and completely worked-out examples." -from the Foreword by John F. Marshall, PhD, Principal, Marshall, Tucker & Associates, LLC "Measuring Market Risk with Value at Risk offers a much-needed intellectual bridge, a translation from the esoteric realm of mathematical finance to the domain of financial managers who seek guidance in applying developments from this important field of research as well as that of MBA-level graduate instruction. I believe the authors have done a commendable job of providing a carefully crafted, highly readable, and most useful work, and intend to recommend it to all those involved in business risk management applications." -Anthony F. Herbst, PhD, Professor of Finance and C.R. and D.S. Carter Chair, The University of Texas, El Paso and Founding editor of The Journal of Financial Engineering (1991-1998) "Finally there's a book that strikes a balance between rigor and application in the area of risk management in the banking industry. This innovative book is a MUST for both novices and professionals alike." -Robert P. Yuyuenyongwatana, PhD, Associate Professor of Finance, Cameron University "Measuring Market Risk with Value at Risk is one of the most complete discussions of this emerging topic in finance that I have seen. The authors develop a logical and rigorous framework for using VaR models, providing both historical references and analytical applications." -Kevin Wynne, PhD, Associate Professor of Finance, Lubin School of Business, Pace University
Author | : J. V. K. Rombouts |
Publisher | : |
Total Pages | : 32 |
Release | : 2009 |
Genre | : |
ISBN | : |
In this paper we examine the usefulness of multivariate semi-parametric GARCH models for evaluating the Value-at-Risk (VaR) of a portfolio with arbitrary weights. We specify and estimate several alternative multivariate GARCH models for daily returns on the Samp;P 500 and Nasdaq indexes. Examining the within sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations.
Author | : Juan Carlos Escanciano |
Publisher | : |
Total Pages | : 30 |
Release | : 2013 |
Genre | : |
ISBN | : |
This article proposes semi-parametric least squares estimation of parametric risk-return relationships, i.e. parametric restrictions between the conditional mean and the conditional variance of excess returns given a set of unobservable parametric factors. A distinctive feature of our estimator is that it does not require a parametric model for the conditional mean and variance. We establish consistency and asymptotic normality of the estimates. The theory is non-standard due to the presence of estimated factors. We provide simple sufficient conditions for the estimated factors not to have an impact in the asymptotic standard error of estimators. A simulation study investigates the nite sample performance of the estimates. Finally, an application to the CRSP value-weighted excess returns highlights the merits of our approach. In contrast to most previous studies using non-parametric estimates, we find a positive and significant price of risk in our semi-parametric setting.
Author | : Aaron K. Han |
Publisher | : |
Total Pages | : 60 |
Release | : 1986 |
Genre | : |
ISBN | : |
Author | : Vasiliki D. Skintzi |
Publisher | : |
Total Pages | : |
Release | : 2005 |
Genre | : |
ISBN | : |
This paper examines the systematic relationship between correlation mis-estimation and the corresponding Value-at-Risk (VaR) mis-calculation. To this end, first a semi-parametric approach, and then a parametric approach is developed. Both approaches are based on a simulation setup. Various linear and non-linear portfolios are considered, as well as variance-covariance and Monte-Carlo simulation methods are employed. We find that the VaR error increases significantly as the correlation error increases, particularly in the case of well-diversified linear portfolios. In the case of option portfolios, this effect is more pronounced for short-maturity, in-the-money options. The use of MC simulation to calculate VaR magnifies the correlation bias effect. Our results have important implications for measuring market risk accurately.
Author | : Xinxin Huang |
Publisher | : |
Total Pages | : 0 |
Release | : 2014 |
Genre | : |
ISBN | : |
Value at Risk (VaR) and Expected Shortfall (ES) are methods often used to measure market risk. Inaccurate and unreliable Value at Risk and Expected Shortfall models can lead to underestimation of the market risk that a firm or financial institution is exposed to, and therefore may jeopardize the well-being or survival of the firm or financial institution during adverse markets. The objective of this study is therefore to examine various Value at Risk and Expected Shortfall models, including fatter tail models, in order to analyze the accuracy and reliability of these models. Thirteen VaR and ES models under three main approaches (Parametric, Non-Parametric and Semi-Parametric) are examined in this study. The results of this study show that the proposed model (ARMA(1,1)-GJR-GARCH(1,1)-SGED) gives the most balanced Value at Risk results. The semi-parametric model (Extreme Value Theory, EVT) is the most accurate Value at Risk model in this study for S&P 500.
Author | : M. R. Leadbetter |
Publisher | : Springer Science & Business Media |
Total Pages | : 344 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461254493 |
Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
Author | : Timotheos Angelidis |
Publisher | : |
Total Pages | : 0 |
Release | : 2009 |
Genre | : Risk management |
ISBN | : 9781607410409 |
Recently risk management has become a standard prerequisite for all financial institutions. Value-at-Risk is the main tool of reporting to the bank regulators the risk that the financial institutions face. This book provides a selective survey of the risk management techniques.