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History of Value-at-Risk: 1922-1998,
Glyn A. Holton, from University Library of Munich, Germany (2002)
Keywords: value-at-risk history
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Comparing Value-at-Risk Methodologies,
Luiz Lima and Breno Pinheiro Néri, from Society for Computational Economics (2006)
Keywords: ARCH Quantile Value-at-Risk
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Evaluating Value-at-Risk models via Quantile Regression,
Wagner Gaglianone, Luiz Lima, Oliver Linton and Daniel Smith, from Universidad Carlos III de Madrid. Departamento de Economía (2009)
Keywords: Value-at-Risk
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Using Value-at-Risk to Control Risk Taking: How Wrong Can you Be?,
Xiongwei Ju and Neil Pearson, from University Library of Munich, Germany (1998)
Keywords: Value-at-Risk
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Comparisons of cashflow maps for value-at-risk,
Marc Henrard, from University Library of Munich, Germany (2003)
Keywords: Value-at-risk, mapping, cashflows
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The Influence of Liquidity Risk on Value-at-Risk Calculations,
Bor Bricelj, Sebastjan Strašek and Timotej Jagric, in Management (2013)
Keywords: value-at-risk, liquidity, backtests
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Diversification and Value-at-Risk,
Christophe Perignon and Daniel Smith, in Journal of Banking & Finance (2010)
Keywords: Value-at-Risk Diversification Dynamic conditional correlation Copulas
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Value-at-Risk for Greek Stocks,
Timotheos Angelidis and Alexandros Benos, in Multinational Finance Journal (2008)
Keywords: value-at-risk,; GARCH; historical simulation; backtesting
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On Some Models for Value-At-Risk,
Philip Yu, Wai Keung Li and Shusong Jin, in Econometric Reviews (2010)
Keywords: GARCH model, Mixtures, Threshold models, Value-at-risk,
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Value-at-Risk: The Delta-normal Approach,
Marc Henrard, from University Library of Munich, Germany (2005)
Keywords: value-at-risk; delta normal approach
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A residual bootstrap for conditional Value-at-Risk,
Eric Beutner, Alexander Heinemann and Stephan Smeekes, in Journal of Econometrics (2024)
Keywords: Residual bootstrap; Value-at-Risk; GARCH;
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Analytical Portfolio Value-at-Risk,
Guy Kaplanski, from University Library of Munich, Germany (2005)
Keywords: Value-at-Risk, Risk measurement, Portfolio Optimization, Downsize Risk
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Risk budgeting and Value-at-Risk,
Keith Pilbeam and Rehan Noronha, in International Journal of Monetary Economics and Finance (2008)
Keywords: value-at-risk; VaR; risk budgeting; risk management; risk attribution; risk decomposition; risk measures.
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Value-at-Risk for Country Risk Ratings,
Michael McAleer, Bernardo da Veiga and Suhejla Hoti, from University of Canterbury, Department of Economics and Finance (2010)
Keywords: Country risk; risk ratings; value-at-risk; risk bounds; risk management
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Value-at-Risk for country risk ratings,
Michael McAleer, Bernardo da Veiga and Suhejla Hoti, in Mathematics and Computers in Simulation (MATCOM) (2011)
Keywords: Country risk; Risk ratings; Value-at-Risk; Risk Bounds; Risk management;
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Market capitalization and Value-at-Risk,
Alexandra Dias, in Journal of Banking & Finance (2013)
Keywords: Market capitalization; Quantitative risk management; Value-at-Risk; Financial crises;
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Nonparametric estimation of value-at-risk,
Seok-Oh Jeong and Kee-Hoon Kang, in Journal of Applied Statistics (2009)
Keywords: value-at-risk, volatility, local homogeneity, quantile estimation, risk management, KOSPI,
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The Effects of Risk Modelling: Assessing Value-at-Risk Accuracy,
Zatul Karamah Ahmad Baharul-Ulum, Ismail Ahmad, Norhana Salamudin and Norzaidi Mohd Daud, in Institutions and Economies (formerly known as International Journal of Institutions and Economies) (2015)
Keywords: Backtesting, Value-at-Risk, Volatility Modelling
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Value-at-risk. Measurement and evaluation methods for market risk,
Alina Grigore, in Theoretical and Applied Economics (2008)
Keywords: Value-at-Risk; GARCH models; backtesting.
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Value-at-Risk and Dynamic Risk Measures,
Zuzana Stuchlíková, in Acta Oeconomica Pragensia (2005)
Keywords: coherent risk measure, dynamic risk measure, value-at-risk
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Integrating ESG risks into value-at-risk,
Paolo Capelli, Federica Ielasi and Angeloantonio Russo, in Finance Research Letters (2023)
Keywords: ESG risk; Financial portfolio; Market risk; Value-at-risk; Volatility;
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Mixed value-at-risk and its numerical investigation,
Anubha Goel and Amita Sharma, in Physica A: Statistical Mechanics and its Applications (2020)
Keywords: Value-at-risk; Mixed value-at-risk; Mixed conditional value-at-risk; Deviation risk measure; Portfolio selection;
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Value-at-Risk in turbulence time,
Benoit Genest and Zhili Cao, from University Library of Munich, Germany (2014)
Keywords: Value-at-risk, GARCH model, Bootstrap, hit function, VaR evaluation.
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Intraday value-at-risk,
Pierre Giot, from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) (2000)
Keywords: Intraday volatility, Intraday Value-at-Risk, Duration models, NYSE.
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Do banks overstate their Value-at-Risk?,
Christophe Perignon, Zi Yin Deng and Zhi Jun Wang, from HAL (2008)
Keywords: Value-at-Risk (VaR),Capital requirement,Backtesting

A note on pivotal Value-at-Risk estimates,
Pflug Georg Ch. and Schaller Peter, in Statistics & Risk Modeling (2009)
Keywords: Value-at-Risk, pivotal statistic, structure model
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Estimating Value-at-Risk for Energy Markets,
Blanka Łęt, from University of Lodz (2012)
Keywords: Value-at-Risk; Energy markets; APARCH filter
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Evaluating Value-at-Risk Models via Quantile Regression,
Wagner Gaglianone, Luiz Lima, Oliver Linton and Daniel Smith, from National Centre for Econometric Research (2010)
Keywords: Value-at-Risk, Backtesting, Quantile Regression
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Nut, gebruik en beperkingen van Value-at-Risk voor risicomanagement,
Andre Lucas, in Economic and Social Journal (Economisch en Sociaal Tijdschrift) (1999)
Keywords: Value-at-Risk, Risicomanagement, Toezicht
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Accurate Value-at-Risk forecast with the (good old) normal-GARCH model,
Christoph Hartz, Stefan Mittnik and Marc S. Paolella, from Center for Financial Studies (CFS) (2006)
Keywords: Bootstrap, GARCH, Value-at-Risk
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Nut, gebruik en beperkingen van value-at-risk voor risicomanagement,
Andre Lucas, from VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics (1998)
Keywords: value-at-risk; risicomanagement; toezicht
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Distributionally robust reinsurance with Value-at-Risk and Conditional Value-at-Risk,
Haiyan Liu and Tiantian Mao, in Insurance: Mathematics and Economics (2022)
Keywords: Value-at-Risk; Conditional Value-at-Risk; Distributional robust reinsurance; Uncertainty; Stop-loss;
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Conditional value-at-risk: Aspects of modeling and estimation,
Len Umantsev and Victor Chernozhukov, in Empirical Economics (2001)
Keywords: Value-at-Risk · Quantiles · Extreme Value Theory
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Value-at-risk and extreme returns,
Jon Danielsson and Casper Vries, from London School of Economics and Political Science, LSE Library (1997)
Keywords: value-at-risk; extreme value theory; riskMetrics; historical simulation; tail density estimation; kernel estimation; capital requirements
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Value-at-Risk and Extreme Returns,
Jon Danielsson and Casper de Vries, from Tinbergen Institute (1998)
Keywords: Value-at-Risk; Extreme Value Theory; RiskMetrics; Historical Simulation; Tail Density Estimation; Financial Regulation
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Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics,
So Yeon Chun, Alexander Shapiro and Stan Uryasev, from University Library of Munich, Germany (2011)
Keywords: Value-at-Risk, Average Value-at-Risk, Conditional Value-at-Risk, Expected Shortfall, linear regression, least squares residual, quantile regression, conditional risk measures, statistical inference
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Dynamic factor Value-at-Risk for large heteroskedastic portfolios,
Sirio Aramonte, Marius del Giudice Rodriguez and Jason Wu, in Journal of Banking & Finance (2013)
Keywords: Risk management; Value-at-Risk; Dynamic factor models;
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Agricultural Applications of Value-at-Risk Analysis: A Perspective,
Mark Manfredo and Raymond M. Leuthold, from University Library of Munich, Germany (1998)
Keywords: Value-at-Risk, risk management, estimation procedures
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Robust scenario-based value-at-risk optimization,
Oleksandr Romanko and Helmut Mausser, in Annals of Operations Research (2016)
Keywords: Risk management, Value-at-risk, Optimization, Algorithms, Robustness
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Robust scenario-based value-at-risk optimization,
Oleksandr Romanko and Helmut Mausser, in Annals of Operations Research (2016)
Keywords: Risk management, Value-at-risk, Optimization, Algorithms, Robustness,
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Value-at-risk optimal policies for revenue management problems,
Matthias Koenig and Joern Meissner, in International Journal of Production Economics (2015)
Keywords: Capacity control; Revenue management; Risk; Value-at-risk;
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An asymptotic test for the Conditional Value-at-Risk,
Péter Vékás, from Corvinus University of Budapest (2015)
Keywords: risk measures, Conditional Value-at-Risk, hypothesis testing, actuarial science
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Optimal Value-at-Risk Disclosure,
Mário Seixas and António Barbosa, from University Library of Munich, Germany (2019)
Keywords: Value-at-Risk, Regulatory Capital, Market Risk Charge, Optimal Disclosure, Dynamic Programming
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Volatility measures and Value-at-Risk,
Dennis Bams, Gildas Blanchard and Thorsten Lehnert, in International Journal of Forecasting (2017)
Keywords: Value-at-Risk; Option implied volatility; Volatility risk premium; Time-series; GARCH models;
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Value relevance of value-at-risk disclosure,
Chee Lim and Patricia Tan, in Review of Quantitative Finance and Accounting (2007)
Keywords: Market risk, Value-at-risk, Value relevance, Earnings-returns relation, Stock return volatility, G18, M41,
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Use of Value-at-Risk for the Quantification of Risks in Insurance,
ARIF Fatima Zahra El, in Review of Knowledge Economy (2014)
Keywords: Value-at-risk, Conditional value-at-risk, Method of generalized scenarios, Insurance, Risk measurement, Alternative measures
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Range Value-at-Risk bounds for unimodal distributions under partial information,
Carole Bernard, Rodrigue Kazzi and Steven Vanduffel, in Insurance: Mathematics and Economics (2020)
Keywords: Model risk; Value-at-Risk; Tail Value-at-Risk; Range Value-at-Risk; Convex ordering; Unimodal distributions; Risk bounds;
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A REMARK CONCERNING VALUE-AT-RISK,
S. Y. Novak, in International Journal of Theoretical and Applied Finance (IJTAF) (2010)
Keywords: Value-at-Risk, Basel committee, the "factor 3" rule, the "square root of time" rule
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Enhancing Value-at-Risk with Credible Expected Risk Models,
Khreshna Syuhada, Rizka Puspitasari, I Kadek Darma Arnawa, Lailatul Mufaridho, Elonasari Elonasari, Miftahul Jannah and Aniq Rohmawati, in IJFS (2024)
Keywords: risk management; Value-at-Risk; credible risk measures; forecast; GARCH; cryptocurrency
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An optimization process in Value-at-Risk estimation,
Alex Huang, in Review of Financial Economics (2010)
Keywords: Value-at-Risk Optimization Back-testing Monte Carlo simulation
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A Bayesian Confidence Interval for Value-at-Risk,
Patricio Contreras and Stephen Satchell, from Faculty of Economics, University of Cambridge (2003)
Keywords: Bayesian Statistics, Confidence Interval, Monte Carlo Simulations, Value-at-Risk
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Bias decomposition in the value-at-risk calculation by a GARCH(1,1),
GholamReza Keshavarz Haddad and Mehrnoosh Hasanzade, in International Journal of Computational Economics and Econometrics (2020)
Keywords: VaR; value-at-risk; GARCH(1;1); second-order bias.
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Forecasting Value-at-Risk under Different Distributional Assumptions,
Manuela Braione and Nicolas Scholtes, in Econometrics (2016)
Keywords: Value-at-Risk; forecast accuracy; distributions; backtesting
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Forecasting Value-at-Risk under Temporal and Portfolio Aggregation,
Erik Kole, Thijs Markwat, Anne Opschoor and Dick van Dijk, in Journal of Financial Econometrics (2017)
Keywords: aggregation, forecast evaluation, model comparison, value-at-risk
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Estimating allocations for Value-at-Risk portfolio optimization,
Arthur Charpentier and Abder Oulidi, in Mathematical Methods of Operations Research (2009)
Keywords: Value-at-Risk, Optimization, Portfolio, Non-parametrics,
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A new set of improved Value-at-Risk backtests,
Daniel Ziggel, Tobias Berens, Gregor N.F. Weiß and Dominik Wied, in Journal of Banking & Finance (2014)
Keywords: Value-at-Risk; Backtesting; Monte Carlo simulation;
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Local Estimation of Copula Based Value-at-Risk,
Eduardo F. L. de Melo and Beatriz Vaz de Melo Mendes, in Brazilian Review of Finance (2009)
Keywords: copulas, local maximum likelihood estimation, value-at-risk.
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Forecasting Value-at-Risk under Temporal and Portfolio Aggregation,
Erik Kole, Thijs Markwat, Anne Opschoor and Dick van Dijk, from Tinbergen Institute (2017)
Keywords: forecast evaluation, aggregation, Value-at-Risk, model comparison
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Decomposing Value-at-Risk: The Case of a Fund of Funds Portfolio,
Joanna Olbrys, from University of Lodz (2007)
Keywords: Value-at-Risk; Fund of funds portfolio; Capital market
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Backtesting Value-at-Risk: A GMM Duration-Based Test,
Gilbert Colletaz, Christophe Hurlin and Sessi Tokpavi, from Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans (2009)
Keywords: Backtesting, Value-at-Risk, GMM, Duration-Based Test
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Backtesting Value-at-Risk: A GMM Duration-Based Test,
Gilbert Colletaz, Christophe Hurlin and Sessi Tokpavi, from Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans (2008)
Keywords: Backtesting Value-at-Risk, GMM, Duration-Based Test
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Measuring market risk: a copula and extreme value approach,
Alexandru Stanga, from Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB (2008)
Keywords: Value-at-Risk
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Value-at-Risk versus Non-Value-at-Risk Traders,
Matjaz Steinbacher, from University Library of Munich, Germany (2009)
Keywords: social networks, portfolio decision-making, stochastic finance, Value-at-Risk
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Exact inference in diagnosing value-at-risk estimates: A Monte Carlo device,
Helmut Herwartz, from Christian-Albrechts-University of Kiel, Department of Economics (2008)
Keywords: Value-at-Risk, Monte Carlo test
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Exact inference in diagnosing Value-at-Risk estimates -- A Monte Carlo device,
Helmut Herwartz, in Economics Letters (2009)
Keywords: Value-at-Risk Monte Carlo test
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The performance of the switching forecast model of value-at-risk in the Asian stock markets,
Yen-Chen Chiu and I-Yuan Chuang, in Finance Research Letters (2016)
Keywords: Value-at-Risk; Switching forecast model;
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Worst-Case Conditional Value-at-Risk with Application to Robust Portfolio Management,
Shushang Zhu and Masao Fukushima, in Operations Research (2009)
Keywords: conditional value-at-risk, portfolio management
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Backtesting value-at-risk based on tail losses,
Woon K. Wong, in Journal of Empirical Finance (2010)
Keywords: Value-at-Risk Tail risk Backtesting Risk management Risk capital
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Backesting Value-at-Risk: From DQ (Dynamic Quantile) to DB (Dynamic Binary) Tests,
Elena Ivona Dumitrescu, from Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans (2011)
Keywords: Backesting, Value-at-Risk
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Conditional autoregressive value-at-risk: all flavours of CAViaR,
Pedro Henrique Melo Albuquerque, Matheus Facure Alves, Maísa Cardoso Aniceto and Gustavo Monteiro Pereira, in International Journal of Business Forecasting and Marketing Intelligence (2020)
Keywords: value-at-risk; VaR; conditional autoregressive value-at-risk; CAViaR; bias-variance dilemma; risk.
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Value-at-risk support vector machine: stability to outliers,
Peter Tsyurmasto, Michael Zabarankin and Stan Uryasev, in Journal of Combinatorial Optimization (2014)
Keywords: Support vector machine, Classification, Conditional value-at-risk, Value-at-risk, Risk management, Optimization
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Using Value-at-Risk for effective energy portfolio risk management,
George Halkos and Apostolos Tsirivis, from University Library of Munich, Germany (2019)
Keywords: Energy commodities, Risk Management, Value-at-Risk (VaR).
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Value-at-risk methodologies for effective energy portfolio risk management,
George Halkos and Apostolos S. Tsirivis, in Economic Analysis and Policy (2019)
Keywords: Energy commodities; Risk management; Value-at-risk (VaR);
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Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics,
So Yeon Chun, Alexander Shapiro and Stan Uryasev, in Operations Research (2012)
Keywords: value-at-risk, average value-at-risk, linear regression, least-squares residuals, M-estimators, quantile regression, conditional risk measures, law-invariant risk measures, statistical inference
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The level and quality of Value-at-Risk disclosure by commercial banks,
Christophe Perignon and Daniel Smith, in Journal of Banking & Finance (2010)
Keywords: Value-at-Risk Disclosure Market risk Proprietary risk management
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Weather risk assessment of Indian power sector: A conditional value-at-risk approach,
Mahuya Basu and Tanupa Chakraborty, in Energy & Environment (2019)
Keywords: Risk assessment; rainfall risk; temperature risk; Indian power sector; value-at-risk; conditional value-at-risk
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Qualitative robustness of set-valued value-at-risk,
Giovanni Paolo Crespi and Elisa Mastrogiacomo, in Mathematical Methods of Operations Research (2020)
Keywords: Set-optimization, Set-valued risk-measure, Robustness, Set-valued value-at-risk
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Exchangeability, extreme returns and Value-at-Risk forecasts,
Chun-Kai Huang, Delia North and Temesgen Zewotir, in Physica A: Statistical Mechanics and its Applications (2017)
Keywords: Value-at-risk; Extreme value; Exchangeability; Block maxima; Peaks-over-threshold;
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Model choice and value-at-risk estimation,
Zisheng Ouyang, in Quality & Quantity: International Journal of Methodology (2009)
Keywords: Value-at-Risk, Back testing, Extreme value distribution, The parametric model, Nonparametric model,
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Incorporating Asymmetric Distributional Information in Robust Value-at-Risk Optimization,
Karthik Natarajan, Dessislava Pachamanova and Melvyn Sim, in Management Science (2008)
Keywords: value-at-risk, robust optimization, coherent risk measures
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Multi-product newsvendor problem with value-at-risk considerations,
Aysun Özler, BarIs Tan and Fikri Karaesmen, in International Journal of Production Economics (2009)
Keywords: Multi-product newsvendor problem Value-at-risk Downside risk
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A value-at-risk approach to optimisation of warranty policy,
Ming Luo and Shaomin Wu, in European Journal of Operational Research (2018)
Keywords: (T); Value-at-risk; Warranty policy optimisation; Mean-risk; Copulas;
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Subadditivity of Value-at-Risk for Bernoulli random variables,
Marius Hofert and Alexander J. McNeil, in Statistics & Probability Letters (2015)
Keywords: Risk measure; Value-at-Risk; Superadditivity; Bernoulli random variables; Portfolio of bonds;
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Improved algorithms for computing worst Value-at-Risk,
Hofert Marius, Memartoluie Amir, Saunders David and Wirjanto Tony, in Statistics & Risk Modeling (2017)
Keywords: Risk aggregation, model uncertainty, Value-at-Risk, Adaptive Rearrangement Algorithm
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On the estimation of Value-at-Risk and Expected Shortfall at extreme levels,
Emese Lazar, Jingqi Pan and Shixuan Wang, in Journal of Commodity Markets (2024)
Keywords: Risk models; Value-at-Risk; Expected Shortfall; Semiparametric model; Oil futures;
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Backtesting and estimation error: value-at-risk overviolation rate,
Georges Tsafack and James Cataldo, in Empirical Economics (2021)
Keywords: Risk management, Value-at-risk, Forecasting, Backtesting, Estimation error
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Value-at-Risk model for hazardous material transportation,
Yingying Kang, Rajan Batta and Changhyun Kwon, in Annals of Operations Research (2014)
Keywords: Hazardous materials transportation, Value-at-Risk, Social risk mitigation,
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Bayesian Value-at-Risk Backtesting: The Case of Annuity Pricing,
Melvern Leung, Youwei Li, Athanasios Pantelous and Samuel Vigne, from University Library of Munich, Germany (2019)
Keywords: Bayesian decision theory; Value-at-Risk; Backtesting; Annuity pricing; Longevity risk
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Bayesian Value-at-Risk backtesting: The case of annuity pricing,
Melvern Leung, Youwei Li, Athanasios A. Pantelous and Samuel A. Vigne, in European Journal of Operational Research (2021)
Keywords: Decision analysis; Value-at-Risk; Backtesting; Bayesian framework; Longevity risk;
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Estimating the Value-at-Risk by Temporal VAE,
Robert Buch, Stefanie Grimm, Ralf Korn and Ivo Richert, in Risks (2023)
Keywords: value-at-risk estimation; variational autoencoders; recurrent neural networks; risk-management; auto-pruning; posterior collapse
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Value-at-risk and Tsallis statistics: risk analysis of the aerospace sector,
Adriana P. Mattedi, Fernando M. Ramos, Reinaldo R. Rosa and Rosario Mantegna, in Physica A: Statistical Mechanics and its Applications (2004)
Keywords: Econophysics; Aerospace sector; Tsallis statistics; Value-at-risk;
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Value-at-Risk: Risk assessment for the portfolio of oil and gas producers,
Frank Asche, Roy Dahl and Atle Oglend, from University of Stavanger (2013)
Keywords: Value-at-Risk; Correlation; Oil; Diversification; Gas; Subordination
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Parametric and Non-Parametric Measures of Volatility: Risk Estimation via the Gini Decompostion and Comparison with the Value-at-Risk,
Stéphane Mussard, in Frontiers in Finance and Economics (2004)
Keywords: Component Value-at-Risk, decomposition, Gini, marginal Value-at-risk, volatility
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Efficient estimation of extreme value-at-risks for standalone structural exchange rate risk,
Zhongfang He, from University Library of Munich, Germany (2014)
Keywords: value-at-risk, structural exchange rate risk, extreme value
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Dynamic hedging of conditional value-at-risk,
Alexander Melnikov and Ivan Smirnov, in Insurance: Mathematics and Economics (2012)
Keywords: IB10; IM01; IM10; IM53; Conditional value-at-risk; Dynamic hedging; Stochastic modeling; Quantile hedging; Unit-linked contracts;
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Range-based models in estimating value-at-risk (VaR),
Nikkin L. Beronilla and Dennis Mapa, in Philippine Review of Economics (2008)
Keywords: value-at-risk, Parkinson range, Garman-Klass range, range-based GARCH
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A nonparametric copula approach to conditional Value-at-Risk,
Gery Geenens and Richard Dunn, in Econometrics and Statistics (2022)
Keywords: Value-at-Risk; copula; nonparametric; kernel estimation; local likelihood;
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One-year Value-at-Risk for longevity and mortality,
Richard Plat, in Insurance: Mathematics and Economics (2011)
Keywords: One-year Value-at-Risk; Stochastic mortality trend model; Solvency 2;
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Value-at-Risk with Application of DCC-GARCH Model,
Tomas Meluzin, Marek Zinecker, Michal Pietrzak, Marcin Faldzinski and Adam Balcerzak, from Institute of Economic Research (2016)
Keywords: capital market, value-at-risk, backtesting, DCC-GARCH model, conditional variance
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Subadditivity re–examined: the case for value-at-risk,
Jon Danielsson, Bjørn Jørgensen, Sarma Mandira, Gennady Samorodnitsky and Casper de Vries, from London School of Economics and Political Science, LSE Library (2005)
Keywords: value–at–risk; subadditivity; regular variation; tail index; heavy tailed distribution
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