TAILIEUCHUNG - Market risk measures using finite Gaussian mixtures

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. | Journal of Applied Finance Banking vol. 4 no. 6 2014 29-45 ISSN 1792-6580 print version 1792-6599 online Scienpress Ltd 2014 Market Risk Measures using Finite Gaussian Mixtures Jorge Rosales Contreras1 Abstract 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. JEL classification numbers C46 G17 Keywords Value at Risk Expected Shortfall Finite Gaussian Mixture Historical Simulation Delta-Normal Backtesting. 1 Introduction According to the Basel Committee failure to capture major on- and off-balance sheet risks . was a key destabalising factor during the crisis. In response to the detected shortcomings in capital requirements the enhanced treatment introduces a stressed Value at Risk VaR capital requirement see BCBS 2011 paragraphs 11 and 12 . VaR the most used market risk measure to estimate daily potential losses in either trading or investment books was not able to grasp the extent of the sub-prime mortgage market collapse in the United States that triggered aggregated losses in market value over 130 billion from February 2007 for firms such as Citigroup Merryl Linch Morgan Stanley UBS among many others. This was mainly due to calculations based on historical simulations heavily dependent on sample window or debatable

• Ngân hàng - Tín dụng
• Value at risk
• Expected shortfall
• Finite gaussian mixture
• Historical simulation
• Delta normal
• Financial holding companies
• Whole operational value
• Financial risk
• Value risk relation model
• Khóa luận tốt nghiệp
• Ứng dụng Value at Risk
• Đo lường rủi ro kinh doanh ngoại tệ
• Đo lường rủi ro
• Rủi ro kinh doanh ngoại tệ
• Kinh doanh ngoại tệ
• Ngân hàng thương mại
• Forecasting Value at Risk
• Evidence from Emerging Economies in Asia
• Emerging Financial Markets
• Recommend the use of GARCH
• Fair value information
• Risk management
• Corporate governance
• Moderating effect
• Fair value information and risk management
• Enterprise risk management
• Company value
• Nairobi stock exchange
• Enterprise risk management implementation
• Value of companies listed
• Mining and energy sector
• Risk free assets
• Portfolio optimization
• Quadratic investment portfolio based
• Return distributions
• Kupiec test
• Belgrade Stock Exchange index
• Risk and uncertainty analysis
• Shrimp trade
• India using value at risk
• Uncertainty analysis for shrimp trade
• Major markets and followed
• Learning management system
• Financial derivatives
• Lecture Financial derivatives
• Market risk
• Worst case scenario analysis
• Financial modeling
• Lecture Financial modeling
• Asset expected return
• Portfolio value at risk
• Random walk simulations
• Monte Carlo simulation
• Master Thesis in Economics
• Master Thesis in Economics sample
• Manufacturing Engineers
• The Value Of Risk Management
• The Pharmaceutical Industry
• Normal market
• Portfolio risk
• Black scholes stochastic process
• Normal distribution
• Neural networks
• Genetic algorithms
• Rial euro exchange rate
• Parametric method
• Exponentially weighting
• BMC Musculoskeletal Disorders
• Bone mineral density
• Fracture risk
• Korean reference value
• Prediction of fracture risk
• T score
• Risk measure
• Investment portfolio
• Spectral risk measures
• Distortion theory
• Tail risk
• Goodness of fit
• Equity market tail events
• Heavy tailed distributions
• Credit value adjustment
• Wrong way risk
• Right way risk
• Credit risk modeling
• Least square Monte Carlo
• Default time approach (DTA)
• Default probability approach
• Lecture Money and Banking
• Bài giảng Tiền tệ và Ngân hàng
• Money and Banking
• Measuring risk
• Value at risk (VAR)
• Risk aversion
• Risk premium
• Đo lường rủi ro trong kinh doanh
• Kinh doanh ngoại hối
• Ngân hàng thương mại Việt Nam
• Ứng dụng của Value At Risk
• Đo lường mức độ rủi ro
• Giá trị có rủi ro
• Lý thuyết về giá trị có rủi ro
• Đặc điểm của VaR
• Phương pháp ước tính VaR
• Khái niệm VaR
• Ứng dụng mô hình VaR
• Mô hình VaR
• Thị trường chứng khoán
• Thị trường chứng khoán Việt Nam
• Quản trị rủi ro
• Danh mục cổ phiếu niêm yết
• Derivatives markets
• Calculating VAR
• Nghiên cứu khoa học sinh viên
• Nhà kinh tế trẻ
• Ứng dụng mô hình Value at Risk
• Quản trị rủi ro tỷ giá
• Hoạt động kinh doanh ngoại tệ
• Chỉ số HHI
• Evaluation of Selected Value
• Risk Approaches
• Extreme Market Conditions
• Normal Market Conditions