Contents
IV.1 Value at Risk and Other Risk Metrics
IV.1.2 An Overview of Market Risk Assessment
IV.1.2.1 Risk Measurement in Banks
IV.1.2.2 Risk Measurement in Portfolio Management
IV.1.2.3 Risk Measurement in Large Corporations
IV.1.3 Downside and Quantile Risk Metrics
IV.1.3.1 Semi-Standard Deviation and Second Order Lower Partial Moment
IV.1.3.2 Other Lower Partial Moments
IV.1.3.3 Quantile Risk Metrics
IV.1.4.1 Confidence Level and Risk Horizon
IV.1.4.3 Mathematical Definition of VaR
IV.1.5 Foundations of Value-at-Risk Measurement
IV.1.5.1 Normal Linear VaR Formula: Portfolio Level
IV.1.5.4 Discounting and the Expected Return
IV.1.6 Risk Factor Value at Risk
IV.1.6.2 Normal Linear Equity VaR
IV.1.6.3 Normal Linear Interest Rate VaR
IV.1.7 Decomposition of Value at Risk
IV.1.7.1 Systematic and Specific VaR
IV.1.7.3 Marginal and Incremental VaR
IV.1.8 Risk Metrics Associated with Value at Risk
IV.1.8.2 Conditional VaR: Expected Tail Loss and Expected Shortfall
IV.1.8.3 Coherent Risk Metrics
IV.1.9 Introduction to Value-at-Risk Models
IV.1.9.2 Historical Simulation
IV.1.9.3 Monte Carlo Simulation
IV.1.9.4 Case Study: VaR of the S&P 500 Index
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