IV.1.1 | Semi-standard deviation and second order LPM |
IV.1.2 | LPM risk metrics |
IV.1.3 | Probability of underperforming a benchmark |
IV.1.4 | VaR with normally distributed returns |
IV.1.5 | Scaling normal VaR with independent and with autocorrelated returns |
IV.1.6 | Adjusting VaR for non-zero expected excess returns |
IV.1.7 | Equity VaR |
IV.1.8 | Normal VaR of a simple cash flow |
IV.1.9 | Benchmark VaR with normally distributed returns |
IV.1.10 | Comparison of different VaR metrics |
IV.1.11 | Non-sub-additivity of VaR |
IV.2.1 | Adjusting normal linear VaR for autocorrelation |
IV.2.2 | Converting a covariance matrix to basis points |
IV.2.3 | Normal linear VaR from a mapped cash flow |
IV.2.4 | Incremental VaR for a cash flow |
IV.2.5 | Normal linear VaR for an exposure to two yield curves |
IV.2.6 | Spread and LIBOR components of normal linear VaR |
IV.2.7 | Applying a cash-flow map to interest rate scenarios |
IV.2.8 | VaR of UK fixed income portfolio |
IV.2.9 | Using principal components as risk factors |
IV.2.10 | Computing the PC VaR |
IV.2.11 | VaR for cash equity positions |
IV.2.12 | Systematic VaR based on an equity factor model |
IV.2.13 | Disaggregation of VaR into systematic VaR and specific VaR |
IV.2.14 | Equity and forex VaR |
IV.2.15 | VaR for international equity exposures |
IV.2.16 | Interest rate VaR from forex exposure |
IV.2.17 | VaR for a hedged international stock portfolio |
IV.2.18 | Estimating student t linear VaR at the portfolio level |
IV.2.19 | Comparison of normal and student t linear VaR |
IV.2.20 | Estimating normal mixture VaR for equity and forex |
IV.2.21 | Comparison of normal mixture and student t linear VaR |
IV.2.22 | Comparison of normal mixture and Student t mixture VaR |
IV.2.23 | Mixture VaR in the presence of autocorrelated returns |
IV.2.24 | Normal mixture VaR – risk factor level |
IV.2.25 | EWMA normal linear VaR for FTSE 100 |
IV.2.26 | Comparison of RiskMetrics™ regulatory and EWMA VaR |
IV.2.27 | Normal ETL |
IV.2.28 | Student t distributed ETL |
IV.2.29 | Normal mixture ETL |
IV.2.30 | Student t mixture ETL |
IV.3.1 | Volatility adjusted VaR for the S&P 500 index |
IV.3.2 | Filtered historical simulation VaR for the S&P 500 index |
IV.3.3 | Using the GPD to estimate VaR at extreme quantiles |
IV.3.4 | Cornish–Fisher expansion |
IV.3.5 | Johnson SU VaR |
IV.3.6 | Volatility-adjusting historical VaR for a stock portfolio |
IV.3.7 | Systematic and specific components of historical VaR |
IV.4.1 | Linear congruential random number generation |
IV.4.2 | Discrepancy of linear congruential generators |
IV.4.3 | Antithetic variance reduction |
IV.4.4 | Stratified sampling from standard uniform distributions |
IV.4.5 | Latin hypercube sampling |
IV.4.6 | Multi-step Monte Carlo with EWMA volatility |
IV.4.7 | Multi-step Monte Carlo with asymmetric GARCH volatility |
IV.4.8 | Multivariate normal Monte Carlo VaR |
IV.4.9 | Multivariate Student t Monte Carlo VaR |
IV.4.10 | Monte Carlo VaR based on copulas |
IV.4.11 | Monte Carlo credit spread VaR |
IV.4.12 | Monte Carlo interest rate VaR with PCA |
IV.4.13 | Monte Carlo VaR with normal mixture distributions |
IV.4.14 | VaR with volatility and correlation clustering |
IV.5.1 | Delta–Normal VaR |
IV.5.2 | Delta–gamma VaR with Johnson distribution |
IV.5.3 | Static and dynamic historical VaR for an option |
IV.5.4 | Historical VaR and ETL of a delta-hedged option |
IV.5.5 | Interest rate, price and volatility risks of options |
IV.5.6 | VaR and ETL for a delta–gamma–vega hedged portfolio |
IV.5.7 | Historical VaR with Greeks approximation |
IV.5.8 | Historical VaR for options on several underlyings |
IV.5.9 | Historical VaR for a path-dependent option |
IV.5.10 | Monte Carlo VaR for a standard European option |
IV.5.11 | Non-linear, non-normal Monte Carlo VaR |
IV.5.12 | Gamma, vega and theta effects in short term VaR |
IV.5.13 | Theta effects in long-term VaR |
IV.5.14 | One-step versus multi-step Monte Carlo VaR |
IV.5.15 | GARCH Monte Carlo VaR for options |
IV.5.16 | Monte Carlo VaR for a path-dependent option |
IV.5.17 | Monte Carlo VaR of strangle: exact revaluation |
IV.5.18 | Monte Carlo VaR with delta–gamma–vega mapping |
IV.5.19 | Monte Carlo VaR with multivariate delta–gamma mapping |
IV.5.20 | Monte Carlo VaR with multivariate delta– gamma–vega mapping |
IV.6.1 | Model risk arising from cash-flow map |
IV.6.2 | Model risk arising from equity beta estimation |
IV.6.3 | Confidence intervals for normal linear VaR |
IV.6.4 | Confidence intervals for quantiles |
IV.6.5 | Unconditional coverage test |
IV.6.6 | Independence test |
IV.6.7 | Regression-based backtest |
IV.6.8 | Coverage tests with volatility clustering |
IV.6.9 | Backtesting ETL |
IV.6.10 | Bias test on normal linear VaR |
IV.6.11 | Likelihood ratio backtest of normal risk models |
IV.6.12 | A dynamic distribution backtest |
IV.7.1 | Historical worst case and distribution scenarios |
IV.7.2 | Hypothetical distribution scenario: bank insolvency |
IV.7.3 | Scenario based VaR for unlisted securities |
IV.7.4 | Scenario interest rate and credit spread VaR |
IV.7.5 | Scenario based VaR for commodity futures |
IV.7.6 | Scenario VaR with a small probability of a market crash |
IV.7.7 | Credit spread normal mixture scenario VaR |
IV.7.8 | Comparison of Bayesian VaR and scenario VaR |
IV.7.9 | A factor push stress test |
IV.7.10 | Worst case loss in specified trust region |
IV.7.11 | Covariance matrix from global equity crash of 1987 |
IV.7.12 | Stressed historical VaR |
IV.7.13 | Finding the ‘nearest’ correlation matrix |
IV.7.14 | Principal component stress tests |
IV.7.15 | Stressed VaR with exogenous illiquidity |
IV.7.16 | Stressed VaR with endogenous liquidity |
IV.7.17 | Adjusting VaR for price-quantity impact |
IV.7.18 | Using FHS for stress testing |
IV.7.19 | Using GARCH with Monte Carlo for stress testing |
IV.8.1 | Calculating GRC for a long-only position using VaR |
IV.8.2 | Comparison of internal and standardized MRC for a hedged position |
IV.8.3 | MRC and economic capital |
IV.8.4 | Aggregation of economic capital |
IV.8.5 | Simple illustration of aggregation risk |
IV.8.6 | Calculating RORAC |
IV.8.7 | Aggregating RORAC |
IV.8.8 | Comparing RAROC for swaps and bonds |
IV.8.9 | Maximizing RAROC for optimal capital allocation |
IV.8.10 | Constrained economic capital allocation |
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