IV.1.1 | Active returns |
IV.1.2 | LPM of various orders relative to two different thresholds |
IV.1.3 | Normal VaR with drift adjustment |
IV.1.4 | The tail of the return distribution and of the active return distribution |
IV.1.5 | Comparison of estimates from different VaR models |
IV.2.1 | Normal linear VaR for different volatilities, significance levels and risk horizons |
IV.2.2 | Risk factor sensitivities |
IV.2.3 | PV01 of cash flows and volatilities of UK and US interest rates |
IV.2.4 | Correlations between UK and US interest rates |
IV.2.5 | PV01 of cash flows and volatilities of LIBOR rates |
IV.2.6 | Correlations between LIBOR rates |
IV.2.7 | Cross correlations between credit spreads and LIBOR rates |
IV.2.8 | Volatilities and correlations of LIBOR and credit spreads |
IV.2.9 | Eigenvalues of covariance matrix of UK spot rates – short end |
IV.2.10 | Net sensitivities on PC risk factors |
IV.2.11 | Stock portfolio characteristics |
IV.2.12 | Characteristics of 10-day returns |
IV.2.13 | Characteristics of an international equity portfolio |
IV.2.14 | Annual covariance matrix Ω of equity and forex risk factor returns |
IV.2.15 | VaR decomposition for diversified international stock portfolio |
IV.2.16 | Volatilities and correlations of risk factors |
IV.2.17 | VaR decomposition into equity and forex factors |
IV.2.18 | Volatilities and correlations of natural gas and silver futures |
IV.2.19 | Commodities trading desk positions on natural gas and silver |
IV.2.20 | 1% 10-day VaR of commodity futures desks |
IV.2.21 | Normal and Student t linear VaR |
IV.2.22 | Moments of the FTSE 100 and S&P 500 indices and of the $/£ forex rate |
IV.2.23 | Estimated parameters of normal mixture distributions (annualized) |
IV.2.24 | Comparison of normal mixture and normal VaR |
IV.2.25 | Sample moments of daily returns on the FTSE 100 index |
IV.2.26 | Normal mixture parameters for FTSE 100 returns |
IV.2.27 | Comparison of normal and Student t linear VaR |
IV.2.28 | Comparison of mixture VaR estimates |
IV.2.29 | Effect of autocorrelation on mixture VaR |
IV.2.30 | Normal mixture parameters for risk factors |
IV.2.31 | EWMA VaR for the FTSE 100 on 18 April 2008 |
IV.2.32 | Volatilities of and correlation between S&P 500 and NASAQ 100 indices |
IV.2.33 | Annual covariance matrix based on Table IV.2.32 |
IV.2.34 | RiskMetrics VaR for US stock portfolio |
IV.2.35 | VaR and ETL for Student t distributions |
IV.2.36 | VaR and ETL for normal, Student t and mixture distributions |
IV.2.37 | Sample statistics for iTraxx Europe 5-year index |
IV.2.38 | Normal mixture parameter estimates: iTraxx Europe 5-year index |
IV.2.39 | VaR and ETL estimates for iTraxx Europe 5-year index |
IV.3.1 | Estimated values of scale exponent for S&P 500 index |
IV.3.2 | Estimated scale exponents for $/£ forex rate and US interest rates |
IV.3.3 | Recommended scale exponents for volatility indices |
IV.3.4 | Scaling 1-day VaR for different risk horizons and scale exponents |
IV.3.5 | GARCH parameters for S&P 500 index |
IV.3.6 | Historical VaR for S&P 500 on 31 March 2008 |
IV.3.7 | Estimated values of scale exponent for volatility adjusted S&P 500 |
IV.3.8 | Scaling VaR versus filtered historical simulation |
IV.3.9 | Historical VaR based on kernel fitting |
IV.3.10 | Estimates of GPD parameters (Matlab) |
IV.3.11 | Sample statistics used for Cornish–Fisher expansion |
IV.3.12 | Historical versus normal VaR for UK bond portfolio |
IV.3.13 | Historical VaR with different volatility adjustments |
IV.3.14 | Total, systematic and specific VaR, US stock portfolio |
IV.3.15 | Decomposition of systematic VaR into equity and forex stand-alone components |
IV.3.16 | Historical marginal VaR for international stock portfolio |
IV.3.17 | Bond position |
IV.3.18 | VaR decomposition for international bond position |
IV.3.19 | Crack spread book, 1 August 2006 |
IV.3.20 | Total VaR and component VaRs for a crack spread trader |
IV.3.21 | Estimates of GPD parameters and historical VaR estimates |
IV.3.22 | Comparison of ETL from parametric fits to historical return distribution |
IV.3.23 | Stand-alone equity and forex ETL for an international stock portfolio |
IV.4.1 | Excel commands for simulations |
IV.4.2 | Simulated returns based on constant and EWMA volatilities |
IV.4.3 | Multi-step Monte Carlo VaR based on constant and EWMA volatilities |
IV.4.4 | A-GARCH model parameters |
IV.4.5 | Multi-step Monte Carlo A-GARCH VaR with positive and negative shocks |
IV.4.6 | Risk factor returns, volatilities, sensitivities and correlations |
IV.4.7 | Volatilities and correlations of LIBOR and credit spreads |
IV.4.8 | Comparison of Monte Carlo VaR estimates for credit spreads |
IV.4.9 | PC sensitivities and the PC Cholesky matrix |
IV.4.10 | Parameters of normal mixture distribution for three stocks |
IV.4.11 | Parameters of normal distribution for three stocks |
IV.4.12 | Comparison of normal and normal mixture Monte Carlo scenario VaR |
IV.4.13 | Bivariate GARCH model parameters |
IV.4.14 | Comparison of normal GARCH and Student t GARCH VaR |
IV.5.1 | Delta and vega effects (symmetric negative price–volatility relationship) |
IV.5.2 | Delta and vega effects (asymmetric negative price–volatility relationship) |
IV.5.3 | Delta and vega effects (asymmetric positive price–volatility relationship) |
IV.5.4 | Characteristics of equity indices and their options |
IV.5.5 | 1% 10-day VaR under different rebalancing assumptions |
IV.5.6 | Comparison of 10% and 0.1% 10-day VaR under different rebalancing assumptions |
IV.5.7 | Comparison of VaR and ETL for long and short calls and puts |
IV.5.8 | Disaggregation of option VaR into price, volatility and interest rate VaRs |
IV.5.9 | Characteristics of European options on S&P 500 futures |
IV.5.10 | Historical VaR with Greeks approximation |
IV.5.11 | Position Greeks of large international stock option portfolio |
IV.5.12 | Value Greeks of a large international stock option portfolio |
IV.5.13 | Historical VaR for a large international stock option portfolio |
IV.5.14 | Limits on value Greeks of the crude oil option portfolio |
IV.5.15 | Historical VaR of the crude oil option portfolio |
IV.5.16 | Historical volatilities and correlations for risk factors of S&P 500 option |
IV.5.17 | Effect of non-linearity and non-normality on 1% daily Monte Carlo VAR |
IV.5.18 | Student t Monte Carlo VAR with and without daily rebalancing |
IV.5.19 | Long-term VaR estimates for static and dynamic portfolios |
IV.5.20 | Bivariate GARCH model parameters |
IV.5.21 | Monte Carlo VaR for option based on constant volatility and GARCH |
IV.5.22 | Risk factor covariance matrix (×104) |
IV.5.23 | Risk factor volatilities and correlations |
IV.5.24 | Comparison of Monte Carlo and historical VaR |
IV.5.25 | Risk factor volatilities and correlations |
IV.5.26 | Monte Carlo versus historical VaR for a large international stock option portfolio |
IV.5.27 | Risk factor correlations |
IV.5.28 | Monte Carlo VaR of the crude oil option portfolio |
IV.5.29 | Eigenvalues of 10-day historical covariance matrix for crude oil futures |
IV.5.30 | Normalized eigenvectors for first two eigenvalues in Table IV.5.29 |
IV.5.31 | Monte Carlo PC VaR for the portfolio of crude oil options |
IV.5.32 | Volatility beta estimates relative to 3-month volatility |
IV.5.33 | Influence of vega mapping on VaR for a portfolio of crude oil options |
IV.6.1 | Advantages and limitations of different levels of risk assessment |
IV.6.2 | Discount rate volatilities and correlations |
IV.6.3 | Computing the cash-flow map and estimating PV01 |
IV.6.4 | OLS and EWMA beta, index volatility and VaR for HBOS stock. |
IV.6.5 | Normal linear VaR estimates and approximate standard errors |
IV.6.6 | VaR standard errors based on volatility and based on quantile |
IV.6.7 | Basel zones for VaR models |
IV.6.8 | Coverage tests on RiskMetrics™ VaR of S&P 500 index |
IV.6.9 | Exceedances and t ratio on standardized exceedance residuals |
IV.6.10 | Results of likelihood ratio test |
IV.7.1 | Scenario categorization, with illustration using the iTraxx index |
IV.7.2 | VaR estimates based on historical scenarios |
IV.7.3 | Prices for crude oil futures ($/barrel) |
IV.7.4 | Expected weekly returns, standard deviations and correlations |
IV.7.5 | Normal mixture VaR versus normal VaR |
IV.7.6 | Analyst's beliefs about credit spreads |
IV.7.7 | Six sigma losses |
IV.7.8 | Results of worst case loss optimization |
IV.7.9 | Sample moments of S&P 500 and FTSE 100 index returns during global crash period |
IV.7.10 | Adjusting VaR for uniform liquidation |
IV.7.11 | Stressed VaR at different confidence levels based on Monte Carlo GARCH |
IV.8.1 | Aggregation of economic capital |
IV.8.2 | Aggregate RORAC as a function of correlation |
IV.8.3 | Effect of cost of capital and correlation on aggregate RAROC |
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