List of Figures

IV.1.1 Probability of underperforming a benchmark by 2% or more
IV.1.2 Illustration of the VaR metric
IV.1.3 Effect of expected active return on benchmark VaR
IV.1.4 P&L distribution for one binary option
IV.1.5 P&L distribution for a portfolio of two binary options
IV.1.6 Simulated P&L density showing 1% VaR
IV.2.1 Illustration of normal linear VaR
IV.2.2 PV01 vector of a UK fixed income portfolio (£000)
IV.2.3 Eigenvectors of covariance matrix of UK spot rates – short end
IV.2.4 First principal component of the UK spot rates – short end
IV.2.5 Systematic and specific VaR based on EWMA
IV.2.6 Total risk factor VaR versus quanto correlation
IV.2.7 Constant maturity futures prices, silver
IV.2.8 Constant maturity futures prices, natural gas
IV.2.9 Comparison of normal VaR and leptokurtic VaR
IV.2.10 FTSE 100 index price
IV.2.11 Comparison of a normal mixture with a normal density of the same variance
IV.2.12 EWMA volatility of the FTSE 100 for different smoothing constants
IV.2.13 NASDAQ 100 and S&P 500 indices
IV.2.14 EWMA volatilities of NASDAQ and S&P 500 indices
IV.2.15 EWMA correlations of NASDAQ and S&P 500 indices
IV.2.16 NASDAQ 100 and S&P 500 indices, 2006–2008
IV.2.17 iTraxx Europe 5-year index
IV.3.1 Log-log plot of holding period versus 5% quantile ratio: S&P 500 index
IV.3.2 Log-log plot of holding period versus quantile ratio: $/£ forex rate
IV.3.3 Log-log plot of holding period versus quantile ratio: US 3-month Treasury bills
IV.3.4 Log-log plot of holding period versus quantile ratio: US 10-year bond
IV.3.5 S&P 500 index and daily returns
IV.3.6 Time series of 1% historical VaR estimates, S&P 500
IV.3.7 Time series of 1% normal linear VaR estimates, S&P 500
IV.3.8 Time series of difference between historical VaR and normal linear VaR, S&P 500
IV.3.9 Exponential probability weights on returns
IV.3.10 Exponentially weighted distribution functions, S&P 500 daily returns
IV.3.11 GARCH volatility estimates for the S&P 500 index
IV.3.12 Returns and A-GARCH volatility adjusted returns
IV.3.13 EWMA adjusted daily returns on S&P 500
IV.3.14 Kernels fitted to standardized historical returns
IV.3.15 Error from Cornish–Fisher VaR approximation
IV.3.16 Tuenter's algorithm for Johnson VaR
IV.3.17 Error from Johnson VaR approximation
IV.3.18 Bank of England short curve
IV.3.19 EWMA volatility of P&L on UK gilts portfolio
IV.3.20 Empirical distribution of UK gilts portfolio P&L on 31 December 2007
IV.3.21 Apple and Citigroup stock prices
IV.3.22 EWMA volatilities of Apple and Citigroup
IV.3.23 EWMA betas for Apple and Citigroup in S&P 100 index
IV.3.24 Systematic returns before and after volatility adjustment for the volatility on (a) 30 October 2006 and (b) 21 April 2008
IV.3.25 S&P 500 and FTSE 100 indices, 1996–2008
IV.3.26 £/$ forex rate, 1996–2008
IV.3.27 Volatilities of UK and US stock markets and the £/$ exchange rate
IV.3.28 US swap rates
IV.3.29 Three-month crack spread futures prices
IV.3.30 EWMA volatilities of heating oil crack spread futures P&L
IV.3.31 EWMA volatilities of gasoline crack spread futures P&L
IV.4.1 Consecutive pseudo-random numbers plotted as points in the unit cube
IV.4.2 Effect of independently permuting stratified samples
IV.4.3 Simulating from a standard normal distribution
IV.4.4 Densities based on stratified and unstratified samples
IV.4.5 Multi-step Monte Carlo price paths
IV.4.6 Simulated returns based on EWMA and GARCH following shock
IV.4.7 Log returns simulated under Markov switching GARCH
IV.4.8 Scatter plot of S&P 500 and Vix daily log returns
IV.5.1 The P&L distribution resulting from delta–gamma approximation
IV.5.2 S&P 500 index price, Vix and 1-month US LIBOR, 1990–2008
IV.5.3 FTSE 100, DAX 30 and S&P 500 indices
IV.5.4 Vftse, Vdax and Vix volatility indices
IV.5.5 NYMEX WTI crude oil futures prices
IV.5.6 NYMEX WTI at-the-money volatilities
IV.6.1 HBOS stock price and FTSE 100 index
IV.6.2 1% 10-day VaR with two-standard-error bounds versus sample size
IV.6.3 1% 10-day VaR with two-standard-error bounds versus EWMA λ
IV.6.4 1% 10-day VaR with two-standard-error bounds – Student t versus normal
IV.6.5 Standard errors of 1% 10-day VaR estimate
IV.6.6 Rolling windows with estimation and test samples
IV.6.7 1% daily VaR and daily P&L
IV.6.8 Indicator of exceedances
IV.6.9 Relation between exceedances and implied volatility
IV.6.10 RiskMetrics™ daily volatility of S&P 500 index
IV.6.11 Standardized exceedance residuals from RiskMetrics™ regulatory VaR
IV.6.12 Standardized exceedance residuals from RiskMetrics™ daily VaR
IV.6.13 Empirical frequencies of the return probabilities
IV.6.14 EWMA standard deviation of the realized return probabilities
IV.7.1 A personal view on credit spread change during the week after a major banking crisis
IV.7.2 Distribution of interest rate changes conditional on a 20 basis point fall in the credit spread
IV.7.3 Distribution of interest rate changes conditional on a 40 basis point rise in the credit spread
IV.7.4 Term structure of crude oil futures now and in one week
IV.7.5 Personal view on credit spread of bond, one year from now
IV.7.6 Comparison of normal posterior with normal mixture
IV.7.7 S&P 500 and FTSE 100 indices during global crash of 1987
IV.8.1 GRC for the US stock portfolio and S&P 100 volatility
IV.8.2 Price of Barclays and Lloyds TSB shares (in pence)
IV.8.3 Internal GRC and standardized MRC for hedged portfolio
IV.8.4 Relationship between economic capital and capitalization
IV.8.5 Effect of correlation on aggregate EC
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