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160 A-GARCH, academic research, 69 conditional variance, 70, 80 leverage coefficient, 80 leverage effect, 68-9, 79 steady-state variance, 99 volatility estimates, 80-1 volatility forecasts, 81, 99 AEX, 85, 89, 217, 363, 364 Algorithms, BHHH algorithm, 80, 95 chaotic dynamics, 403-5 DFP algorithm, 95 gradient algorithm, 96 nearest neighbour algorithms, 404-5 parameter estimation, 92-5 quasi-Newton variable, 95 Alpha, capital asset pricing model (CAPM), 231, 238 high frequency data, 83 I-GARCH, 77, 78 single outliers, 96 symmetric GARCH, 73 Annualized volatility, definition, 5 AORD, 87, 89 Arbitrage pricing theory (APT), multi-factor models, 181, 233, 247 risk factors, 233 ARCH. conditional variance, 71, 83 high frequency data, 82, 393 volatility clustering, 386 Asian calf 104. 105 Asian crisis. 90. 185 Asset management. country indices. 186 risk, 236 Asymmetric GARCH see A-GARCH, E-GARCH, N-GARCH asymmetric power GARCH, 81 conditional variance, 79 equity markets, 31 multivariate GARCH, 114 volatility clustering, 68, 79 At the money see ATM ATM options, Black-Scholes model, 136, 297, 306-7 call options, 24, 30 gamma, 44 marked-to-market (MtM) value, 135, 136-7 short-term, 33 vega, 44 ATM volatility, changes, 171 constant, 37 deviations, 157-9, 161-2 market regimes, 36-8, 39, 43 maturity. 36 straddles, 125, 386 underlying price, 39 volatility sensitivity, 167, 168, 169 Augmented Dickey-Fuller test (ADF), 327, 328, 354-6, 372, 373, 379 Autocorrelation, Box-Pierce test, 66, 68, 97, 315, 335-7, 386 common autocorrelation, 384-6 Durbin-Watson test, 431 high frequency data, 391-3 omitted variables, 430-1 ordinary least squares (OLS), 431, 432 over/under-differencing, 431 residual analysis, 429-32 squared returns, 63, 65-6, 68, 97 structural breaks, 430 Autoregression, multivariate time series, 340-1 univariate time series, 329-31
Autoregressive conditional heteroscedasticity, ARCH, 70-1 GARCH see GARCH models volatility clustering, 63, 65-7, 97 Autoregressive moving average (ARMA), forecasting, 338-9 testing down, 337-8 time series models, 313, 315, 332-3, 337-9 unit root tests, 324 Backtesting, cointegration, 375-81 prediction, 444-5 VaR (value-at-risk) models, 125, 250, 275-7 BARRA Growth and Value Indexes, 234 Basel Accord (1988), Amendment (1996), 38, 201, 249, 251, 252, 275-6, 279 Basel 2: 249, 255 Basel Committee on Banking Supervision, 249, 255 credit risk capital requirement (CRR), 252, 255 G10, 251, 252 market risk capital requirement (MRR), 251, 252, 255, 276, 279 solvency ratio, 251, 252 Bayesian methods, Bayes1 rule, 240-2 estimation, 242-5 factor sensitivities, 239-46 BEKK model, convergence, 217 correlation estimates, 109, 110 diagonal BEKK, 114 parameter estimates, 220 scalar BEKK, 114 Benchmark downside risk, 258-9 regression, 144 tracking models, 172 volatility forecasts, 118 Beta, capital asset pricing model (CAPM), 231, 238 high frequency data, 83 single outliers, 96 time-varying correlation, 109, 238 VaR (value-at-risk) models, 109 weighted average, 109 BHHH algorithm, 80, 95 Binomial trees, 34, 38, 43, 98 Bivariate GARCH, academic research, 111 calibration, 111 conditional correlation, 108 conditional mean, 108 conditional variance, 108 convergence, 108, 109 correlation estimates, 109, 110, 205 covariance, 110 parameterization, 108, 111 time-varying correlation, 16 time-varying hedge ratios, 64, 111 Black Monday, 52-3, 57, 85, 185 Black-Scholes model, assumptions, 21, 26, 30, 34, 61, 104 ATM options, 136, 297, 306-7 constant volatility, 21, 24, 26, 30, 34, 61 delta, 32, 44 gamma, 32 geometric Brownian motion (GBM), 10, 21, 30 implied volatility, 12, 22, 23-6, 33, 34, 106 ITM, 136, 297, 306, 309 moneyness, 23, 24, 25, 44 option pricing, 1, 10, 21, 104, 106, 305-6 OTM, 136, 297, 306, 309 process volatility, 11, 23 quanto correlation, 46 risk-free rate of return, 21, 23 risk-neutrality hypothesis, 32 spread options, 367 strike, 23, 24, 26, 30 vega, 32, 44 Wiener process, 21 Black-Scholes volatility, meaning, 10 Box-Pierce test, autocorrelation, 66, 68, 97, 315, 335-7. 386 Breush-Pagan test, 433 Butterflies, 118 CAC index, 71, 72, 76, 85, 89, 111, 117, 129, 174, 202, 217, 239, 363, 364 Call options, Asian call, 104, 105 ATM options. 24, 30 average price, 104 Black-Scholes model, 24 implied volatility, 26-8 ITM, 24, 26, 28, 30, 31 OTM, 24, 30 rising markets, 27 volatility term structures, 31, 32 Capital allocation, efficient frontier, 190 risk-adjusted performance measures (RAPM), 193-4 risk-adjusted returns, 186, 187
Capital asset pricing model (CAPM), beta, 231, 238 covariance matrices, 115, 238 decomposing risk, 230-2 market sensitivity, 109 ordinary least squares (OLS), 111 risk factors, 232 Sharpe-Lintner version, 230 Cash-flow maps, covariance VaR models, 263-5 factor models, 262 risk measurement, 256 Chaotic dynamics, academic research, 404 algorithms, 4031 Lyapunov exponents, 403, 404 multivariate embedding models, 405-7 nearest neighbour algorithms, 404-5 price prediction models, 401-7 testing for chaos, 4011 time-delay embedding, 402 Cholesky decomposition, 182, 1831 Co-dependency, copulas, 8 correlation, 7, 8 Co-monotonic dependency, 8 Coherent risk measures, 259 Cointegration, causality, 361-6 commodity markets, 367 common features, 381-7 common trends, 350-3 correlation, 349-50 currency markets, 366 Engle-Granger methodology, 353, 354-7, 360-1, 368 equity markets, 368-9 error correction model (ECM), 347, 355, 362-6 financial markets, 347, 366-9 futures, 367 introduction, 348-53 investment analysis, 369-81 Johansen methodology, 357, 361, 363, 368 long-run equilibria, 350-3 long-short strategies, 374-6 market integration, 368-9 meaning, 347-38 spread options, 367 stock selection/allocation, 369-71 term structures, 368 testing, 353-61 tracking models, 372 Collinearity, multicollinearity, 144, 172-4, 436-7 principal component analysis (PCA), 143, 144, 171 Combined forecasts, 118, 129-34 Commodity markets, cointegration, 367 correlation estimates, 15, 56 futures, 55, 60 GARCH parameters, 77, 85 mean-reversion, 75 spot-future correlations, 55 time-varying futures hedge, 111 volatility clustering, 65 Components GARCH, 78-9 Conditional correlation, see also Time-varying correlation bivariate GARCH, 108 orthogonal GARCH, 211 unstable estimates, 16-17 Conditional covariance, capital asset pricing model (CAPM), 238 parameters, 114 principal component analysis (PCA), 162-3 Conditional distribution, 12, 13 Conditional heteroscedasticity, see GARCH models Conditional mean, bivariate GARCH, 108 GARCH models, 69-70, 100 high frequency data, 82 leptokurtic distribution, 82 models, 12, 13, 14 multivariate GARCH, 111 Conditional variance, ARCH, 71, 83 asymmetric response, 79 bivariate GARCH, 108 constant volatility, 13 covariance matrices, 114 GARCH models, 70, 72, 73, 78, 79, 80, 83-4, 97, 98, 109 linear regression models, 64 time-varying volatility models, 13 Conditional volatility, GARCH models, 81, 96-7 time-varying volatility models, 12, 14 Confidence intervals, combined forecasts, 129-34 for variance, 126 for volatility, 118, 119, 126-34 GARCH models, 128-9 Granger-Ramanarthan procedure. 118. 129 interval predictions, 133-4 meaning, 4214-
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