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-