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Index

Bank for International Settlements (BIS),
absolute returns volatility, 10“11
129
actual volatility, 101
Barone-Adesi and Whaley quadratic
ADC (asymmetric dynamic covariance)
approximation, 89“90, 92“5
model, 65“6
Basel Accords, 129“31
ARCH (autoregressive conditional
Basel Committee, 129“31
heteroscedasticity) models, 7, 10,
BEKK model, 66
17, 31, 37“44, 121, 122, 126
biased forecast, 29
Engle (1982), 37“8
bid“ask bounce, 16, 90, 91, 117
forecasting performance, 43“4
Black model, 127
LM-ARCH, 51, 53
Black-Scholes model, 49“50, 71“95
see also GARCH
binomial method, 80“6
autoregressive conditional
matching volatility with u and d,
heteroscedasticity models
83“4
see ARCH models
two-step binomial tree and
ARFIMA model, 34, 51, 53, 127
American-style options, 85“6
ARIMA model, 34
dividend and early exercise premium,
ARMA model, 7, 34
88“90
Asian ¬nancial crisis, 9
dividend yield method, 88“9
asymmetric dynamic covariance (ADC)
Heston price and, 99“102
model, 65“6
implied volatility smile, 74“7, 97
at the money (ATM), 76
investor risk preference, 91“2
implied volatility, 101, 106, 107,
known and ¬nite dividends, 88
116“17
measurement errors and bias, 90“2
options, 87, 91, 106, 117, 119
no-arbitrage pricing, 77“80
autocorrelation, 19
stock price dynamics, 77
of absolute returns, 8
partial differential equation, 77“8
asset returns, 7
solving the partial differential
lack of, 7
equation, 79“80
autocorrelation function, decay rate, 7
option price, 97
autoregressive model, 126
for pricing American-style options,
72, 85“6
backtest, 132“3
for pricing European call and put
three-zone approach to, 133“5
options, 71“7
backward induction, 86
216 Index


forecasting volatility, 16“17
Black-Scholes model (continued )
fractionally integrated model, 46, 50“4
risk, 91
positive drift in fractional integrated
testing option pricing model, 86“7
series, 52“3
Black-Scholes implied volatility (BSIV),
forecasting performance, 53“4
49, 50, 73“4, 91, 100
see also FIGARCH; FIEGARCH
break model, 46
fractionally integrated series, 54
Brownian motion, 18

GARCH, 18, 34, 38“9, 121, 122, 126
Capital Accord, 130
component GARCH (CGARCH), 55
CGARCH (component GARCH), 55
EVT-GARCH, 135
Chicago Board of Exchange (CBOE), 2
exponential (EGARCH), 34, 41, 43,
close-to-open squared return, 14
121, 122
component GARCH (CGARCH), 55
GARCH(1,1) model, 12, 17, 38,
conditional variance, 22
40, 46
conditional volatility, 10
GARCH(1,1) with occasional break
constant correlation model, 66
model, 55
GARCH-t, 135
deep-in-the-money call option, 76
GJR-GARCH, 41“2, 43, 44, 122
deep-out-of-the-money call option, 76
integrated (IGARCH), 39“40, 45
delta, 89, 90
quadratic (QGARCH), 42
Diebold and Mariano asymptotic test, 25,
regime switching (RSGARCH), 57“8,
26“7
122
Diebold and Mariano sign test, 25, 27
smooth transition (STGARCH), 58
Diebold and Mariano Wilcoxon sign-rank
TGARCH, 42
test, 27
generalized ARCH see GARCH
discrete price observations, 15
generalized method of moments (GMM),
60
EGARCH, 34, 41, 43, 121, 122
generalized Pareto distribution, 137
equal accuracy in forecasting models,
Gibbs sampling, 61
tests for, 25
GJR-GARCH, 41“2, 43, 44, 46, 122
error statistics, 25
Gram“Charlier class of distributions, 12
EVT-GARCH method, 135
EWMA (exponentially weighted moving
Heath-Jarrow-Morton model, 127
average), 31, 33, 40, 44
Heston formula, 99, 102
explained variability, proportion of,
Heston stochastic volatility option
29“30
pricing model, 98“9
exponential GARCH (EGARCH), 34, 41,
assessment, 102“4
43, 121, 122
zero correlation, 103
exponential smoothing method, 33
nonzero correlation, 103“4
exponentially weighted moving average
Black-Scholes implied and, 99“102
(EWMA), 31, 33, 40, 44
market price of volatility risk, 107“13
extreme value method see high-low
case of stochastic volatility, 107“8
method
constructing the risk-free strategy,
108“10
factor ARCH (FARCH) model, 66
correlated processes, 110“11
FARCH (factor ARCH) model, 66
Ito™s lemma for stochastic variables,
fat tails 7
107
FIEGARCH, 50“1, 52“4
market price of risk, 111“13
FIGARCH, 50, 51“2, 53, 122
volatility forecast using, 105“7
¬nancial market stylized facts, 3“9
heteroscedasticity-adjusted Mean Square
forecast biasedness, 117“19
Error (HMSE), 23“4
forecast error, 24
Index 217


long memory effect of volatility, 7
high-low method (H-L), 12“14, 17, 21
long memory SV models, 60
historical average method, 33
historical volatility models, 31“5
market risk, 130
forecasting performance, 35
Markov chain, 60
modelling issues, 31“2
maximum likelihood method, 11
regime switching, 34“5
MCMC (Monte Carlo Markov chain), 59
single-state, 32“4
MDH (mixture of distribution
transition exponential smoothing,
hypothesis), 148
34“5
mean 2
types, 32“5
Mean Absolute Error (MAE), 23, 44
HISVOL, 121, 122
Mean Absolute Percent Error (MAPE),
23, 44
implied standard deviation (ISD), 116,
Mean Error (ME), 23
121, 122
Mean Logarithm of Absolute Errors
implied volatility method, 30, 91, 101
(MLAE), 24
at the money, 101, 106, 107
Mean Square Error (MSE), 23
Black-Scholes (BSIV), 49, 50, 73“4,
MedSE (median standard error), 44
91, 100
mixture of distribution hypothesis
implied volatility smile, 74“7, 97
(MDH), 148
importance sampling, 60
Monte Carlo Markov chain (MCMC), 59,
independent and identically distributed
60“3
returns (iid), 16, 136
parameter w, 62“3
in-sample forecasts, 30
volatility vector H , 61“2
integrated cumulative sums of squares
moving average method, 33
(ICSS), 55
multivariate volatility, 65“9
integrated GARCH (IGARCH), 39“40,
applications, 68“9
45
bivariate example, 67
integrated volatility, 14, 39, 40
interest rate, level effect of, 58
nearest-to-the-money (NTM), 116“17
in-the-money (ITM) option, 87
near-the-money (NTM), 76, 106
intraday periodic volatility patterns,
negative risk premium, 102
15“16
nonsynchronous trading, 15
inverted chi-squared distribution, 62
normal distribution, 2
IOSCO (International Organization of
Securities Commissions), 130
operational risk, 131
Ito™s lemma, 77, 107, 108, 110
option forecasting power, 115“19
option implied standard deviation,
Jensen inequality, 11
115“16
option pricing errors, 30
kurtosis, 4, 17
stochastic volatility (SV) option pricing
model, 97“113
large numbers, treatment of, 17“19
Ornstein-Uhlenbeck (OU) process,
Legal & General, 4
108
level effect in interest rates, 58
orthogonality test, 28“30
leverage effect (volatility asymmetry), 8,
outliers, removal of, volatility persistence
37, 56, 148
and, 18“19
likelihood ratio statistic, 139
out-of-sample forecasts, 30
LINEX, 24
out-of-the-money (OTM) put option, 76,
liquidity-weighted assets, 130
87, 92, 119
LM-ARCH model, 51, 53
out-of-the money (OTM) implied
log-ARFIMA, 51, 53, 127
volatility, 101
lognormal distribution, 2
218 Index


MCMC approach, 60“3
quadratic GARCH (QGARCH), 42
parameter w, 62“3
quadratic variation, 14“15
volatility vector H , 61“2
quasi-maximum likelihood estimation
option pricing model, 97“113
(QMLE), 60, 136
stock market crash, October, 1987 18
strict white noise, 16
random walk (RW) model, 32“3, 44, 126
strike price effect, 101
range-based method, 12, 17
Student-t distribution, 17
realized bipower variation, 15
switching regime model, 54
realized volatility, 14“16
recursive scheme, 25
tail event, 135, 136
regime-switching GARCH (RSGARCH),
TAR model, 34, 43, 58
57“8, 122
Taylor effect, 8, 46
regime-switching model, 19, 46
TGARCH, 42
regression-based forecast ef¬ciency,
Theil-U statistic, 24
28“30
threshold autoregressive model (TAR),
risk 1
34, 43, 58
risk management, volatility models in,
time series, 4“7
129“41
trading volume weighted, 117
risk-neutral long-run level of volatility,
trimming rule, 18
98
risk-neutral price distribution, 101
UK Index for Small Capitalisation Stocks
risk-neutral probability measure, 83,
(Small Cap Index), 4
85
unbiased forecast, 29
risk-neutral reverting parameter, 98
unconditional volatility, 10
risk-neutrality, 49
risk-weighted assets, 130
value-at-risk (VaR), 129, 131“5
rolling scheme, 25
10-day VaR, 137“8
Root Mean Square Error (RMSE), 23, 44
evaluation of, 139“41
RSGARCH, 57“8, 122
extreme value theory and, 135“9
model, 136“7
serial correlation, 28
multivariate analysis, 138“9
Sharpe ratio, 1“2
variance as volatility measure, 1
sign test, 25
variance“covariance matrix, 65
simple regression method, 33“4
VAR-RV model, 51, 53
skewness, 4
VDAX, 126
smile effect, 75
VECH model, 66
smirk, 75
vega, 89, 90
smooth transition GARCH (STGARCH),
vega weighted, 117
58
VIX (volatility index), 126
smooth transition exponential smoothing,
new de¬nition, 143“4
34“5
old version (VXO), 144“5
squared percentage error, 24
reason for change, 146
squared returns models, 11
volatility asymmetry see leverage effect
Standard and Poor market index
volatility breaks model, 54“5
(S&P100), 4
volatility clustering, 7, 147
standard deviation as volatility measure,
volatility component model, 46, 54
1, 2
volatility dynamic, 132
STGARCH 58
volatility estimation, 9“17
stochastic volatility (SV), 31, 59“63, 121
realized volatility, quadratic variation
forecasting performance, 63
and jumps, 14“16
innovation, 59“60
Index 219


scaling and actual volatility, volatility index see, VIX
16“17 volatility long memory
using high“low measure, 12“14 break process, 54“5
using squared returns, 11“12 competing models for, 54“8
volatility forecasting records, 121“8 components model, 55“7
getting the right conditional variance de¬nition, 45“6
and forecast with the ˜wrong™ evidence and impact, 46“50
models, 123“4 forecasting performance, 58
predictability across different assets, regime-switching model
124“8 (RS-GARCH), 57“8
exchange rate, 126“7 volatility persistence, 17“19, 45, 136
individual stocks, 124“5 volatility risk premium, 119
other assets, 127“8 volatility skew, 76, 116
stock market index, 125“6 volatility smile, 101, 116
which model?, 121“3 volatility spillover relationships, 65
volatility forecasts, 21“30 volume-volatility, 147“8
comparing forecast errors of different
models, 24“8 weighted implied, 116“17
error statistics and form of µt , 23“4 weighted least squares, 117
form of X t , 21“2 Wilcoxon single-rank test, 25
wildcard option, 91
see also volatility forecasting
records
volatility historical average, 126 yen“sterling exchange rate, 4

Index compiled by Annette Musker

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