spiky, 73, 78, 85, 86, 91 statistical see Statistical volatility stochastic see Stochastic volatility surfaces see Volatility smile surface;

Volatility surfaces term structures see Volatility term

structures time horizon, 18

time-varying volatility models, 12-14 uncertainty, 18

unconditional see Unconditional volatility Volatility clustering, asymmetry, 68, 79

autoregressive conditional heteroscedasticity (ARCH), 63, 65-7, 97, 386

commodity markets, 65 currency markets, 65, 97 equity markets, 65 excess kurtosis, 66, 67 mean-reversion, 31 news announcements, 65-6 skews, 66, 67

square root of time rule, 97 Volatility cones, 29 Volatility estimates and forecasts,

A-GARCH, 80-1, 99

academic research, 120

benchmark forecast, 118

central values, 119

combined forecasts, 118, 129-34

confidence intervals, 118, 119, 126-34

different horizons, 29, 98

evaluation, 117

exponential GARCH (E-GARCH), 80

exponentially weighted moving average

(EWMA), 57-8, 60, 119 extreme values, 119 GARCH, 73-5, 81, 93, 98, 99-100 historic volatility, 50-2, 57, 128 I-GARCH. 76, 77 implied volatility, 117-18, 124-5 long-term. 85-91, 92, 98, 99 look-back periods, 57 mark-to-model values, 135 mean-reversion. 75, 79 moving averages. 126-8 out-of-sample likelihood. 121 point forecasts. 118. 126 process volatility 117. 118. 129 n>k honzon>. 11. 43. 57. 60. 117 root mean square error (RMSE),

122-3

standard deviation. 121

standard error, 118-19, 126, 127

straddles, 124

uncertainty, 119

underlying volatility, 117

variance, 50 Volatility sensitivity,

ATM volatility, 167, 168, 169

option vega, 24

prices, 34, 43, 44 Volatility smile surface,

implied volatility, 106, 154

N-GARCH, 81, 106, 107

volatility surface distinguished, 33 Volatility surfaces,

implied volatility, 32-4

parameterization, 167-70

quadratic, 38, 45, 144, 168

Taylor approximations, 169

volatility process, 11

volatility smile surface distinguished, 33

Volatility term structures, call options, 31, 32 constant volatility, 61, 99 convergence, 12, 75, 76, 97-8, 102-3 currency markets, 102 equity markets, 101-3 GARCH models, 32, 50, 61, 64, 80,

85, 98-103, 212 implied volatility, 31-2, 78 mean-reversion, 61, 98, 109, 111 put options, 31, 32 returns of different frequencies, 5 scenario analysis, 92

Weibull distribution, 293, 294 Weighted average,

see also Historic correlation, Historic volatility

beta, 109

EWMA .see Exponentially weighted

moving average ghost features, 53, 60, 125 historic volatility, 49, 50, 52-3 RiskMetrics data, 179, 201 sampling error, 49 short-term, 53

unconditional correlation, 49

unconditional variance, 50

unconditional volatility, 49

variance forecasts, 126 Whites test, 432 Wiener process, 21. 104 WTI (West Texas Intermediate). 55. "8. Ill

Yield curves, scenario analysis, 143

modelling multiple yield curves, 149-53 trend/tilt/convexity, 147-9 principal component analysis (PCA),

147-53 Zero-coupon bonds, 147-8, 182,