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˜less-one™ method) weekly squared
GARCH deviations to are not in¬‚uenced
by ˜outliers™.
GARCH-t proxy ˜actual
(ranked) vol.™ Performance of
GARCH-t is
consistently much
worse. Same results
for all four stock
markets
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

41. Franses and Stock indices 1986“94 W QGARCH 1 week ahead MedSE QGARCH is best if
Van Dijk (Germany, RW GARCH estimated from data has no
(1996) Netherlands, GJR rolling 4 years. extremes. RW is
Spain, Italy, (ranked) Use weekly best when 87™s crash
Sweden) squared is included. GJR
deviations to cannot be
proxy ˜actual recommended.
vol.™ Results are likely to
be in¬‚uenced by
MedSE that penalize
nonsymmetry.
Brailsford and Faff
(1996) support GJR
as best model
although it
underpredicts over
70% of the time
42. Frennberg and VW Swedish In: M 1 month ahead MAPE, R 2 is S: seasonality
AR12 (ABS)-S RW,
Hansson stock market 1919“1976 estimated from 2“7% in ¬rst adjusted. RW model
ImpliedBS ATM Call
(1996) returns Out: 1977“82, (option maturity recursively period and seems to perform
1983“90 closest to 1 month) re-estimated 11“24% in remarkably well in
Index option Jan87“Dec90 GARCH-S, ARCH-S expanding second, more such a small stock
(European (ranked) sample. Use volatile period. market where
style) daily ret. to returns exhibit
H0 : ±implied = 0
Models that are not
compile strong seasonality.
and βimplied = 1
adj. for seasonality
monthly vol., cannot be Option was
did not perform as
adjusted for rejected with introduced in 86 and
well
autocorrelation robust SE covered 87™s crash;
outperformed by
RW. ARCH/
GARCH
did not perform as
well in the more
volatile second
period
43. Fung, Lie and £/$, C$/$, 1/84“2/87 D Option RMSE, MAE of Each day, 5 options
ImpliedOTM>ATM
Moreno FFr$, DM/$, (pre-crash) maturity; overlapping were studied; 1
Impliedvega, elasticity
(1990) ¥/$ & SrFr/$ overlapping forecasts ATM, 2 just in and 2
Impliedequal weight
options on periods. Use just out. De¬ne
HIS40 days , ImpliedITM
PHLX (ranked, all implied sample SD of ATM as S = X,
are from calls) daily returns OTM marginally
over option outperformed ATM.
maturity to Mixed together
proxy ˜actual implied of different
vol.™ contract months
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

44. Fung and S&P500, DM$ 3/83“7/89 D (15 min) RV-AR(n) 1 day ahead. RMSE and MAE RV: Realized vol.
Hsieh (1991) US T-bond (DM/$ Use 15-min from 15-min returns.
ImpliedBAW NTM Call/Put of log σ
futures from RV, RW (C-t-C) data to AR(n):
Futures and 26 Feb 85) HL construct autoregressive lags
futures options (ranked, some of the ˜actual vol.™ of order n. RW
differences are (C-t-C): random
small) walk forecast based
on close to close
returns. HL:
Parkinson™s daily
high-low method.
Impact of 1987
crash does not
appear to be drastic
possibly due to
taking log. In
general,
high-frequency data
improves
forecasting power
greatly
45. Gemmill 13 UK stocks May78“Jul83 M 13“21 non- ME, RMSE, Adding HIS
ImpliedITM
(1986) LTOM options. overlapping MAE aggregated increases R 2 from
ImpliedATM, vega WLS
option maturity across stocks and 12% to 15%. But ex
Impliedequal, OTM, elasticity
Stock price Jan 78“Nov83 D
(each average time. R 2 are ante combined
HIS20 Weeks
(ranked, all implied are 19 weeks). Use 6“12% (pooled) forecast from HIS
from calls) sample SD of and 40% (panel and ImpliedITM
weekly returns with ¬rm speci¬c turned out to be
over option intercepts). All worse than
maturity to individual forecasts.
± > 0, β < 1
proxy ˜actual Suffered small
vol.™ sample and
nonsynchroneity
problems and
omitted dividends
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

46. Gray (1996) US 1m T-Bill 1/70“4/94 W RSGARCH with time 1 week ahead R 2 calculated Volatility follows
varying probability (model not without constant GARCH and CIR
GARCH re-estimated). term, is 4 to 8% square root process.
Constant variance Use weekly for RSGARCH, Interest rate rise
(ranked) squared negative for increases probability
deviation to some CV and of switching into
proxy volatility GARCH. high-volatility
Comparable regime
RMSE and MAE Low-volatility
between persistence and
GARCH and strong rate level
RSGARCH mean reversion at
high-volatility state.
At low-volatility
state, rate appears
random walk and
volatility is highly
persistent
47. Guo (1996a) PHLX US$/¥ Jan91“Mar93 D Information not Regression with Use mid of bid“ask
ImpliedHeston
options available robust SE. No option price to limit
ImpliedHW
information on ˜bounce™ effect.
ImpliedBS
GARCH R 2 and forecast Eliminate
biasedness ˜nonsynchroneity™
HIS60
(ranked) by using
simultaneous
exchange rate and
option price. HIS
and GARCH contain
no incremental
information.
ImpliedHeston and
ImpliedHW are
comparable and are
marginally better
than ImpliedBS .
Only have access to
abstract
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

48. Guo (1996b) PHLX US$/¥, Jan86“Feb93 Tick 60 days ahead. US$/DM R 2 is 4, Conclusion same as
ImpliedHW (WLS, 0.8
US$/DM Use sample 3, 1% for the Guo (1996a). Use
< S/X < 1.2, 20 <
options variance of three methods. Barone-
T < 60 days)
GARCH (1, 1) daily returns to (9, 4, 1% for Adesi/Whaley
Spot rate D
proxy actual US$/¥) All approximation for
HIS60 days
(ranked) volatility forecasts are American options.
biased No risk premium for
volatility variance
± > 0, β < 1
with robust SE risk. GARCH has no
incremental
information. Visual
inspection of ¬gures
suggests implied
forecasts lagged
actual
49. Hamid (1998) S&P500 futures 3/83“6/93 D 13 schemes (including Non- RMSE, MAE Implied is better
options HIS, implied cross- overlapping 15, than historical and
strike average and 35 and 55 days cross-strike
intertemporal ahead averaging is better
averages) than intertemporal
(ranked, see comment) averaging (except
during very
turbulent periods)
50. Hamilton and Excess stock 1/65“6/93 M Bivariate RSARCH 1 month ahead. MAE Found economic
Lin (1996) returns Univariate RSARCH Use squared recessions drive
(S&P500 minus GARCH+L monthly ¬‚uctuations in stock
T-Bill) & Ind. ARCH+L residual returns returns volatility. ˜L™
Production AR(1) to proxy denotes leverage
(ranked) volatility effect. RS model
outperformed
ARCH/GARCH+L
51. Hamilton and NYSE VW 3/7/62“ W RSARCH+L 1, 4 and 8 MSE, MAE, Allowing up to
Susmel stock index 29/12/87 GARCH+L weeks ahead. MSLE, MALE. 4 regimes with t
(1994) ARCH+L Use squared Errors calculated distribution.
(ranked) weekly residual from variance RSARCH with
returns to proxy and log variance leverage (L)
volatility provides best
forecast. Student-t is
preferred to GED
and Gaussian
52. Harvey and S&P100 (OEX) Oct85“Jul89 D 1 day ahead R 2 is 15% for Implied volatility
ImpliedATM calls+puts
Whaley (American binomial, implied for use calls and 4% for changes are
(1992) in pricing next puts (excluding statistically
shortest maturity >
15 days) day option 1987 crash) predictable, but
(predict changes in market was ef¬cient,
implied) as simulated
transactions (NTM
call and put and
delta hedged using
futures) did not
produce pro¬t
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

53. Heynen and 7 stock indices 1/1/80“ D SV(?) Non- MedSE SV appears to
Kat (1994) and 5 exchange 31/12/92 EGARCH overlapping 5, dominate in index
rates GARCH 10, 15, 20, 25, but produces errors
In: 80“87 RW 50, 75, 100 that are 10 times
Out: 88“92 (ranked, see also days horizon larger than
comment) with constant (E)GARCH in
(87™s crash
update of exchange rate. The
included in
parameters impact of 87™s crash
in-sample)
estimates. Use is unclear. Conclude
sample standard that volatility model
deviations of forecasting
daily returns to performance
proxy ˜actual depends on the asset
vol.™ class
54. Hol and S&P100 (VXO) 2/1/86“ D SIV 1, 2, 5, 10, 15 R 2 ranges SVX is SV with
Koopman 29/6/2001 SVX+ and 20 days between 17 and impliedVXO as an
(2002) SV ahead. Use 33%, MSE, exogenous variable
Out:
(ranked) 10-min returns MedSE, MAE. while SVX+ is SVX
Jan97“Jun01
to construct with persistence
± and β not
˜actual vol.™ reported. All adjustment. SIV is
forecasts stochastic implied
underestimate with persistence
actuals parameter set equal
to zero
55. Hwang and LIFFE stock 23/3/92“ D Log-ARFIMA-RV Forecast
1, 5, 10, 20, . . . , MAE, MFE
Satchell options 7/10/96 Scaled truncated 90, 100, 120 impliedATM BS of
(1998) Detrended days ahead IV shortest maturity
240 daily out-
Unscaled truncated estimated from option (with at 15
of-sample
a rolling sample trading days to
MAopt n=20 -IV
forecasts.
of 778 daily maturity). Build MA
Adj MAopt n=20 -RV
GARCH-RV observations. in IV and ARIMA
(ranked, forecast Different on log (IV). Error
implied) estimation statistics for all
intervals were forecasts are close
tested for except those for
robustness GARCH forecasts.
The scaling in
Log-ARFIMA-RV
is to adjust for
Jensen inequality
56. Jorion (1995) DM/$, ¥/$, 1/85“2/92 D 1 day ahead and R 2 is 5% (1-day) Implied is superior
ImpliedATM BS call+put
SrFr/$ futures 7/86“2/92 option maturity. or 10“15% to the historical
GARCH (1, 1), MA20
options on 3/85“2/92 (ranked) Use squared (option methods and least
CME returns and maturity). With biased. MA and
aggregate of robust SE, GARCH provide
square returns only marginal
±implied > 0 and
to proxy actual incremental
βimplied < 1 for
volatility long horizon and information
is unbiased for
1-day forecasts
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

57. Jorion (1996) DM/$ futures Jan85“Feb92 D 1 day ahead, R 2 about 5%. R 2 increases from
ImpliedBlack, ATM
options on GARCH(1, 1) use daily 5% to 19% when
H0 : ±implied = 0,
CME (ranked) squared to unexpected trading
βimplied = 1
proxy actual cannot be volume is included.
volatility rejected with Implied volatility
robust SE subsumed
information in
GARCH forecast,
expected futures
trading volume and
bid“ask spread
58. Karolyi 74 stock 13/1/84“ M 20 days ahead MSE Bayesian adjustment
Bayesian impliedCall
(1993) options 11/12/85 volatility to implied to
ImpliedCall
incorporate
HIS20,60
(Predict option price cross-sectional
not ˜actual vol.™) information such as
¬rm size, leverage
and trading volume
useful in predicting
next period option
price
59. Klaassen US$/£, 3/1/78“ D RSGARCH 1 and 10 days MSE of variance, GARCH(1, 1)
(1998) US$/DM and 23/7/97 RSARCH ahead. Use regression forecasts are more
US$/¥ GARCH(1, 1) mean adjusted though R 2 is not variable than RS
Out: 20/10/87“
(ranked) 1- and 10-day reported models. RS provides
23/7/97
return squares statistically
to proxy actual signi¬cant
volatility improvement in
forecasting volatility
for US$/DM but not
the other exchange
rates
60. Kroner, Futures options Jan87“Dec90 D 225 calendar MSE, ME GR: Granger and
GR > COMB
Kneafsey and on cocoa, (kept last 40 days (160 Ramanathan
ImpliedBAW Call
Claessens cotton, corn, observations working days) (1984)™s regression
(WLS > AVG
(1995) gold, silver, for out-of- ahead, which is weighted combined
> ATM)
sugar, wheat sample longer than forecast, COMB: lag
HIS7 weeks > GARCH
forecast) (ranked) average implied in GARCH
conditional variance
Futures prices Jan87“ Jul91
equation. Combined
method is best
suggests option
market inef¬ciency
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

61. Lamoureux Stock options for 19/4/82“ D 90 to 180 days ME, MAE, Implied volatility is
ImpliedHull-White NTM Call
and 10 non-dividend- 31/3/84 (intermediate term to matching option RMSE. best but biased. HIS
Lastrapes paying stocks maturity, WLS) maturity estimated Average provides incremental
(1993) (CBOE) using rolling 300 implied is info. to implied and
HISupdated expanding estimate
GARCH observations and lower than has the lowest RMSE.
(ranked, based on expanding sample. actual for all When all three
regression result) Use sample stocks. R 2 on forecasts are included;
variance of daily variance varies ± > 0,
returns to proxy between 3 and 1 > βimplied > 0,
˜actual vol.™ 84% across βGARCH = 0,
stocks and βHIS < 0 with robust
models SE. Plausible
explanations include
option traders
overreact to recent
volatility shocks, and
volatility risk
premium is nonzero
and time-varying
62. Latane and 24 stock options 5/10/73“ W In-sample forecast Cross-section Used European model on
Implied vega weighted
Rendleman from CBOE 28/6/74 and forecast that correlation American options and
HIS4 years
omitted dividends.
(1976) (ranked) extend partially into between
volatility ˜Actual™ is more
the future. Use
weekly and monthly estimates for 38 correlated (0.686) with
returns to calculate weeks and a ˜Implied™ than HIS
actual volatility of 2-year period volatility (0.463) Highest
various horizons correlation is that
between implied and
actual standard
deviations which were
calculated partially into
the future

63. Lee (1991) $/DM, $/£, $/¥, 7/3/73“ W Kernel (Gaussian, 1 week ahead (451 RMSE, MAE. It Nonlinear models are, in
$/FFr, $/C$ 4/10/89 (Wed, truncated) observations in is not clear how general, better than linear
(Fed. Res. 12pm) Index (combining sample and 414 actual volatility GARCH. Kernel method
Out: 21
Bulletin) ARMA and observations was estimated is best with MAE. But
Oct81
GARCH) out-of-sample) most of the RMSE and
“11
EGARCH (1, 1) MAE are very close.
Oct89.
GARCH (1, 1) Over 30 kernel models
IGARCH with were ¬tted, but only
trend those with smallest
(rank changes see RMSE and MAE were
comment for reported. It is not clear
general how the nonlinear
assessment) equivalence was
constructed. Multi-step
forecast results were
mentioned but not shown
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

64. Li (2002) $/DM, $/£, $/¥ 3/12/86“ Tick 1, 2, 3 and 6 months MAE. R 2 ranges Both forecasts have
ImpliedGK OTC ATM
30/12/99 (5 min) ahead. Parameters 0.3“51% (implied), incremental
ARFIMArealised
OTC ATM
In: 12/8/86“ (implied better at not re-estimated. 7.3“47% (LM), information
options
11/5/95 shorter horizon Use 5-min returns 16“53% especially at long
$/£, $/¥
D and ARFIMA to construct ˜actual (encompass). For horizon. Forcing:
19/6/94“
$/DM
D better at long vol.™ both models, H0 :
13/6/99 ± = 0, β = 1
19/6/94“ horizon) produce
± = 0, β = 1 are
30/12/98 rejected and low/negative R 2
(especially for long
typically β < 1
with robust SE horizon). Model
realized standard
deviation as
ARFIMA without
log transformation
and with no
constant, which is
awkward as a
theoretical model
for volatility
65. Lopez C$/US$, 1980“1995 D SV-AR(1)-normal 1 day ahead and MSE, MAE, LL is the logarithmic
(2001) DM/US$, GARCH-gev probability forecasts LL, HMSE, loss function from Pagan
¥/US$, US$/£ EWMA-normal for four ˜economic GMLE and QPS and Schwert (1990),
In: 1980“1993
events™, viz. cdf of (quadratic HMSE is the
Out: GARCH-normal, -t
speci¬c regions. Use probability heteroscedasticity-adj.
1994“1995 EWMA-t
daily squared residuals scores) MSE from Bollerslev
AR(10)-Sq, -Abs
to proxy volatility. Use and Ghysels (1996) and
Constant
empirical distribution GMLE is the Gaussian
(approx. rank, see
to derive cdf quasi-ML function from
comments)
Bollerslev, Engle and
Nelson (1994). Forecasts
from all models are
indistinguishable. QPS
favours SV-n, GARCH-g
and EWMA-n

RMSE,
66. Loudon, FT All Share Jan71“Oct97 D EGARCH, GJR, Parameters estimated TS-GARCH is an
regression on
Watt and TS-GARCH, in period 1 (or 2) used absolute return version
Sub-periods:
log volatility
Yadav TGARCH to produce conditional of GARCH. All
Jan71“Dec80
(2000) NGARCH, variances in period 2 and a list of GARCH speci¬cations
Jan81“Dec90
diagnostics. R 2
VGARCH, (or 3). Use GARCH have comparable
Jan91“Oct97
GARCH, squared residuals as is about 4% in performance though
MGARCH ˜actual™ volatility period 2 and 5% nonlinear, asymmetric
(no clear rank, in period 3 versions seem to fare
forecast better. Multiplicative
GARCH vol.) GARCH appears worst,
followed by NGARCH
and VGARCH (Engle
and Ng 1993)
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

67. Martens S&P500 Jan94“ Tick Heteroscedasticity Scaled down one large
ImpliedBAW VXOstyle Non-overlapping 1, 5,
and futures, Dec2000 Log-ARFIMA 10, 20, 30 and 40 days adjusted RMSE. oil price.
Zein ¥/US$ futures, Jan96“ GARCH ahead. 500 daily R 2 ranges Log-ARFIMA
(2004) Dec2000 (ranked, see observations in 25“52% truncated at lag 100.
Crude Jun93“ comment also) in-sample which (implied), Based on R 2 , Implied
oil futures Dec2000 expands on each 15“48% (LM) outperforms GARCH
iteration across assets and in every case, and
horizons. Both beats Log-ARFIMA in
models provide ¥/US$ and crude oil.
incremental info. Implied has larger
to encompassing HRMSE than
regr. Log-ARFIMA in most
cases. Dif¬cult to
comment on implied™s
biasedness from
information presented

68. McKenzie 21 A$ bilateral Various length D Square vs. power 1 day ahead absolute RMS, ME, MAE. The optimal power is
(1999) exchange rates from 1/1/86 or transformation returns Regressions closer to 1 suggesting
4/11/92 to (ARCH models suggest all ARCH squared return is not
31/10/95 with various lags. forecasts are the best speci¬cation
See comment for biased. No R 2 in ARCH type model
rank) was reported for forecasting purpose
ME, MAE, CGARCH is the
69. McMillan, FTSE100 Jan84“Jul96 D, W, RW, MA, ES, EWMA j = 1 day, 1 week and
RMSE for component GARCH
Speight and FT All Share Jan69“Jul96 M GARCH, 1 month ahead based
on the three data symmetry loss model. Actual
Gwilym TGARCH,
function. volatility is proxied by
(2000) EGARCH, frequencies. Use j
Out: period squared returns MME(U) and mean adjusted squared
CGARCH
1996“1996 for to proxy actual MME(O), mean returns, which is likely
HIS, regression,
both series. (ranked) volatility mixed error that to be extremely noisy.
penalize Evaluation conducted
under/over on variance, hence
predictions forecast error statistics
are very close for most
models. RW, MA, ES
dominate at low
frequency and when
crash is included.
Performances of
GARCH models are
similar though not as
good
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

70. Noh, Engle S&P500 index Oct85“Feb92 D GARCH adj. for Option maturity. Equate Regression with
and options weekend and Based on 1000 days forecastability with call+put implieds,
Kane hols rolling period pro¬tability under daily dummies and
(1994) estimation the assumption of previous day returns to
ImpliedBS
weighted by an inef¬cient option predict next day
trading volume market implied and option
(ranked, predict prices. Straddle
option price strategy is not vega
not ˜actual neutral even though it
vol.™) might be delta neutral
assuming market is
complete. It is possible
that pro¬t is due to
now well-documented
post 87™s crash higher
option premium

M EGARCH(1, 2) 1 month ahead. Use
71. Pagan and US stock market 1834“1937 R 2 is 7“11% for The nonparametric
squared residual
Schw- Out: 1900“ GARCH(1, 2) 1900“25 and 8% models fared worse
2-step conditional monthly returns to
ert 1925 (low for 1926“37. than the parametric
(1990) volatility), variance proxy actual Compared with R 2 models. EGARCH
volatility
1926“1937 RS-AR(m) for variance, R 2 for came out best because
(high Kernel (1 lag) log variance is of the ability to capture
volatility) Fourier (1 or 2 smaller in 1900“25 volatility asymmetry.
lags) and larger in Some prediction bias
(ranked) 1926“37 was documented
72. Pong, US$/£ In: Jul87“ 1 month and 3 ME, MSE, Implied, ARMA and
5-, 30-min ImpliedATM, OTC
Shackleton, Dec93 (bias adj. months ahead at regression. R 2 ARFIMA have similar
quote
Taylor and Out: Jan94“ using rolling 1-month interval ranges between performance.
Xu (2004) Dec98 regr. on last 22 and 39% GARCH(1, 1) clearly
5 years monthly (1-month) and inferior. Best
data) 6 and 21% combination is
Log-ARMA(2, 1) (3-month) Implied + ARMA
Log-ARFIMA (2, 1). Log-AR(FI)MA
(1, d, 1) forecasts adjusted for
GARCH(1, 1) Jensen inequality.
Dif¬cult to comment
(ranked)
on implied™s
biasedness from
information presented

73. Poteshman S&P500 1Jun88“ D Option maturity BS R 2 is over
ImpliedHeston F test for H0 : ±BS = 0,
(2000) (SPX) & 29Aug97 (about 3.5 to 4 50%. Heston
ImpliedBS (both βBS = 1 are rejected
futures implieds are weeks, non- implied produced though t-test supports
Heston futures
from WLS of all overlapping). Use similar R 2 but H0 on individual
estimation: Tick
5-min futures very close to coef¬cients. Show
options <7
1Jun93“
inferred index being unbiased biasedness is not
months but >6
29Aug97
calendar days) return to proxy caused by bid“ask
˜actual vol.™
HIS1, 2, 3, 6 months spread. Using in σ ,
S&P500 7Jun62“May93 M (ranked) high-frequency
realized vol., and
Heston model, all help
to reduce implied
biasedness
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

74. Randolph S&P500 2/1/1986“ Daily Non-overlapping 20 ME, RMSE, MAE, Mean reversion model
MRMATM HIS
and Najand futures options 31/12/88 opening days ahead, re- MAPE (MRM) sets drift rate of
MRMATM implied
(1991) (crash included) Tick GARCH(1, 1) estimated using volatility to follow a
expanding sample. mean reverting process
HIS20 day
ATM calls only In: First 80
ImpliedBlack taking impliedATM (or
observations
HIS) as the previous day
(ranked though the
vol. Argue that GARCH
error statistics
did not work as well
are close)
because it tends to
provide a persistent
forecast, which is valid
only in period when
changes in vol. are small

75. Schmalensee 6 CBOE stock 29/4/74“23/5/75 W 1 week ahead. Statistical tests Find implied rises when
ImpliedBS call
and Trippi options (simple average ˜Actual™ proxied by reject the stock price falls, negative
56 weekly
(1978) of all strikes and weekly range and hypothesis that IV serial correlation in
observations
all maturities) average price responds positively changes of IV and a
(Forecast implied deviation to current volatility tendency for IV of
not actual different stocks to move
volatility) together. Argue that IV
might correspond better
with future volatility
76. Scott and DM/$, £/$, 14/3/83/“ Daily Non-overlapping MSE, R 2 ranges Simple B-S forecasts
ImpliedGk (vega,
Tucker C$/$, ¥/$ & 13/3/87 closing Inferred ATM, option maturity: 3, 6 from 42 to 49%. just as well as
(1989) SrFr/$ (pre-crash) tick NTM) and 9 months. Use In all cases, sophisticated CEV
American sample SD of daily model. Claimed
ImpliedCEV ± > 0, β < 1.
options on (similar rank) returns to proxy HIS has no omission of early
PHLX ˜actual vol.™ incremental info. exercise is not
content important. Weighting
scheme does not matter.
Forecasts for different
currencies were mixed
together

77. Sill (1993) S&P500 1959“1992 M HIS with exo 1 month ahead R 2 increase from Volatility is higher in
variables 1% to 10% when recessions than in
HIS additional expansions, and the
(see comment) variables were spread between
added commercial-paper and
T-Bill rates predict
stock market volatility

78. Szakmary, Futures options Various dates D Overlapping option R 2 smaller for
ImpliedBk, NTM HIS30 and GARCH
Ors, Kim on S&P500, 9 between maturity, shortest but ¬nancial have little or no
2Calls + 2Puts eq al weight
and interest rates, 5 Jan 83 and (23“28%), higher incremental
HIS30 , >10 days. Use sample
Davidson currency, 4 May 2001 GARCH SD of daily returns for metal and information content.
(2002) energy, 3 (ranked) over forecast horizon agricult. ±implied > 0 for 24
metals, 10 to proxy ˜actual vol.™ (30“37%), highest cases (or 69%), all 35
agriculture, 3 for livestock and cases βimplied < 1 with
livestock energy (47“58%) robust SE
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

79. Taylor JW DAX, 6/1/88“30/8/95 W STES (E, AE, 1 week ahead using ME, MAE, Models estimated based
(2004) S&P500, (equally split EAE) a moving window RMSE, R 2 on minimizing in-sample
Hang Seng, between in- and GJR of 200 weekly (about 30% for forecast errors instead of
FTSE 100, out-) (+Smoothed returns. Use daily HK and Japan ML. STES-EAE (smooth
Amsterdam variations) squared residual and 6% for US) transition exponential
EOE, Nikkei, GARCH returns to construct smoothing with return
Singapore All weekly ˜actual™ and absolute return as
MA20 weeks,
Share Riskmetrics volatility transition variables)
(ranked) produced consistently
better performance for
1-step-ahead forecasts

Represent one of the
80. Taylor SJ 15 US stocks Jan66“Dec76 D EWMA 1 and 10 days ahead Relative MSE
earliest studies in ARCH
(1986) FT30 Jul75“Aug82 Log-AR(1) absolute returns.
Various length ARMACH-Abs 2/3 of sample used class forecasts. The issue
6 metal
Nov74“Sep82 ARMACH-Sq in estimation. Use of volatility stationarity
£/$
5 agricultural Various length HIS daily absolute is not important when
futures (ranked) returns deviation as forecast over short
4 interest rate ˜actual vol.™ horizon. Nonstationary
Various length ARMACH-Sq is
futures series (e.g. EWMA) has
similar to
the advantage of having
GARCH
fewer parameter
estimates and forecasts
respond to variance
change fairly quickly
81. Taylor SJ DM/$ futures 1977“83 D High, low and 1, 5, 10 and 20 days RMSE Best model is a weighted
(1987) closing prices ahead. Estimation average of present and
(see comment) period, 5 years past high, low and
closing prices with
adjustments for weekend
and holiday effects

82. Taylor SJ DM/$ 1/10/92“30/9/93 1 hour ahead MAE and MSE on 5-min return has
Quote Implied + ARCH
and Xu In: 9 months combined estimated from 9 std deviation and information incremental
(1997) Out: 3 months Implied, months in-sample variance to daily implied when
ARCH period. Use 5-min forecasting hourly
returns to proxy volatility
HIS9 months
DM/$ options ˜actual vol.™
D HISlast hour realised vol Friday macro news ARCH model includes
on PHLX (ranked) seasonal factors with hourly and 5-min
See comment for have no impact on returns in the last hour
details on implied forecast accuracy plus 120 hour/day/week
and ARCH seasonal factors. Implied
derived from NTM
shortest maturity (>9
calendar days) Call+Put
using BAW
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

83. Tse (1991) Topix Nikkei In: 1986“1987 D EWMA 25 days ahead ME, RMSE, MAE, Use dummies in mean
Stock Average Out: 88“89 HIS estimated from MAPE of variance equation to control for
ARCH, GARCH rolling 300 of 21 non- 1987 crash.
(ranked) observations overlapping 25-day Nonnormality provides
periods a better ¬t but a poorer
forecast. ARCH/GARCH
models are slow to
react to abrupt change
in volatility. EWMA
adjust to changes very
quickly

84. Tse and Singapore, 5 19/3/75 to D EWMA 25 days ahead RMSE, MAE EWMA is superior,
Tung (1992) VW market & 25/10/88 HIS estimated from GARCH worst.
industry GARCH rolling 425 Absolute returns > 7%
indices (ranked) observations are truncated. Sign of
nonstationarity. Some
GARCH
nonconvergence
85. Vasilellis Stock options In: W 3 months ahead. RMSE Implied: 5-day average
Combine (Implied +
and Meade 12 UK stocks 28/3/86“27/6/86 GARCH) Use sample SD of dominates 1-day
(1996) (LIFFE) Implied (various, see daily returns to implied vol. Weighting
In2 (for combined
comment) proxy ˜actual vol.™ scheme: max vega >
forecast):
GARCH vega weighted >
28/6/86’25/3/88
EWMA elasticity weighted >
Out: 6/7/88’ max elasticity with ˜>™
HIS3 months
21/9/91 (ranked, results indicates better
not sensitive to forecasting
basis use to performance.
combine) Adjustment for div.
and early exercise:
Rubinstein > Roll >
constant yield. Crash
period might have
disadvantaged time
series methods

86. Vilasuso C$/$, FFr/$, In: 13/3/79“ D FIGARCH 1, 5 and 10 days MSE, MAE, and Signi¬cantly better
(2002) DM/$, ¥/$, 31/12/97 GARCH, ahead. Used daily Diebold- forecasting
£/$ IGARCH squared returns to Mariano™s test for performance from
Out: 1/1/98“ (ranked, proxy actual sig. difference FIGARCH. Built
31/12/99 GARCH volatility FIARMA (with a
marginally better constant term) on
than IGARCH) conditional variance
without taking log.
Truncated at lag 250

Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

87. Walsh and Australian 1Jan 93“ 5-min to form EWMA GARCH 1 hour, 1 day and 1 MSE, RMSE, Index with larger
Tsou (1998) indices: 31 Dec95 H, D and W (not for weekly week ahead MAE, MAPE number of stock is
VW20, VW50 returns returns) estimated from a easier to forecast due to
In: 1 year
& VW300 HIS, IEV 1-year rolling diversi¬cation, but gets
Out: 2 years (improved sample. Use square harder as sampling
extreme-value of price changes interval becomes
method) (non-cumulative) as shorter due to problem
(ranked) ˜actual vol.™ of nonsynchronous
trading. None of the
GARCH estimations
converged for the
weekly series, probably
too few observations

88. Wei and SrFr/$, 2/83“1/90 M Use European formula
Implied GK ATM call Non-overlapping 1 R 2 30%(£), 17%
Frankel DM/$, ¥/$, (shortest month ahead. Use (DM), 3%(SrFr), for American style
(1991) £/$ options maturity) option. Also suffers
sample SD of daily 0%(¥). ± > 0,
(PHLX) from nonsynchronicity
exchange rate return β < 1 (except that
problem. Other tests
to proxy ˜actual vol.™ for £/$, ± > 0,
reveal that implied
β = 1) with
D
Spot rates heterosced. tends to overpredict
consistent SE high vol. and
underpredict low vol.
Forecast/implied could
be made more accurate
by placing more weight
on long-run average
89. West and C$/$, FFr/$, 14/3/73“ W GARCH(1, 1) RMSE and Some GARCH forecasts
j = 1, 12, 24 weeks
Cho (1995) DM/$, ¥$/$, 20/9/89 IGARCH (1, 1) estimated from regression test on mean revert to
£/$ AR(12) in absolute rolling 432 weeks. variance, R 2 varies unconditional variance in
In: 14/3/73“
AR(12) in squares Use j period squared from 0.1% to 4.5% 12 to 24 weeks. It is
17/6/81
Homoscedastic returns to proxy dif¬cult to choose
Out: 24/6/81“ Gaussian kernel actual volatility between models.
12/4/89 (no clear rank) Nonparametric method
came out worst though
statistical tests for do not
reject null of no
signi¬cance difference in
most cases

90. Wiggins S&P500 4/82“12/89 D ARMA model with 1 week ahead and 1 Bias test, ef¬ciency Modi¬ed Parkinson
(1992) futures 2 types of month ahead. test, regression approach is least biased.
estimators: Compute actual C-t-C estimator is three
1. Parkinson/Garmen- volatility from daily times less ef¬cient than
Klass extreme observations EV estimators. Parkinson
value estimators estimator is also better
2. Close-to-close than C-t-C at forecasting.
estimator 87™s crash period
(ranked) excluded from analysis
Continued
Data Data Forecasting Forecasting Evaluation
Author(s) Asset(s) period frequency methods and rank horizon and R-squared Comments

91. Xu and £/$, DM/$, ¥/$ In: Jan 85“Oct89 D ME, MAE, Implied works best and is
ImpliedBAW NTM TS or Non-overlapping 4
Out:
Taylor & SrFr/$ weeks ahead, RMSE, When unbiased. Other forecasts
short
(1995) PHLX options 18Oct89“4Feb92 have no incremental
GARCHNormal or GED estimated from a ±implied is set
rolling sample of equal to 0, information. GARCH
HIS4 weeks
Corresponding
(ranked) 250 weeks daily forecast performance not
βimplied = 1
futures rates
data. Use cannot be sensitive to distributional
cumulative daily rejected assumption about
squared returns to returns. The choice of
proxy ˜actual vol.™ implied predictor (term
structure, TS, or short
maturity) does not affect
results

92. Yu (2002) NZSE40 Jan80“Dec98 D SV (of log variance) 1 month ahead RMSE, MAE, Range of the evaluation
GARCH (3, 2), estimated from Theil-U and measures for most
In: 1980“1993
GARCH (1, 1) previous 180 to 228 LINEX on models is very narrow.
Out: 1994“1998
months of daily variance Within this narrow
HIS, MA5 yr or 10 yr
data. Use aggregate range, SV ranked ¬rst,
ES and EWMA
of daily squared performance of GARCH
(monthly revision)
returns to construct was sensitive to
Regressioniag-1
actual monthly evaluation measure;
ARCH(9), RW,
volatility regression and EWMA
(ranked)
methods did not perform
well. Worst performance
from ARCH(9) and RW.
Volatile periods (Oct 87
and Oct 97) included in
in- and out-of-samples
93. Zumbach USD/CHF, 1/1/89“ H LM-ARCH 1 day ahead RMSE. Realized LM-ARCH, aggregates
(2002) USD/JPY 1/7/2000 F-GARCH estimated from volatility measured high-frequency squared
GARCH previous 5.5 years using hourly returns returns with a set of
And their integrated power law weights, is the
counterparts best though difference is
(ranked) small. All integrated
versions are more stable
across time

Ranked: models appear in the order of forecasting performance; best performing model at the top. If two weighting schemes or two forecasting models appear
at both sides of ˜>™, it means the l.h.s. is better than the r.h.s. in terms of forecasting performance. SE: Standard error. ATM: At the money. NTM: Near the
money. OTM: Out of the money. WLS: an implied volatility weighting scheme used in Whaley (1982) designed to minimize the pricing errors of a collection of
options. In some cases the pricing errors are multiplied by trading volume or vega to give ATM implied a greater weight. HIS: Historical volatility constructed
based on past variance/standard deviation. VXO: Chicago Board of Option Exchange™s volatility index derived from S&P100 options. VXO was renamed VXO
in September 2003. The current VXO is compiled using a model-free implied volatility estimate. All the research papers reviewed have used VXO (i.e. the old
VIX.) RS: Regime switching. BS: Black“Scholes. BK: Black model for pricing futures option. BAW: Barone-Adesi and Whaley American option pricing formula.
HW: Hull and White option pricing model with stochastic volatility. FW: Fleming and Whaley (1994) modi¬ed binomial method that takes into account wildcard
option. GK: Garman and Kohlhagan model for pricing European currency option. HJM: Heath, Jarrow and Morton (1992) forward rate model for interest rates.
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