forecasting volatility: roles of sampling frequency and forecasting horizon

We would like to acknowledge with thanks help received from the Hong Kong Exchanges and Clearing Ltd.in providing the data. The authors thank Jayaram Muthuswamy and participants at the 20th Asia PacificFutures Research Symposium, particularly Bob Webb (the editor) for many helpful comments and sugges-tions. This study is based, in part, on Cheng’s Ph.D. thesis at Hong Kong Baptist University. The viewsexpressed in this study are those of the authors, and do not necessarily reflect those of the Hong KongInstitute for Monetary Research, its Council of Advisors, or the Board of Directors.

*Correspondence author, Department of Finance and Decision Sciences, Hong Kong Baptist University,Hong Kong, China; e-mail: [email protected]

Received June 2010; Accepted June 2010

■ Wing Hong Chan is an Associate Professor of Economics, Department of Economics, WilfridLaurier University, Ontario, Canada and also at Department of Economics, City University ofHong Kong, Kowloon, Hong Kong, China.

■ Xin Cheng is a Ph.D. Candidate, Department of Finance and Decision Sciences, Hong KongBaptist University, Kowloon, Hong Kong, China.

■ Joseph K.W. Fung is a Professor of Finance, Department of Finance and Decision Sciences,Hong Kong Baptist University, Kowloon, Hong Kong, China and also a Member of theCouncil of Advisors, Hong Kong Institute for Monetary Research, Central, Hong Kong, China.

The Journal of Futures Markets, Vol. 30, No. 12, 1167–1191 (2010)© 2010 Wiley Periodicals, Inc.View this article online at wileyonlinelibrary.comDOI: 10.1002/fut.20476

FORECASTING VOLATILITY:ROLES OF SAMPLING

FREQUENCY AND FORECASTING

HORIZON

WING HONG CHANXIN CHENGJOSEPH K.W. FUNG*

This study empirically tests how and to what extent the choice of the samplingfrequency, the realized volatility (RV) measure, the forecasting horizon and thetime-series model affect the quality of volatility forecasting. Using highly syn-chronous executable quotes retrieved from an electronic trading platform, the

1168 Chan, Cheng, and Fung

Journal of Futures Markets DOI: 10.1002/fut

study avoids the influence of various market microstructure factors in measuringRV with high-frequency intraday data and in inferring implied volatility (IV) fromoption prices. The study shows that excluding non-trading-time volatility pro-duces significant downward bias of RV by as much as 36%. Quality of predictionis significantly affected by the forecasting horizon and RV model, but is largelyimmune from the choice of sampling frequency. Consistent with prior research,IV outperforms time-series forecasts; however, the information content of histor-ical volatility critically depends on the choice of RV measure. © 2010 WileyPeriodicals, Inc. Jrl Fut Mark 30:1167–1191, 2010

INTRODUCTION

Forecasting volatility is of critical importance in option pricing and risk man-agement. Over the past two decades, much effort has been devoted to developingsophisticated forecasting models, improving forecasting evaluation techniques,and testing the forecasting performance for various markets. This studyextends the literature and examines how the choices of forecasting model andrealized volatility (RV) measure affect the quality of volatility forecast.

There are two major types of forecasting models—time-series models thatmake projections based on historical volatility (TS-HV), and implied volatility(IV) that is inferred from option prices. Poon and Granger’s (2003) surveyshows that IV, though it is biased under some circumstances, generally outper-forms TS-HV volatility forecasts.1

On the other hand, actual volatility or RV is an abstract concept and canonly be estimated subject to measurement error. Merton (1980) shows that thestandard deviation of RV measure is a monotonic decreasing function of sam-pling frequency. However, Andersen, Bollerslev, Diebold and Labys (2000) findthat measures of RV become unstable with extremely high sampling frequen-cies such as 5 and 10 seconds. Therefore, Andersen, Bollerslev, Diebold andLabys (2001) argue that intraday returns provide better estimates of RV but 5-minute sampling is perhaps optimal, taking into account the impact of marketmicrostructure factors (such as bid–ask bounce and non-trading) on measuresbased on high-frequency data. Similarly, Aït-Sahalia, Mykland and Zhang(2005) argue that if the microstructure noise is unaccounted for, the optimalsampling frequency is finite, say 5-minutes.

Corsi, Zumbach, Muller, and Dacorogna (2001) and Zumbach, Corsi, andTrapletti (2002) show that the market microstructure impacts on RV estimationcan be corrected by using pre-filtered return data that directly factor in the cor-relation structure in high-frequency data. This result is consistent with the

1See also Day and Lewis (1988), Canina and Figlewski (1993), Figlewski (1997), Taylor and Xu (1997),Davidson, Kim, Ors, and Szakmary (2001), Szakmary, Ors, Kim, and Davidson (2003), Koopman,Jungbacker, and Hol (2005).

Forecasting Volatility 1169


finding of Aït-Sahalia et al. (2005), who show that better volatility estimationcan be obtained with high-frequency data as long as there is an adjustment forthe spurious correlation structure. On the other hand, using IBM transactiondata, Oomen (2005) also finds that the optimal sampling frequency can bereduced to 12 seconds, after incorporating an error correction scheme to allevi-ate the bias, from 2.5 minutes before the adjustment. Benchmarking on the“true” return variance, Bandi and Russell (2006, 2008) find the estimationerror associated with the 5-minute sampling frequency is acceptable, but thatassociated with the 15-minute interval is highly volatile.

In the presence of overnight market closure, the optimal sampling proce-dure is different. The overnight returns are found to be noisy and are likely toerase the benefit of increasing the sampling frequency. To put it another way,the problem caused by sampling too frequently may be dwarfed by noisyovernight returns. Therefore, for the purpose of forecast performance evalua-tion, it is important to choose the appropriate adjustment for non-trading-timereturns as well as sampling frequency. The empirical studies about testingvolatility forecasting models against high-frequency volatility are limited. Blair,Poon and Taylor (2001) and Martens and Zein (2004) measure RV with intradaydata and still find that IV dominates TS-HV models in forecasting volatility.

Owing to the finite maturity of futures contracts, the characteristics ofactual volatility may change when expiration day approaches. Samuelson (1965)hypothesizes that futures volatility rises as the contracts approach expiration. IfSamuelson is correct, then the quality of forecasts from different models shoulddecline when the prediction horizon shortens. Fleming (1998) finds a decayingpattern in IV forecasts as the horizon rises from 1 to 10 days. However, Jorion(1995) finds that IV prediction is more accurate for longer horizons.

Although most recent studies find that IV outperforms TS-HV in forecast-ing volatility, many studies (Chan, Kalimipalli, & Jha 2009; Poon & Granger,2003) show that TS-HV provides incremental information over IV. On theother hand, practitioners have been using both IV and TS-HV in forming theirforecasts. As the volatility structure may change over different maturity hori-zons of the derivatives, the information share between IV and TS-HV may alsovary as the options and futures expire.

This study empirically tests how and to what extent the choice of samplingfrequency, RV measure, forecasting horizon, and time-series model affect thequality of volatility forecast. The data set from the Hong Kong market for anextended time period from July 2000 to December 2006 contains highly syn-chronous executable quotes retrieved from an electronic trading platform, whichremoves the influence of bid–ask price bounce and non-trading in measuring RVwith high-frequency intraday data and in inferring IV from option prices. Thestudy shows that excluding non-trading-time volatility produces significant



downward bias of RV by as much as 36%. Quality of prediction is significantlyaffected by the forecasting horizon and RV model, but is largely immune fromthe choice of sampling frequency. Consistent with prior research, IV outper-forms time-series forecasts; however, the information content of historicalvolatility critically depends on the choice of RV measure.

The rest of the study is organized as follows: Section 2 describes the dataand research methodology; Section 3 summarizes and interprets the empiricalresults; and Section 4 concludes.

DATA AND METHODOLOGY

Data

The study uses complete bid and ask quotes of the Hang Seng Index (HSI)options and futures for the period July 2000 to December 2006 obtained fromthe “Bid and Ask Record—All Futures/Options” CDs published by the HongKong Stock Exchange. The Hong Kong market setting is very convenient fortesting the predictive power of IV. The HSI option is European style. It has thesame trading time as HSI futures. It uses futures-style margining so a modifiedBlack’s (1976) model can be used to further reduce the number of parameters.All of these can reduce the measurement error.

The options and futures are both traded on the electronic trading platformand the quotes represent firm commitments of market participants and arepotentially executable. As trading in both contracts is concentrated in the twonearest month maturity contracts, the study focuses on the spot and nextmonth contracts. There are two trading sessions each day for both options andfutures, namely, 9:45 a.m. to 12:30 p.m. and 2:30 p.m. to 4:15 p.m. The spotmonth contract ceases trading at 4:00 p.m. on the last trading day (or expira-tion day) of the contract. The contract expires on the day before the last busi-ness day of the month. There are no afternoon sessions on Christmas and NewYear Eves, or when the area is under severe weather conditions.

The data contain the best bid and ask prices and the corresponding quan-tities. The quotes are refreshed throughout the trading sessions wheneverchanges occur. The quotes are good until there are indications that a particularbid or offer is being lifted or withdrawn. Records associated with price quotesof “0” such as “99999” or “999999” are deleted from the data.

For option quotes which appear in the same trading session with the samematurity, the first bid (ask) is matched with the immediately following ask (bid)only if the bid is lower than the ask. If the updated bid (ask) is lower (higher)than the ask (bid) in the current pair, the new pair is recorded. If the updatedbid (ask) is higher (lower) than the ask (bid) in the current pair, the current pair



is discarded and the updated quote should be matched with the following ask(bid). In addition, we match each bid with the ask of the same contract thatrefreshes within 1 minute. Then each option pair is matched with the synchro-nous futures bid–ask pair that has the same time to maturity. The futures dataare treated in a similar manner.

Measures of RV

Four classes of RV are used in the empirical tests. The first measure is basedonly on intraday trading-hour returns; the second measure is estimated by asimple sum of trading-hour and non-trading-hour returns; the third measure isbased on a weighted sum of trading-hour and non-trading-hour returns; andthe fourth measure is the standard deviation of close-to-close returns.

Intraday volatility measure

This measure only includes trading-hour returns and is estimated as the sum ofsquared intraday returns as follows:2

(1)

where ri, j � pi, j � pi, j�1, pi , j is the natural logarithm of the middle futuresquotes at the end of the j-th interval on day i,3 annual_trading_time andremaining_ futures_lifetime are both in second, T is the number of trading daysto futures maturity, and N is the number of sampling intervals within 1 day.

Total volatility measure

Following Blair et al., (2001), the total volatility is calculated as the sum of trading-hour squared returns and non-trading-hour squared returns as follows:

(2)

where rt,L and rt,N are the lunch-break and overnight returns respectively, 242 isthe average number of trading days annually from 2000 to 2006.

Total volatility � B242T

aaT

i�1r2

i,N � aT

i�1r2

i,L � aT

i�1aN

j�1r2

i,jb

Intraday volatility � Bannual_trading_time

remaining_futures_lifetimeaT

i�1aN

j�1r2

i,j

2A similar approach is used in Jiang and Tian (2005) to measure realized volatility with high-frequencydata.3Although most of the studies use data sampled over regular time intervals, Oomen (2005, 2006) and someother studies use non-regular sampling intervals.



Scaled total volatility measure

Following Hansen and Lunde (2005), the following scaled total volatility meas-ure is used to reduce the impact of the noisiness of the non-trading-hour vari-ance on the measure:

(3)

where is a scale that adjusts the weightings of the

trading-hour and non-trading-hour variances in the volatility measure, rt

is the close-to-close return on day t, and is the average close-to-close return dur-ing the sample period.4

Close-to-close volatility measure

This is the traditional RV measure defined by the standard deviation of the daily returns. The daily return is given by the first difference of the loga-rithmic daily closing prices.

Estimation of Option IV

Daily IV for different option classes is extracted from option mid-quotes observedwithin the last 30 min of a trading session. The mid-quotes are used in order toavoid bid–ask bounce. Option quotes that violated no-arbitrage conditions arediscarded. Option quotes that are below the minimum size of one tick and thatare arbitrarily large are discarded. Following Whaley (1982) and Lamoureux andLastrapes (1993), the daily IV for each option class is obtained by minimizing themean squared error between the market and model prices, i.e.:

(4)

where market_option_pricei represents the mid-quote of option i, Black_priceis the modified Black (1976) commodity option pricing model, N is the numberof option quotes on a particular day, and iv is the daily IV estimate.

As HSI options and futures share the same trading schedule and expira-tion cycle (for short-dated options) and HSI options are European style, theHSI options can be priced as if they are options on the futures (Duan & Zhang,

min 1Na

N

i�1 (market_option_pricei � Black_price iv)2

r

c � ad

k�1(rk � r)2�a

d

k�1an

j�1r2

k,j

Scaled total volatility � B242T

a T

i�1ca

N

j�1r2

i,j

4The intuition behind is to scale the intraday volatility up to the expected value. Hansen and Lunde (2005)also demonstrate such estimator is approximately unbiased under reasonable assumptions.



2001). The non-synchronous problem is minimized by using intraday HSIfutures and option data. Besides, as the HSI options adopt future-style margin-ing, Black’s model can be further simplified as follows:5

)(5)

where F represents the mid-quote of futures, X is the exercise price, s is thevolatility, and h is the time to maturity.

Forecasting Models

Four different time-series models are used to forecast future volatility, namely,moving average model (MA), generalized autoregressive conditional het-eroskedastic model (GARCH), autoregressive fractionally integrated movingaverage model (ARFIMA), and ARFIMA with Jump (ARFIMA_J) model.

Moving average

The MA forecast is the simple average of the past 124 days’ daily RV.

(6)

GARCH

The GARCH(1, 1) model has often been found to outperform other time-seriesmodels for both in-sample and out-of-sample forecasts; see for exampleEderington and Guan (2005). Therefore, it is adopted in this study for modelcomparison. The error variance is specified as follows:

(7)

The estimation window is 124 days and rolls forward.

ARFIMA

The ARFIMA(1, 1) specification is used to capture long range dependence (orlong memory) in the volatility dynamics. The estimation window is 124 daysand rolls forward.

s2t � a0 � a1e

2t�1 � b1s

2t�1.

s2t �

1124

at�1

i�t�124s2

i

d2 � d1 � s2h

d1 � [ln(F�X) � 1�2s2h]�(s2h

put � �FN(�d1) � XN(�d2)

call � FN(d1) � XN(d2)

5See Lieu (1990).



(8)

where the fractional parameter d between zero and one represents a long mem-ory structure implying slow hyperbolic decay in autocorrelations.

ARFIMA-J

The jump component J is defined according to Andersen, Bollerslev andDiebold (2007).

(9)

where � is the sampling frequency, RVt refers to the RV constructed by sum-ming high-frequency squared returns, and BVt is the bipower variation.

Test Whether the Choice of RV Construction MethodAffects the Forecasting Performance

As different RV measures also have different distribution characteristics, it isworth testing whether those measures, sampled at the same frequency, havesimilar forecasting performance. Therefore, we regress different RV measureswith the same sampling frequency on five forecasting models and then com-pare the regression results.

(10)

where RVt�1,T refers to a certain RV measure sampled at 5 minutes, 3 minutes,1 minute and 30 seconds, and forecastt is a certain model’s forecast based onday t and can be IV, MA, GARCH, ARFIMA and ARFIMA-J.

Test Whether Volatility Smile Affects the ForecastingPerformance

Given the volatility smile pattern described in the previous section, we exam-ine to what extent different moneyness IV varies in their forecasting per-formance.

(11)

where i refers to certain option moneyness group.

ln RVt�1,T � a � b ln IVi,t � et

ln RVt�1, T � a � b ln forecastt � et

(1 � L)d ln s2t � v � g1 ln s2

t�1 � g2Jt�1 � et

BVt � (22p)�2 a1�¢

j�20r2

t�j¢,¢ 0 r2t�( j�1)¢,¢ 0

Jt � max(RVt � BVt, 0)

(1 � L)d ln s2t � v � g ln s2

t�1 � et



Encompassing Regression

To investigate whether time-series models have additional information to IV, weemploy the classic encompassing regression framework.

(12)

where IVt is the volatilities implied by ATM calls and puts, and Time_series_forecastt is one of the four time-series models mentioned earlier.

Separate-Horizon Regressions

To avoid the overlapping problem in the pooled-horizon regressions, we sepa-rate the options and the underlying futures contracts according to their time tomaturity. Such arrangement also provides some insights about how the predic-tive power of a certain model varies as it approaches maturity. The regressionformula is the same as in the univariate regression, except that we repeat theregression 30 times for horizons between 6 and 35 days.

(13)

where i is the index for different horizons.We also repeat the encompassing regression 30 times for horizons between

6 and 35 days.

(14)

EMPIRICAL RESULTS

Table I reports the summary statistics of volatility measures used in this study,namely, intraday volatility, total volatility, scaled total volatility, and close-to-close volatility. The results show that the standard deviation of each high-frequency volatility measure declines as sampling frequency increases. Thestandard deviation of volatility is positively, related to volatility levels. In addi-tion, the levels of different volatility measures vary. The highest and secondhighest measures are close-to-close volatility and scaled total volatility, with thedifference being approximately 2%. The intraday volatility, which does notinclude non-trading-time volatility, is only 60% of close-to-close volatility.

The statistical measures above confirm that the difference of RV measuresis significant. In particular, the choice of volatility measure has a greater impacton the mean level and variation than the choice of sampling frequency. It istherefore more important to choose an appropriate adjustment for market-break returns than to choose a sampling frequency in the forecasting practice.

ln RVi;t�1,T � a � b1 ln IVi,t � b2 ln time_series_forecasti,t � ei,t.

ln RVt�1,T � a � b ln forecasti,t � et

ln RVt�1,T � a � b1 ln IVt � b2 ln time_series_forecastt � et



Figure 1 illustrates how close the levels of intraday volatility with returns sam-pled at different frequencies are. For total and scaled total volatility, the resultsare not reported in this study.

Table II presents the correlation matrix among the four volatility measureswith different return sampling frequencies. It shows that all the volatilitymeasures are highly correlated. In particular, the correlation coefficientsbetween the same volatility measures with different sampling frequencies areas high as 99%.

The summary statistics of option IV for different moneyness are reported in Table III. We exclude options with time to maturity beyond 5–38 days.

TABLE I

Summary Statistics of Realized Volatility of HSI Futures (July 3, 2000–December 29, 2006)

Close-to-close

Sampling Intraday Volatility Total Volatility Scaled Total Volatility Volatility

Frequency Mean Median SD Mean Median SD Mean Median SD Mean Median SD

5 minutes 12.79 11.99 4.28 18.29 16.76 6.98 19.50 18.25 6.503 minutes 12.69 11.95 4.20 18.21 16.77 6.95 19.49 18.29 6.41 20.04 18.45 7.981 minutes 12.29 11.51 4.00 17.91 16.40 6.83 19.39 18.10 6.2330 seconds 12.02 11.22 3.94 17.72 16.21 6.80 19.36 18.09 6.22

Note. Intraday volatility includes in the calculation only futures returns observed within the trading sessions. Total volatility is equalto the simple sum of the lunch hour volatility, overnight volatility, and the respective intraday volatility. Scaled total volatility is equal toa weighted sum of the lunch hour volatility, overnight volatility, and the respective intraday volatility. Close-to-close volatility is calcu-lated with the close-to-close futures returns.

8

10

5 10 15 20 25 30

Daily5 min3 min1 min30 sec

35 40

12

14

16

18

20

22

FIGURE 1Levels of intraday volatility measures and the level of the close-to-close volatility over

different time horizon.

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TM

if F

/X �

1.0

6, r

espe

ctiv

ely.

The

impl

ied

vola

tility

is b

ased

on

the

mod

ified

Bla

ck’s

(19

76)

mod

el in

Equ

atio

n (5

). T

he o

bser

vatio

ns a

reba

sed

on th

e m

iddl

e of

the

bid

ask

quot

es o

f the

opt

ions

sam

pled

in th

e 30

min

utes

inte

rval

bet

wee

n 3:

45 p

.m. a

nd 4

:15

p.m

. The

tim

e-to

-mat

urity

of t

he o

ptio

ns is

bet

wee

n 6

and

37 d

ays.



The implied volatilities are divided into five groups according to the ratio of theunderlying futures mid-quote (F) to the corresponding options’ exercise prices(X). The five groups, are F/X � 0.94, 0.94 � F/X � 0.97, 0.97 � F/X � 1.03,1.03 � F/X � 1.06, and F/X � 1.06, respectively. There exists a smile pattern inoption implied volatilities. The ATM IV is the lowest, the ITM IV is the highest,and the OTM IV is in the middle. The pattern is consistent with the volatilitysmile identified in the previous literature.

Figure 2 plots IV and RV for different horizons. It shows that ATM, OTMand ITM implied volatilities deviate largely from intraday volatility while theyare close to the other three volatility measures. In addition, ATM IV movesbetween close-to-close volatility and total volatility. However, OTM and ITMimplied volatilities are more volatile and significantly higher than all RV meas-ures for most horizons. The DITM and DOTM options are even higher and arenot plotted here. The simple comparison between IV and ex-post volatility suggests ATM IV is the best candidate to forecast total volatility, scaled totalvolatility, and close-to-close volatility, and all three measures incorporate non-trading-time volatility.

The impact of the choice of sampling frequency on the forecasting per-formance is reported in Table IV. To project ATM IV on total volatility, differentsampling frequencies only produce minor differences in forecasting perform-ance. For the case of intraday volatility at the top panel, the ATM impliedvolatilities are biased with coefficients range from 0.8341 to 0.8575 and signif-icantly different from one. These are attributable to the fact that the intradayvolatility omits the overnight non-trading return. By contrast, the ATM impliedvolatilities are unbiased forecasts for the total volatilities with all the slopecoefficients close to one. Increasing the sampling frequency from 5 minutes to30 seconds leads to no more than a 3% change in goodness of fit, R2, for boththe intraday and total volatilities. The regression coefficients show little varia-tions. For the other RV measures and forecasting models, the choice of sam-pling frequency also has a small impact and the results are not reported in thisstudy. The finding is consistent with the previous discussion about the levels ofRV measures for various sampling frequencies.

Table V shows whether the choice of RV measure affects the predictivepower of five forecasting models, namely, ATM IV,6 MA(124), GARCH(1, 1),ARFIMA(1, 1), and ARFIMA(1, 1)_J. As sampling frequency has a small impacton the forecasting results, the full analysis focuses on the frequency of 5 min-utes,7 which also facilitates comparison with previous studies. Owing to theoverlapping problem, we report Hansen’s (1982) standard error. The five models

6We use ATM IV here and discuss the choice of IV in the next section.7Results of the other sampling frequencies are consistent with 5-minute results and are not reported in thisstudy.



105 10 15 20

Call(a)

25 30 35 40

15

20

25

30

IV/R

V in

%

35

105 10 15 20

Put(b)

25 30 35 40

15

20

25

30

IV/R

V in

%

35

105 10 15 20

All options(c)

25 30 35 40

15

20

25

30

IV/R

V in

%

35

OTMATMITMIntraday volTotal volScaled total volClose-to-close vol



FIGURE 2Implied volatility and realized volatility.



are all informational about future RV as their regression coefficients are all sig-nificantly different from zero. It is important to note that ATM IV in general issuperior to all time-series models using historical data in the sense that it pro-vides a significant improvement in accuracy of forecasting RV. The improve-ments range from an additional 10% R2 with the intraday volatility, to as high asan additional 17% for the total volatility over the best performing time-seriesmodel. The regressions for different sampling frequencies from 30 seconds to5 minutes, not reported in this study, give essentially identical results.

Furthermore, the method of constructing RV affects the forecasting performance. For example, using intraday volatility as a dependent variable,ATM IV overestimates the future RV, where the intercept term is significantlybelow zero and the slope coefficient is significantly different from one. Whenthe scaled total volatility is employed, the bias is reduced substantially. Withthe total volatility as the targeting RV, we cannot reject the null hypothesis thatATM IV is an unbiased forecast. Using the historical data, no time-series model

TABLE IV

Impact of the Choice of Sampling Frequency on Forecasting Performance

Dependent Var: Intraday Volatility Independent Var: ATM IV

Sampling Frequency Intercept Coefficient R2 F-stat

5 minutes � 0.7005a 0.8575b 0.6768 4,426.86(0.0714) (0.0393) (0.0000)

3 minutes � 0.7088a 0.8564b 0.6908 4,723.75(0.0693) (0.0383) (0.0000)

1 minute � 0.7774a 0.8323b 0.6904 4,714.91(0.0686) (0.0379) (0.0000)

30 seconds � 0.7973a 0.8341b 0.6998 4,927.37(0.0672) (0.0370) (0.0000)

Dependent Var: Total Volatility Independent Var: ATM IV

5 minutes � 0.0939 1.0104a 0.6807 4,507.14(0.0810) (0.0448) (0.0000)

3 minutes � 0.0953 1.0120a 0.6820 4,533.12(0.0807) (0.0448) (0.0000)

1 minute � 0.1209 1.0056a 0.6752 4,393.97(0.0809) (0.0450) (0.0000)

30 seconds � 0.1254 1.0099a 0.6772 4,435.36(0.0807) (0.0448) (0.0000)

Note. The table reports the regression results for Equation (10). The figures in the parentheses under the coefficient estimates areHansen (1982) standard errors. F-stat refers to the F test for the null hypothesis of b� 0 and the figures in the parentheses are p-values.aSignificantly different from zero at the 1% level. bSignificantly different from one at the 1% level. cSignificantly different from zero atthe 5% level. dSignificantly different from one at the 5% level.

TA

BL

E V

Cho

ice

of t

he D

epen

dent

Var

iabl

e (R

ealiz

ed V

olat

ility

Mea

sure

) on

For

ecas

ting

Per

form

ance

Dep

ende

nt V

ar: I

ntra

day

Vola

tili

ty (

5m

inut

es)

Dep

ende

nt V

ar: T

otal

Vol

atil

ity

(5m

inut

es)

Inte

rcep

tC

oeffi

cien

tR

2F

-sta

tIn

terc

ept

Coe

ffici

ent

R2

F-s

tat

AT

M IV

�0.

7005

a0.

8575

b0.

6768

4,42

6.86

AT

M IV

�0.

0939

1.01

040.

6807

4,50

7.14

(0.0

714)

(0.0

393)

0(0

.081

)(0

.044

8)0

MA

�0.

7775

a0.

7715

b0.

5689

2,78

9.75

MA

�0.

2712

c0.

8598

d0.

5119

2,21

6.68

(0.0

889)

(0.0

473)

0(0

.117

)(0

.062

9)0

GA

RC

H�

0.94

30a

0.70

36b

0.56

72,

768.

28G

AR

CH

�0.

4136

a0.

8089

b0.

543

2,51

1.51

(0.0

661)

(0.0

359)

0(0

.086

4)(0

.047

6)0

AR

FIM

A�

0.88

15a

0.72

79b

0.56

862,

786.

23A

RF

IMA

�0.

3526

a0.

8313

b0.

5372

2,45

3.94

(0.0

724)

(0.0

395)

0(0

.099

8)(0

.055

3)0

AR

FIM

A-J

�0.

8632

a0.

7377

b0.

5884

3,02

1.66

AR

FIM

A_J

�0.

3383

a0.

8386

b0.

5508

2,59

2.62

(0.0

716)

(0.0

391)

0(0

.100

7)(0

.055

8)0

Dep

ende

nt V

ar: S

cale

d To

tal V

olat

ilit

y (5

min

utes

)D

epen

dent

Var

: Clo

se-t

o-cl

ose

Vola

tili

ty

AT

M IV

�0.

2724

a0.

8602

b0.

6744

4,37

8.93

AT

M IV

�0.

0562

0.98

810.

5857

2,98

7.97

(0.0

715)

(0.0

394)

0(0

.086

0)(0

.049

4)(0

.000

0)M

A�

0.33

88a

0.78

00b

0.57

592,

871.

09M

A�

0.28

05c

0.81

190.

4106

1,47

2.78

(0.0

889)

(0.0

473)

0(0

.129

0)(0

.070

3)(0

.000

0)G

AR

CH

�0.

5073

a0.

7107

b0.

5729

2,83

5.39

GA

RC

H�

0.46

57a

0.73

40b

0.40

211,

421.

53(0

.065

6)(0

.035

6)0

(0.0

958)

(0.0

549)

(0.0

000)

AR

FIM

A�

0.44

56a

0.73

50b

0.57

412,

850.

13A

RF

IMA

�0.

3705

a0.

7774

b0.

4226

1,54

7.16

(0.0

719)

(0.0

392)

0(0

.107

6)(0

.061

0)(0

.000

0)A

RF

IMA

-J�

0.42

73a

0.74

48b

0.59

43,

092.

87A

RF

IMA

_J�

0.34

55a

0.79

10b

0.44

081,

666.

63(0

.071

1)(0

.038

8)0

(0.1

079)

(0.0

611)

(0.0

000)

Not

e.T

he ta

ble

repo

rts

the

regr

essi

on r

esul

ts fo

r E

quat

ion

(10)

. F-s

tat r

efer

s to

the

Fte

st fo

r th

e nu

ll hy

poth

esis

of b

�0

and

the

figur

es in

the

pare

nthe

ses

are

p-va

lues

. a Sig

nific

antly

diffe

rent

from

zer

o at

the

1% le

vel.

b Sig

nific

antly

diff

eren

t fro

m o

ne a

t the

1%

leve

l. c S

igni

fican

tly d

iffer

ent f

rom

zer

o at

the

5% le

vel.

d Sig

nific

antly

diff

eren

t fro

m o

ne a

t the

5%

leve

l.



provides an unbiased forecast for total volatility and scaled total volatility.However, using total volatility as a dependent variable, the intercept term hasthe smallest absolute value and the slope coefficient is closest to one for allforecasting models, including both the ATM IV and time-series forecasts, indi-cating that the models being studied in this study are the most appropriate forforecasting total volatility.

Table VI records the forecasting performance of implied volatilities for thecall and put options with different strike levels. The results of pooling both calland put options, reported on the first row, show that ATM IV is an accurateforecast for the RV with high R2, in the range of 58 and 68%. These results arerobust across different RV measures. In addition, the slope coefficients are notsignificantly different from one for total volatility and close-to-close volatilityimplying that the ATM IV is an unbiased forecast. There is no significant dif-ference between the put options and the call options. For example, in the caseof intraday volatility, switching from ATM puts to ATM calls results in a lessthan 0.6% change in goodness of fit. The information content conveyed largelyvaries among different moneyness groups. (D)ITM call IV and (D)OTM put IVare the least informative, given their low R2. This finding is consistent with thehypothesis that different moneyness options have varying information contentsabout future RV. On the other hand, the ATM call and put IV, which combinesthe information from both the ATM call and put is slightly superior to the rest. Thedifference in the performance of ATM IV measures with either call or putoptions is insignificant and therefore for the rest of the analysis we focus on theATM IV constructed from pooling both call and put options.

Table VII summarizes the results of combined forecasts with IV and time-series models. Using intraday volatility as a dependent variable in Panel (a), nostand alone forecasting model is unbiased. The ATM IV outperforms the alter-native models by 10% in terms of goodness of fit while the GARCH model hasthe lowest value of 56.7%. The two ARFIMA models from the encompassingregressions are slightly worse than the MA model. However, including the jumpcomponent does improve the performance of the ARFIMA model. Further, thetime-series models contain additional information about the future volatilitythat is not already contained in the IV. It is shown by the R2 of all four encom-passing regressions being higher than the one from the stand alone ATM IVmodel. The F-stat2 rejects the hypothesis that the single IV forecast is superiorto the combined model.

It is immediately apparent from Panel (c) that under the assumption ofscaled total volatility as true volatility measure, both option IV and time-seriesforecasts effectively generate the same results as the ones from the intradayvolatility. The results of these two RV measures in Panels (a) and (c) are indis-tinguishable in terms of the relative rankings of the R2 and the magnitudes and

TA

BL

E V

I

Cho

ice

of I

mpl

ied

Vola

tilit

y

Dep

ende

nt V

ar: S

cale

d To

tal

Dep

ende

nt V

ar: I

ntra

day

Vola

tili

ty (

5m

inut

es)

Dep

ende

nt V

ar: T

otal

Vol

atil

ity

(5m

inut

es)

Vola

tili

ty (

5m

inut

es)

Dep

ende

nt V

ar: C

lose

-to-

clos

e Vo

lati

lity

Inde

pend

ent

Var

Inte

rcep

tC

oeffi

cien

tA

dj. R

2F

-sta

tIn

terc

ept

Coe

ffici

ent

Adj

. R2

F-s

tat

Inte

rcep

tC

oeffi

cien

tA

dj. R

2F

-sta

tIn

terc

ept

Coe

ffici

ent

Adj

. R2

F-s

tat

IV A

TM

opt

ions

�0.

7005

a0.

8575

b0.

6766

4,42

6.86

�0.

0939

1.01

040.

6806

4,50

7.14

�0.

2724

a0.

8602

b0.

6743

4,37

8.93

�0.

0562

0.98

810.

5855

2,98

7.97

(0.0

714)

(0.0

393)

0(0

.081

)(0

.044

8)0

(0.0

715)

(0.0

394)

0(0

.086

)(0

.049

4)0

IV D

OT

M c

all

�0.

6865

a0.

8397

b0.

6253

3,53

0.77

�0.

0638

0.99

720.

639

3,74

5�

0.25

60a

0.84

37b

0.62

523,

528.

72�

0.05

780.

9573

0.52

962,

382.

61(0

.074

7)(0

.041

)0

(0.0

863)

(0.0

476)

0(0

.074

5)(0

.040

8)0

(0.0

903)

(0.0

513)

0IV

OT

M c

all

�0.

6899

a0.

8405

b0.

6824

4,54

5.34

�0.

079

0.99

180.

6883

4,67

1.8

�0.

2600

a0.

8442

d0.

6817

4,53

0.18

�0.

0517

0.96

410.

585

2,98

2.62

(0.0

721)

(0.0

39)

0(0

.082

1)(0

.044

4)0

(0.0

722)

(0.0

39)

0(0

.087

)(0

.048

8)0

IV A

TM

cal

l�

0.69

71a

0.85

97b

0.67

694,

432.

87�

0.08

991.

0129

0.68

084,

512.

37�

0.26

77a

0.86

32b

0.67

584,

409.

01�

0.05

110.

9914

0.58

663,

002.

09(0

.071

4)(0

.039

4)0

(0.0

81)

(0.0

448)

0(0

.071

5)(0

.039

4)0

(0.0

861)

(0.0

495)

0IV

ITM

cal

l�

1.36

87a

0.45

06b

0.18

6148

4.59

�0.

9387

a0.

4971

b0.

164

415.

96�

0.90

02a

0.47

70b

0.20

6655

1.71

�0.

8152

a0.

5257

b0.

165

419.

09(0

.074

5)(0

.045

9)0

(0.0

991)

(0.0

602)

0(0

.074

8)(0

.046

)0

(0.1

045)

(0.0

633)

0IV

DIT

M c

all

�1.

7575

a0.

2140

b0.

0525

118.

15�

1.40

27a

0.21

62b

0.03

8786

.06

�1.

3098

a0.

2277

b0.

0589

133.

35�

1.25

47a

0.25

78b

0.04

9611

1.37

(0.0

566)

(0.0

345)

0(0

.069

1)(0

.040

8)0

(0.0

574)

(0.0

348)

0(0

.073

4)(0

.043

8)0

IV D

OT

M p

ut�

1.14

51a

0.52

37b

0.18

7148

7.93

�0.

4964

a0.

6813

b0.

2296

631.

25�

0.69

53a

0.53

76b

0.19

5351

4.26

�0.

4632

a0.

6593

b0.

1933

507.

77(0

.084

8)(0

.045

8)0

(0.1

12)

(0.0

599)

0(0

.085

1)(0

.046

)0

(0.1

112)

(0.0

602)

0IV

OT

M p

ut�

1.03

76a

0.61

13b

0.32

671,

027.

11�

0.44

11a

0.74

81b

0.35

451,

162.

68�

0.57

73a

0.63

17b

0.34

551,

117.

36�

0.37

39a

0.74

38b

0.31

5297

4.56

(0.0

777)

(0.0

437)

0(0

.097

3)(0

.054

5)0

(0.0

776)

(0.0

435)

0(0

.1)

(0.0

566)

0IV

AT

M p

ut�

0.71

38a

0.84

92b

0.67

094,

312.

63�

0.11

021.

0002

0.67

434,

378.

83�

0.28

67a

0.85

12b

0.66

764,

249.

45�

0.07

320.

9776

0.57

942,

914.

05(0

.071

1)(0

.039

1)0

(0.0

809)

(0.0

447)

0(0

.071

3)(0

.039

2)0

(0.0

859)

(0.0

492)

0IV

ITM

put

�0.

6615

a0.

9280

0.63

073,

613.

18�

0.04

91.

0927

0.63

363,

658.

04�

0.22

42a

0.93

660.

6362

3,70

0.14

�0.

0055

1.07

300.

5495

2,58

0.36

(0.0

789)

(0.0

463)

0(0

.087

1)(0

.051

5)0

(0.0

783)

(0.0

459)

0(0

.092

9)(0

.056

9)0

IV D

ITM

put

�0.

8088

a0.

8775

b0.

5069

2,17

4.79

�0.

2309

a1.

0278

0.50

372,

147.

25�

0.36

58a

0.89

03c

0.51

672,

261.

76�

0.16

821.

0197

0.44

591,

703.

23(0

.075

8)(0

.046

5)0

(0.0

849)

(0.0

527)

0(0

.075

3)(0

.046

3)0

(0.0

911)

(0.0

585)

0

Not

e.T

he t

able

rep

orts

the

reg

ress

ion

resu

lts f

or E

quat

ion

(11)

. Lo

garit

hmic

RV

and

IV

are

use

d in

the

reg

ress

ions

. Thr

ee r

ealiz

ed v

olat

ility

mea

sure

s (in

trad

ay v

olat

ility

, to

tal v

olat

ility

, an

d sc

aled

tot

al v

olat

ility

)ar

e co

nstr

ucte

d ac

cord

ing

to S

ectio

n 2

and

for

each

mea

sure

, int

rada

y re

turn

s ar

e sa

mpl

ed a

t 5-m

inut

e in

terv

al. I

ntra

day

vola

tility

is c

alcu

late

d w

ith tr

adin

g-tim

e re

turn

s. T

otal

vol

atili

ty is

cal

cula

ted

with

trad

ing-

time

retu

rns,

ove

rnig

ht r

etur

ns a

nd lu

nch-

brea

k re

turn

s. S

cale

d to

tal v

olat

ility

use

d tr

adin

g-tim

e re

turn

s, lu

nch-

brea

k re

turn

s an

d sc

aled

ove

rnig

ht r

etur

ns.

Clo

se-t

o-cl

ose

vola

tility

is t

he s

tand

ard

devi

atio

n of

clo

se-t

o-cl

ose

retu

rns.

AT

M o

ptio

ns a

re d

efine

d as

thos

e w

ith F

/X b

eing

bet

wee

n0.9

7 an

d 1.

03. D

OT

M o

r D

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TABLE VII

Realized Volatility Regressed on Various Forecasting Estimators

Independent Variables

Intercept IV_ATM MA GARCH ARFIMA ARFIMA_J R2 F-stat1 F-stat2

(a) Dependent Var: Intraday Volatility (5minutes)

�0.7005a 0.8575b 0.6768 4,426.86(0.0714) (0.0393) (0.0000)

�0.7775a 0.7715b 0.5689 2,789.75(0.0889) (0.0473) (0.0000)

�0.9430a 0.7036b 0.5670 2,768.28(0.0661) (0.0359) (0.0000)

�0.8815a 0.7279b 0.5686 2,786.23(0.0724) (0.0395) (0.0000)

�0.8632a 0.7377b 0.5884 3,021.66(0.0716) (0.0391) (0.0000)

�0.5962a 0.6375b 0.2685b 0.7012 2,478.88 172.26(0.0743) (0.0529) (0.0539) (0.0000) (0.0000)

�0.6837a 0.6937b 0.1717b 0.6859 2,306.64 60.93(0.0704) (0.0679) (0.0563) (0.0000) (0.0000)

�0.6865a 0.7480b 0.1145b 0.6798 2,243.44 20.08(0.0716) (0.0614) (0.0541) (0.0000) (0.0000)

�0.6823a 0.7003b 0.1631b 0.6828 2,274.45 40.12(0.0709) (0.0678) (0.0579) (0.0000) (0.0000)

(b) Dependent Var: Total Volatility (5minutes)

�0.0939 1.0104 0.6807 4,507.14(0.0810) (0.0448) (0.0000)

�0.2712c 0.8598d 0.5119 2,216.68(0.1170) (0.0629) (0.0000)

�0.4136a 0.8089b 0.5430 2,511.51(0.0864) (0.0476) (0.0000)

�0.3526a 0.8313b 0.5372 2,453.94(0.0998) (0.0553) (0.0000)

�0.3383a 0.8386b 0.5508 2,592.62(0.1007) (0.0558) (0.0000)

�0.0251 0.8654a,d 0.1770b 0.6884 2,333.98 52.03(0.0912) (0.0576) (0.0635) (0.0000) (0.0000)

�0.0814 0.8889a 0.1274b 0.6843 2,290.37 24.18(0.0820) (0.0700) (0.0619) (0.0000) (0.0000)

�0.0923 0.9982a 0.0127b 0.6807 2,252.79 0.18(0.0842) (0.0746) (0.0782) (0.0000) (0.6714)

�0.0887 0.9660a 0.0460b 0.6811 2,256.11 2.30(0.0838) (0.0784) (0.0810) (0.0000) (0.1296)

(c) Dependent Var: Scaled Total Volatility (5minutes)

�0.2724a 0.8602b 0.6744 4,378.93(0.0715) (0.0394) (0.0000)

�0.3388a 0.7800b 0.5759 2,871.09(0.0889) (0.0473) (0.0000)

�0.5073a 0.7107b 0.5729 2,835.39(0.0656) (0.0356) (0.0000)

(Continued)



significances of the coefficients. In the standalone regressions, ATM IV is supe-rior to the time-series models and most importantly the combined forecastsonce again outperform the single forecasts.

Turning now to total volatility as proxy for RV in Panel (b), we cannotreject the null hypotheses that the intercept is equal to zero and the slope isequal to one for the ATM IV. The alternative models are all biased. The encom-passing regressions show that even though the coefficients of the two ARFIMAmodels are statistically significant, these two models provide no additional

TABLE VII (Continued)

Independent Variables

Intercept IV_ATM MA GARCH ARFIMA ARFIMA_J R2 F-stat1 F-stat2

�0.4456a 0.7350b 0.5741 2,850.13(0.0719) (0.0392) (0.0000)

�0.4273b 0.7448b 0.5940 3,092.87(0.0711) (0.0388) (0.0000)

�0.1610c 0.6253b 0.2867b 0.7019 2,487.93 195.03(0.0745) (0.0525) (0.0542) (0.0000) (0.0000)

�0.2538a 0.6785b 0.1905b 0.6855 2,302.34 74.17(0.0702) (0.0675) (0.0560) (0.0000) (0.0000)

�0.2556a 0.7289b 0.1374b 0.6787 2,232.19 28.49(0.0715) (0.0620) (0.0550) (0.0000) (0.0000)

�0.2515a 0.6802b 0.1868b 0.6822 2,268.27 51.99(0.0708) (0.0683) (0.0588) (0.0000) (0.0000)

(d) Dependent Var: Close-to-close Volatility

�0.0562 0.9881 0.5857 2,987.97(0.0860) (0.0494) (0.0000)

�0.2805c 0.8119b 0.4106 1,472.78(0.1290) (0.0703) (0.0000)

�0.4657a 0.7340b 0.4021 1,421.53(0.0958) (0.0549) (0.0000)

�0.3705a 0.7774b 0.4226 1,547.16(0.1076) (0.0610) (0.0000)

�0.3455a 0.7910b 0.4408 1,666.63(0.1079) (0.0611) (0.0000)

�0.0207 0.9133a 0.0914b 0.5875 1,504.65 9.42(0.0967) (0.0736) (0.0789) (0.0000) (0.0022)

�0.0649 1.0725a �0.0885b 0.5872 1,502.96 8.02(0.0862) (0.0856) (0.0738) (0.0000) (0.0047)

�0.0749 1.1338a �0.1524b 0.5892 1,515.04 18.04(0.0880) (0.0965) (0.0940) (0.0000) (0.0000)

�0.0667 1.0790a �0.0943b 0.5870 1,501.37 6.70(0.0876) (0.0989) (0.0956) (0.0000) (0.0097)

Note. The table reports the regression results for Equation (12). The figures in the parentheses under the coefficient estimates areHansen (1982) standard errors. F-stat1 refers to the F test for the null hypothesis of b1 � 0, b2 � 0. F-stat2 tests the null hypothesisof b2 � 0. The figures in the parentheses under F-stat1 and F-stat2 are their p-values. aSignificantly different from zero at the 1%level. bSignificantly different from one at the 1% level. cSignificantly different from zero at the 5% level. dSignificantly different from oneat the 5% level.



information over the IV based on the F tests. Conversely, the MA and GARCHmodels have significant incremental effects in the encompassing regressionsthough the coefficients are small compared with the IV coefficients.

The results in Panel (d) show that ATM IV subsumes all the relevant infor-mation contained in the time-series models about future volatility if the tradi-tional RV measure, close-to-close volatility, is used. In the encompassingregressions, the intercept terms and time-series model coefficients are not sig-nificantly different from zero and the IV coefficients do not significantly deviatefrom one.

The IV is an unbiased forecast of both total volatility and close-to-closevolatility. However, the R2 is 10% higher in the total volatility regression. It isalso the case for the four time-series models. This finding is consistent with theexisting literature that states using intraday returns to construct RV is morefavorable in volatility forecasting. In addition, changing the forecasting targetsignificantly changes the information share between IV and time-series models.Although improving R2, incorporating high-frequency returns in the construc-tion of RV decreases the informational content of IV while increasing the infor-mational share of time-series models.

Separate regressions for different horizons can demonstrate whethershort-term volatility is easier to predict and whether the ranking of differentforecasting models remains as the forecasting horizon changes. To conservespace, we repeated the above regression analysis for different forecasting hori-zons with two RV proxies: close-to-close and scaled total volatility. Table VIIIreports the combined forecast results with IV and time-series models for differ-ent forecasting horizons. The MA model does not provide any incremental infor-mation to IV to forecast close-to-close volatility for 1 through 6 weeks. Whenthe forecasting target is changed to scaled total volatility, the MA model obtainsinformational share. In addition, the coefficients of the MA model increase asthe horizon rises from 1 to 6 weeks. However, the overall quality of the forecastis still dominated by IV as the coefficients and R2 both decline as the horizonrises.

Figure 3 plots the R2 of the univariate regressions against time to maturity.For scaled total volatility, R2 of IV rises as it approaches maturity, indicatingnear-term volatility is easier to forecast, which is also consistent with Fleming’s(1998) results. The MA model, on the other hand, has a declining pattern. Theother three time-series models do not exhibit a clear pattern along time. Whenthe forecasting target is changed to total volatility, R2 of IV and MA both rise asit approaches maturity. Therefore, the impact of forecasting horizon does notonly depend on forecasting models but also on the choice of ex-post volatility.In general, the choice of RV is at least as important as the choice of forecastingmodels.



CONCLUSIONS

In this study, we examine how the sampling frequency, forecasting horizon,choice of RV measures, and choice of time-series models affect the quality ofvolatility forecasting. Inclusion of non-trading-hour volatility, but not the sam-pling frequency, significantly impacts the distribution of RV and the forecastingperformance. Combining the IV and time-series forecasts only produces mar-ginal benefits in forecasting future volatility. Furthermore, the time-series modelsprovide no incremental information in forecasting total volatility and close-to-close volatility. The information share between forecasting models is affectedby the choice of RV.

The informational content of different forecasting models for differenthorizons varies. The temporal pattern is affected by both the choice of

TABLE VIII

Encompassing Regressions for Various Horizons

Horizon Nobs Intercept IV_ATM MA R2 F-stat1 F-stat2

Dependent Var: Close-to-close Volatility

1-week 72 �0.0395 1.1110 �0.1192 0.4492 29.95 0.25(0.2305) (0.2471) (0.2367) (0.0000) (0.6162)

2-weeks 72 �0.0170 1.3225 �0.3192 0.6097 56.44 3.02(0.1690) (0.1983) (0.1837) (0.0000) (0.0867)

3-weeks 72 �0.0549 1.0386 �0.0492 0.5606 46.29 0.07(0.1753) (0.2131) (0.1925) (0.0000) (0.7992)

4-weeks 69 �0.0329 1.0924 �0.0923 0.6215 56.83 0.31(0.1608) (0.1811) (0.1647) (0.0000) (0.5772)

5-weeks 71 �0.1783 0.9262 �0.0121 0.6252 59.38 0.01(0.1415) (0.1575) (0.1385) (0.0000) (0.9307)

6-weeks 68 �0.1195 0.9269 0.0273 0.5872 48.66 0.02(0.1613) (0.2057) (0.1775) (0.0000) (0.8783)

Dependent Var: Scaled Total Volatility

1-week 72 �0.2579a 0.7082b 0.1700 0.7224 93.37 2.69(0.1189) (0.0978) (0.1037) (0.0000) (0.1058)

2-weeks 72 �0.2057c 0.6136b 0.2674a 0.7111 88.40 6.54(0.1184) (0.1011) (0.1046) (0.0000) (0.0128)

3-weeks 72 �0.0784 0.6503b 0.2943a 0.6941 81.55 6.14(0.1284) (0.1227) (0.1188) (0.0000) (0.0157)

4-weeks 69 �0.1747 0.6236b 0.2734a 0.6860 75.28 5.43(0.1273) (0.1200) (0.1173) (0.0000) (0.0228)

5-weeks 71 �0.2313a 0.5608b 0.3122a 0.6947 80.65 7.98(0.1194) (0.1112) (0.1105) (0.0000) (0.0062)

6-weeks 68 �0.1497 0.5602b 0.3617a 0.6833 73.28 8.84(0.1305) (0.1280) (0.1217) (0.0000) (0.0041)

Note. The table reports the regression results for Equation (12). F-stat1 refers to the F test for the null hypothesis of b1 � 0, b2 � 0.F-stat2 tests the null hypothesis of b2 � 0. The figures in the parentheses under F-stat1 and F-stat2 are their p-values. aSignificantlydifferent from zero at the 1% level. bSignificantly different from one at the 1% level. cSignificantly different from zero at the 5% level.dSignificantly different from one at the 5% level.



forecasting models and the choice of forecasting targets. In the univariate fore-casting, IV outperforms all the time-series models against all four RV measuresacross different horizons. IV is more predictive in the short term against scaledtotal volatility while it is more informational in the long term against close-to-close volatility. The MA model has higher R2 against both volatility measures.The patterns for the GARCH, ARFIMA and ARFIMA-J models are not clear.

The results show that the choice of RV model is an important determinantof the performance of the volatility forecast. In view of the findings, furtherresearch on option pricing and risk management with different volatility fore-casts is warranted. A more systematic exploration of the correlation between

0.26 11

(a) close-to-close volatility

IV MA GARCH ARFIMA ARFIMA_J

16 21 26 31 35

0.3

0.4

0.5

0.6

0.7

0.8

0.26 11

(b) Scaled total volatility

16 21 26 31 35

0.3

0.4

0.5

0.6

0.7

0.8

IV MA GARCH ARFIMA ARFIMA_J

FIGURE 3The goodness of fits, R2, of univariate regression against time to maturity (a) close-to-close volatility

(b) scaled total volatility Note. Intraday returns are sampled at 5-minute interval.



option pricing errors and the information shares between the IV and time-series models is also a good direction for future research.

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