Stock Market Volatility Forecasting with the Option Trading Information

Ming Jing Yang a, * and Meng-Yi Liu b

a Department and Graduate Institute of Finance College of Finance, Feng Chia University, Taichung 40724, Taiwan

b Department of Insurance and Financial Management, Takming University of Science and Technology, Taipei 11451, Taiwan

Abstract

Volatility forecasting plays a crucial role in investment decision-making and risk

management. This study investigates the volatility forecasting ability of the Absolute

Restricted Least Squares model, developed by Ederington and Guan (2005, 2010a, 2010b),

compared with the conventional time-series models, using the evidence from Taiwan’s stock

and option markets. Based on the out-of-sample forecasts, this study demonstrates that the

Absolute Restricted Least Squares model performs better than the conventional time-series

models for forecasting the future volatility. In addition, we further construct the forecasting

models with the vega-weighted net demand for volatility to extract the important information

contained in the option markets. The empirical results of the study show that the trading

volume information from the option markets can be employed to predict the dynamics of

future stock market volatility, especially for the longer forecast periods.

JEL classification: G12; G15; G17

Keywords: Volatility Forecasting; Option Trading Information; Volatility Demand

* Corresponding author: Associate Professor, Department and Graduate Institute of Finance, Feng Chia

University, Taichung 40724, Taiwan, Tel: +886-4-24517250 Ext.4158; Fax: +886-4-24513796 E-mail address: mjyang@fcu.edu.tw (Ming Jing Yang, Ph.D.)

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1. Introduction

In financial markets, volatility plays a very important role for market participants,

researchers, and decision makers. Volatility forecasting is of great importance to investors

and enterprises since it enables them to execute many different trading strategies. Over the

last two decades, volatility forecasting has become one of the major concerns of financial

economists in risk management and asset pricing.

Many studies have focused on the model efficiency in predicting volatility, and two

approaches are widely used to estimate volatility: (1) the time-series models that rely on the

past property of the underlying asset prices to predict the future movements and (2) the

models that estimate the implied volatility from the option prices to capture the expected

volatility. Although several studies claim that the implied volatility is an informationally

efficient predictor of future market movement, (Christensen and Prabhala, 1998; Yu et al.,

2010, etc.), questions related to the measurement errors and variations in different market

microstructures, such as liquidity and bid-ask spreads, are still unresolved. Owing to the

fact that different implied volatilities can be derived from different option strike prices, which

of the implied volatilities should be used to forecast the future volatility remains under

discussion. Moreover, options are found in only a few markets and are not available for all

financial assets. As a result, the time-series models remain an important source for volatility

forecasting.

In the past two decades, volatility forecasting has proved to be a particularly productive

topic for finance researchers. Poon and Granger (2003, 2005) provide an extensive

comparison of volatility forecasting studies over the last 20 years, dividing the studies into

three main categories of time-series models: the historical volatility models, the ARCH class

models, and the stochastic volatility models. Of the 93 papers surveyed by Poon and

Granger (2003, 2005), 46 papers compare different types of time-series models and find that

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there is no single model significantly better than the others.

Although the efficiency of model predictions has been addressed by several studies, the

results are still unclear. Ederington and Guan (2005) explore this topic in a different way.

They focus on why some models forecast better than the others and point out that the

forecasting error of some GARCH-type models is caused by the models’ inherent weighting

scheme. Ederington and Guan (2005) demonstrate that the GARCH and GJR-GARCH

models do not weight the older observations enough and weight the recent observations too

much when the property of long memory in financial markets is encountered. They show

that the accuracy of the in-sample forecast appears more sensitive to the weighting scheme

than that of the out-of-sample forecast. Ederington and Guan (2005) also argue that

different parameter estimation procedures, such as maximizing the likelihood or minimizing

the variance of forecast errors, generate very different parameter estimates even for the same

model. They further claim that there is a large impact on volatility forecasts from a single

extreme observation when the model is formed according to the squared surprise returns.

To address these issues, Ederington and Guan (2005, 2010a, 2010b) construct the Absolute

Restricted Least Squares (ARLS) model, which is estimated using a two-stage least squares

procedure and based on the absolute return innovations.

In addition, Ni et al. (2008) construct the net demand function for volatility to

investigate the presence of volatility information trading in the option market. They study

the extent to which the information variables can predict the future volatility using the

volatility demand derived from option trading volume. Their empirical results indicate that

option trading volume contains important information about the future volatility because

market participants are aware of volatility and act accordingly, which affects the trading of

the underlying assets. As pointed out by Poon and Granger (2005), whether the volatility

forecasting ability can be improved by using the exogenous variables is an interesting and

worthwhile research area.

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Our empirical investigation benefits greatly from the unique non-public data set

exclusively provided by the Taiwan Futures Exchange, which contains the comprehensive

transaction records of intraday options trading. The complete purchase and sale transactions

of call and put options are utilized to measure investors’ volatility demands and to examine

the occurrence of volatility information trading by different types of investors, including the

foreign institutional investors, domestic institutional investors, and individual traders in the

Taiwan option market.

Financial derivatives in many emerging markets, such as Taiwan, are important

components of investors’ international portfolios. In Asia, index options trading has grown

rapidly over the past few years, with trading volume rising from 40 million in 1998 to 3

billion contracts in 2008 during the financial crisis, a 54% compound annual growth rate

exceeding those in America and Europe. In 2015, the options and futures trading volume on

Asian derivatives exchanges jumped 34% to 9.7 billion contracts with a global market share

of 39.2%, which is much greater than that on European derivatives exchanges (with a trading

volume of 4.77 billion contracts, growth rate of 8.2%, and global market share of 19.3%) and

also greater than that on North American derivatives exchanges (with a trading volume of

8.19 billion contracts, growth rate of -0.2%, and global market share of 33.1%). In 2001,

Taiwan Futures Exchange (TAIFEX) launched the Taiwan Stock Exchange Capitalization-

Weighted Stock Index (TAIEX) options, whose trading volume has increased dramatically in

recent years. According to the Futures Industry Association (FIA) Annual Volume Survey1, the

TAIEX options are the world’s sixth-most-traded index options in 2015, the third largest index

options market in Asia with a trading volume of 191.5 million contracts. On May 15, 2014,

Eurex and the Taiwan Futures Exchange even created the Eurex/TAIFEX Link to make

1 According to the FIA 2015 Annual Volume Survey, the 10 largest index options in the world are listed as follows: 1. CNX Nifty Options, National Stock Exchange of India, 2. SPDR S&P 500 ETF Options, 3. Kospi 200 Options, Korea Exchange, 4. Euro Stoxx 50 Options, Eurex, 5. S&P 500 Options, Chicago Board Options Exchange, 6. TAIEX Options, Taiwan Futures Exchange, 7. S&P Sensex Options, BSE, 8. CBOE Volatility (VIX) Options, Chicago Board Options Exchange, 9. iShares Russell 2000 ETF Options, 10. Bank Nifty Options, National Stock Exchange of India.

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TAIEX derivatives also tradable on Eurex Exchange after Taiwanese trading hours, during

European and U.S. core trading hours. It demonstrates the increasing importance of TAIEX

options in the international portfolios and global asset management.

This paper attempts to evaluate the volatility forecasting performance by comparing the

forecasting abilities of the ARLS, historical volatility, GARCH, and GJR-GARCH models,

and also to determine which types of option participants possess the volatility information in

Taiwan’s stock market. The empirical results of our study show that the ARLS model is

very powerful in predicting the future price movements in Taiwan’s stock market. Among

the models examined, the ARLS model generally yields the better in-sample and

out-of-sample volatility forecasts than the GARCH and GJR-GARCH models over different

forecast horizons. Overall, our empirical findings suggest that the ARLS model, based on

the past absolute return innovations, dominates the GARCH and GJR-GARCH models, based

on the past squared return deviations. In addition, the results of our research also indicate

that the volatility demands derived from the option trading volumes of different types of

investors contain important information for predicting the future stock market volatility.

Furthermore, the model that incorporates both the forecasts from the ARLS model and the

volatility demands of different types of investors is able to generate better forecasts for the

future stock market volatility, especially for the longer forecast horizon.

Although there are lots of time-series volatility forecasting models, the empirical

evidence on the ARLS model, as developed by Ederington and Guan (2005, 2010a, 2010b), is

still very limited. Since there are some advantages of the ARLS model over the

conventional time-series volatility forecasting models, it’s worthwhile to investigate whether

the ARLS model can forecast the future volatility better in different financial markets. In

contrast to the previous studies, this study first investigates the forecasting capability of the

ARLS model for one of the emerging markets, Taiwan. Specifically, we attempt to examine

whether the ARLS model, based on the past absolute return innovations and with more

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weight on the more distant past observations, will have a distinctive performance in

forecasting the future volatility, especially when the property of long memory and volatility

persistence in financial markets occurs. Then, this study also explores whether the volatility

forecasting power can be further enhanced by using the vega-weighted net demand for

volatility, as presented by Ni et al. (2008), as well as the time-series volatility forecasts over

the multi-period forecast horizons.

The remainder of the paper is organized as follows. The existing literature focusing

on the volatility forecasting models is discussed in Section 2. The research methodology

and data used in this study are described in Section 3. The empirical results for the

forecasting performance of the different models with information variables of volatility

demand in predicting the future stock market volatility are analyzed in Section 4. Finally,

the conclusions drawn from the study are presented in section 5.

2. Volatility Forecasting Models

Various types of models have been suggested for volatility forecasting, which can be

generally grouped into the time-series models and the implied volatility models derived from

the option prices (Figlewski, 1997; Corrado and Miller, 2005, etc.). The main types of the

time-series volatility forecasting models include the historical volatility models (Canina and

Figlewski, 1993; Yu et al., 2010, etc.), GARCH-type volatility models (Nelson, 1991; Mittnik

et al., 2015, etc.), and stochastic volatility models (Singleton, 2001; Hautsch and Ou, 2012,

etc.). A survey of 93 research papers (Poon and Granger, 2003, 2005) explores the volatility

forecasting studies in the past two decades and finds the forecasting ability of option implied

volatility is superior to that of time-series models. As for the time-series model categories,

both the historical volatility and GARCH-type volatility models have about the same

forecasting performance. These results should not be surprising since the option implied

volatility contains the important information sets available to investors. However, options

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are designed for limited types of assets, and there are no option contracts in some equity

markets. Besides, the implied volatility of options is not very stable over time, and the

variations and measurement errors may also be caused by the bid-ask spreads from the

transaction prices of options and the underlying assets. Thus, the implied volatility of

options is documented to be biased for volatility forecasting. Consequently, Poon and

Granger (2005) and Ederington and Guan (2005) suggest that the time-series models persist

and act as the major source of volatility forecasting and remain an important factor in

predicting the future volatility.

Ederington and Guan (2005) develop the ARLS model and compare the model with the

popular time-series models.2 They find that the GARCH model attaches too much weights to

the recent observations versus the older observations and that the volatility forecast accuracy

of in-sample results is more sensitive to the weighting scheme than that of out-of-sample

results. Besides, the estimation procedures of the parameters in the time-series models also

influence the volatility forecasting results. Moreover, the models based on the squared

return deviations are affected by the extreme values more than the models based on the

absolute return deviations are. The GARCH and GJR-GARCH models seem to

overestimate the high volatility and underestimate the low volatility. The forecast bias is

found to be especially serious when the predicted volatility is high, prompting the

construction of the ARLS model (Ederington and Guan, 2010b). The ARLS model forecasts

the standard deviation of returns directly and incorporates the mean reversion process. In

addition, the ARLS model is based on the absolute surprise returns rather than the squared

surprise returns. The ARLS model is similar to the GARCH model but with the different

parameter estimation procedures. Ederington and Guan (2005) examine the volatility

forecasting abilities of these models across nine financial markets: the S&P 500 index, the

Japanese yen/US dollar exchange rate, the three-month Eurodollar rate, the ten-year treasury

2 The derived formulas of ARLS model are illustrated in the next section.

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bond rate, and five US equities. Their results indicate that the volatility forecasting ability

of the ARLS model dominates that of GARCH and EGARCH models, and the GARCH

models outperform the historical volatility and the exponentially weighted moving average

models. There is no significant difference in forecasting performance between the GARCH

and EGARCH models.

As shown in the past studies (Granger and Ding, 1996; Andersen and Bollerslev, 1998;

Ederington and Guan, 2005; Lee, 2009, etc.), financial market volatility has a number of

properties, including that volatility has a long memory. As a result, volatility forecasting for

a long period is required for the option valuation and long-term value at risk models.

Ederington and Guan (2010a) study the volatility forecasts of GARCH, EGARCH,

GJR-GARCH, and ARLS models across different markets, including interest rates, exchange

rates, stock market indexes, individual stocks, and commodities. Their findings document

that the older observations associated with a long forecast horizon in volatility forecasting are

more important than the recent observations. When the out-of-sample forecast capabilities

of the models are compared, the ARLS model clearly performs better than the GARCH,

EGARCH, and GJR-GARCH models across the different markets and different forecast

horizons. Furthermore, Ederington and Guan (2010b) also point out that the forecasts of the

standard deviation of surprise returns in the GARCH, GJR-GARCH, and EGRACH models

are observed to be biased. Since the GARCH and GJR-GARCH models are based on the

past squared return deviations, both tend to generate upward biased forecasts. Their

empirical evidence shows that the GARCH and GJR-GARCH models seriously over-estimate

the realized standard deviation of returns following the highly volatile days; nevertheless, the

volatility forecasts of the ARLS model are still unbiased.

A different group of research has focused on the informational role of exogenous

variables, such as the stock market trading volume (Admati and Pfleiderer, 1998), the implied

volatility of options (Giot, 2005), the open interest of index options and futures (Pan and

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Poteshman, 2006), the investor sentiment (Wang et al., 2006; Seo and Kim, 2015), and the

volatility demand of investors (Ni et al., 2008), in forecasting volatility. As suggested by

Poon and Granger (2005), it is worth exploring how to improve the volatility forecasting

power by means of the exogenous variables. Several empirical studies (Kawaller et al.,

2001; Jayaraman, et al., 2001; Poteshman, 2006) show that the trading volume and open

interest of option markets have significant predictive power for the future stock market

volatility. Fleming et al. (1996), Simon (2003), and Giot (2005) provide evidence that the

volatility indexes, derived from option prices to reflect investor sentiment, capture the

information about the future stock price movement. Besides, Fung (2007) uses the implied

volatility, trading volume, and open interest of index options to investigate the predictive

ability of these variables in the period of the 1997 Hong Kong financial crisis. The results

of the study also show that the implied volatility dominates the other predictors in forecasting

the future stock market volatility.

In addition, Ni et al. (2008) develop the net demand for volatility from the option

markets. Using the daily data, the study investigates the relationship between the trading

volume of option markets and the future volatility of the underlying stocks during the period

between 1990 and 2001. They find that the volatility demand extracted from the trading

volume of option markets is positively related to the corresponding underlying stock market

movements. A possible explanation for their findings is that investors possess the private

information and act independently in option markets. Hence, the trading volume of option

markets is informative and useful in forecasting the future stock market volatility.

In sum, the previous studies suggest that the information contained in option markets

may be useful while predicting the future stock market movements. This study intends to

compare the volatility forecasting capabilities of the ARLS, historical volatility, GARCH, and

GJR-GARCH models and to examine whether the forecasting power of the models can be

further improved by including the information variables, namely the volatility demand from

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the option markets.

3. Research Methodology

3.1. Data

Data used in this study are collected from the Taiwan Stock Exchange and Taiwan

Futures Exchange. The closing prices of Taiwan stock index are obtained from the Taiwan

Economic Journal (TEJ) database. To compute the volatility demand, based on the

vega-weighted net demand for volatility as presented in Ni et al. (2008), the valuable detailed

intraday transaction data of Taiwan stock index options are collected exclusively from Taiwan

Futures Exchange (TAIFEX) non-public database, including the trading dates, investor

identification codes, trading positions, call or put options, trading volumes, opening or

closing positions, etc. The investors are then further classified into four groups, consisting

of the foreign institutional investors, domestic institutional investors, individual investors,

and market makers,3 according to the various confidential investor identification codes to

measure the trading information from the different types of investors in option markets.4

However, since market makers usually work as liquidity providers, they have less

information than the informed traders. On average, the expected loss of market makers

from trading with the informed investors would be offset by the expected gain from dealing

with the uninformed investors (see Bailey, 2005). Therefore, the information variables of

volatility demands are constructed by using the option trading volume of the three main

components from the non-market makers (see Ni et al., 2008).

3.2. Volatility Measures and Models

3 There are actually more than 109 categories of investors in Taiwan option markets. After substantial

discussions with the specialists in Taiwan futures exchange, most investors are classified into foreign institutional investors, domestic institutional investors, individual investors, and market makers. However, there are still some investors who cannot be clearly classified into the four groups and thus are excluded in the study.

4 The sample period consists of 3,735 trading days between January 02, 2002 and January 31, 2017. The sample period of this study is restricted to the limited access databases provided by Taiwan Futures Exchange.

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3.2.1. Realized Volatility

Following Corrado and Miller (2005) and Sheu and Wei (2011), the realized volatility is

defined for the next n days on day t, which is measured as the sample standard deviation of

returns over the period from day t+1 through day t+n. According to Poon (2005), it is

assumed that 252 trading days are required to annualize the standard deviation of daily log

returns as follows:

n

inttitt RR

nRV

1

2

,11

252 (1)

where RVt is the annualized realized volatility over the next n days; Rt+i = ln(Pt+i /Pt+i-1); Pt+i

is the TAIEX daily closing price on day t+i; Rt+i is the TAIEX return on day t+i; nttR ,1

represents the mean of the TAIEX return during days t+1 to t+n.5

3.2.2. Historical Volatility

The method for measuring the historical volatility in the study of Ederington and Guan

(2005) is utilized and expressed as follows:

21

0)1(,1

252

n

jnttjtt RR

nHV (2)

where HVt is the annualized historical volatility over the past n days; Rt-j = ln(Pt-j /Pt-j-1); Pt-j is

the closing price of the TAIEX on trading date t-j; Rt-j is the TAIEX return on day t-j;

)1(, nttR is the TAIEX average return over the n-day historical period from t to t-(n-1).

3.2.3. The ARLS Model

The ARLS model, which directly forecasts standard deviation of returns, was

developed by Ederington and Guan (2005, 2010a, 2010b). The model incorporates the

mean reversion process and its past volatility weights fall exponentially. In addition, the

5 We have performed many robustness tests for the mean return. In the earlier versions of the paper, the

annualized realized volatility is obtained by setting the mean return equal to the average daily return over the entire sample period, and the main conclusions are unchanged.

11

ARLS model is based on the absolute surprise returns rather than the squared surprise returns.

The ARLS model is similar to the GARCH model but with the different parameter estimation

procedures. A brief formulation can be generated as follows by assuming the log-return at

time t, Rt, is normally distributed with mean and variance th . The surprise return is

tt R and th follows the process

ttt hh 2

101 (3)

Since 12

110 ttt hh and 122

112

1001 )( tttt hh , the recursive

substitution procedure produces the following expression

J

jjt

jth

0

21

'01

(4)

where

J

jJt

Jj h0

10

'0 . Since ttt hE )( 2 , the expected volatility at a future time

t+k based on the information ( t ) available at time t is

2

01

1110 )()(|

k

jt

kjtkt hh

(5)

Summing the expected volatility (ht+k) from k=1 to s and dividing the result by s can obtain

the (average) integrated volatility forecast (H(s)t) over the future period from t+1 to t+s as

follows, see Andersen et al. (2006):

J

jjt

j

s

k

J

jjt

jks

k

k

j

kj

s

k

k

j

s

k

J

jjt

jkjs

kktt

ss

ssh

ssH

0

2

1 0

211

1

1

2

0

11

'010

1

2

0 1 0

21

'0

111

0

1

)()()(1

)()()1

()(1

)(

(6)

where

J

jJt

Jj h0

10

'0 . In Equation (6), the volatility forecast is based on the

squared surprise returns. Ederington and Guan (2005) find that the forecasts of Equation (6)

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are more sensitive to outliers than the volatility forecast based on the absolute surprise returns,

and they develop the ARLS model in response to the problem. A return distribution

assumption is required for the ARLS model. They assume the log returns Rt=ln(Pt /Pt-1) are

normally distributed with mean , /2)( tE where tt R , and

1

0

)2/(n

jjtjZE where

1

0

1n

jjZ . They define a regression model with

exponentially declining weights based on the absolute surprise returns as follows:

J

jjt

jttt ZwhereZsRV

0

2/,)( (7)

where tsRV )( is the realized volatility (standard deviation of returns) over the period from

t+1 through t+s. Equation (7) regresses the ex-post standard deviation of returns on Zt,

defined in terms of the absolute surprise returns. The first step of this model is to produce

the series tZ , using the values of from 0.500 through 1.000 in increments of 0.005.

The second step is to regress tsRV )( on tZ and repeat the regression for all values of

. Finally, the regression result with the minimum residual sum of squares is chosen, and

the estimation values of , , and are determined. Specifically, the integrated

volatility forecast of the ARLS model over the period from t+1 to t+s is expressed as

follows:

J

jjt

jtsARLS

0

ˆ2/ˆˆ)( (8)

3.2.4. The GARCH Model6

The GARCH model assumes that the return on day t, Rt, is normally distributed with

mean return and conditional variance th on day t. The surprise return is tt R

6 Following Covrig and Low (2003), Ederington and Guan (2005, 2010a, and 2010b), Yu et al. (2010),

we use the GARCH (1,1) and GJR-GARCH (1,1) models in our study, which have been found to be the most suitable models.

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and th follows the process:

ttt hh 2

101

(9)

The same derivation holds for the GARCH model as with the ARLS model, and the

integrated volatility forecast of the GARCH model for the interval from t+1 through t+s can

be expressed as follows:

J

jjt

jtsGARCH

0

2)( (10)

where

s

k

k

j

kjs1

2

0

11

'010 )()()/1( and

s

k

ks1

111 )()/( . Note

that Equations (8) and (10) are similar except that ARLS and GARCH models forecast

volatility differently, and they utilize different estimation methods for parameters , , and

. While the parameters of ARLS model are estimated using the two-stage least squares

procedure to minimize the sum of squared errors, the parameters of GARCH model are

estimated using the maximum likelihood procedure. In addition, the ARLS model is based

on the absolute, rather than the squared past surprise returns.

3.2.5. The GJR-GARCH Model

In order to observe the asymmetric effect of good news and bad news on the

conditional volatility, this study also uses the GJR-GARCH model, provided by Glosten et al.

(1993), to capture the asymmetric effect. The GJR-GARCH model can be shown as

follows:

ttttt hDh 2

22

101

(11)

where ht+1 is the conditional volatility on day t+1, εt is the return residual, and Dt is a dummy

variable which is equal to one if εt is negative and zero otherwise. An indicator variable, Dt,

captures the asymmetric impact of shocks on volatility (good news εt > 0; bad news εt < 0).

The same derivation from the ARLS and GARCH models applies here, and the integrated

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volatility forecast of the GJR-GARCH model for the interval from t+1 through t+s can be

expressed as follows:

J

jjtjt

jJ

jjt

jt DsGARCHGJR

0

22

0

21)( ,

(12)

where

s

k

k

j

kjs1

2

0

11

'010 )()()/1( ,

s

kks

111 )/1( ,

s

kks

122 )/1( , and

2

021 )(

k

jjtk D . As in the GARCH model, the

parameters of GJR-GARCH model are estimated using the maximum likelihood procedure.7

3.3. Forecast Evaluation

Once the forecasting models are determined, the forecasting abilities of these models

are compared. In order to choose the best model that provides the most precise forecast, the

forecasting errors for various competitive models are calculated in terms of the difference

between the actual and the forecast annualized standard deviations of returns. Thus, the root

mean squared forecast error (RMSFE) is further considered and defined as follows:

2

1

2

1

))()(()/1(

M

ttt sFVsRVMRMSFE

(13)

where tsRV )( is the annualized realized volatility (standard deviation of returns), as defined

in Equation (1); tsFV )( represents the annualized forecast volatility (standard deviation of

returns) for a time horizon of s trading days starting on day t, which is measured by utilizing

the volatility forecasting models discussed above, and M denotes the number of forecast

periods. When the RMSFE is based on variance, a few extreme values may dominate the

outcome (Ederington and Guan, 2005, 2010a). As documented in Poon and Granger (2003),

7 The annualized volatility forecasts are computed from the average daily volatility forecasts of the ARLS,

GARCH, and GJR-GARCH models. To be compared with the volatility forecasts of the ARLS model, the annualized standard deviation forecasts are further calculated from the variance forecasts of the GARCH and GJR-GARCH models.

15

standard deviation is better than variance because the latter is more sensitive to outliers.

Therefore, all the volatility variables are annualized and based on standard deviation of

returns in calculating RMSFE.

3.4. Volatility Demand

One of the main purposes of volatility forecasting is to provide an insight into the

dynamics of future stock market movements. A number of studies (Kawaller et al., 2001;

Pan and Poteshman, 2006; Poteshman, 2006; Fung, 2007) find that the trading volume of

option markets contains information about the future stock market movement. Compared

with spot market mechanisms, options are highly leveraged speculative instruments.

Options allow investors who own superior private information to enhance their investment

returns. Investors may change their trading strategies frequently in the option markets

according to the information available to them. Thus, the change in the trading volume of

option markets could reflect the information of future market movements. This study

further examines the performance of the volatility forecasting based on the models

encompassing information variables, namely the volatility demand, obtained from the option

markets.

The vega-weighted net demand for volatility, as proposed by Ni et al. (2008), is used to

measure the information content of the trading volume in option markets. The volatility

demand (VDt) at time t can be expressed as follows:

K T

TKt

TKt

t

TKt

K T

TKt

TKt

t

TKt

t

SellPutBuyPutP

SellCallBuyCallC

VD

,,,

,,,

ln

ln

(14)

where )( ,, TKt

TKt PC is the price of the call (put) with strike price K and maturity T at time t,

t is the volatility of the TAIEX options, )( ,, TKt

TKt BuyPutBuyCall is the number of call

(put) contracts bought with strike price K and maturity T on day t, and

16

)( ,, TKt

TKt SellPutSellCall is the number of call (put) contracts sold with strike price K and

maturity T on day t. This study further estimates )/ln(/ln ,,t

TKtt

TKt PC with

Black-Scholes call (put) vega as follows, see Ni et al. (2008):

t

TKt

TKtt

TKt C

C

C

,

,

, 1ln and

t

TKt

TKtt

TKt P

P

P

,

,

, 1ln (15)

In Equation (14), the volatility demand (VDt) is measured by the change in option

trading volume when traders possess volatility information and act in the option markets.

Vega is the rate of change in the prices of call (put) options with volatility and is positive for

both call and put options. If investors have long positions of call or put options, the

volatility demand will increase. On the other hand, volatility demand will decrease when

investors sell call or put options. Besides, the vega of options is liable to be affected by

option maturities as well as exercise prices. Thus, the net demands, obtained by subtracting

sell volumes from buy volumes, are weighted with the return to the option per unit of change

in volatility for each option contract, to construct the daily demand for volatility.

Moreover, the volatility demands (VD) of different classes of traders, including the

foreign institutional investors (FIVD), domestic institutional investors (DIVD), and individual

investors (IIVD), are further constructed by using the daily option trading volume (including

the opening new trades only, and the opening and closing trades both) of the three main

components to obtain the different types of information variables. The regression model,

incorporating the volatility forecasts with the information variables of volatility demand, is

then developed as follows:

tttttt IIVDCDIVDCFIVDCsFVCCsRV 14131210 )()( (16)

where tsRV )( is the realized volatility (standard deviation of returns) over the period from

t+1 through t+s, and tsFV )( denotes the forecast volatility (standard deviation of returns)

for a time period of s trading days starting on day t, which is measured by using one of the

17

four volatility forecasting models: ARLS, historical volatility, GARCH, and GJR-GARCH

models. 1tFIVD , 1tDIVD , and 1tIIVD represent the volatility demands of the three

classes of traders on day t-1, respectively. In Equation (16), our empirical study examines

whether the information on the future movement of stock prices can be revealed by the option

trading volume of different traders. If investors possess private information about the future

movement of underlying assets and act in option markets, there will be a positive relationship

between the volatility demand of the investors and the realized volatility of the underlying

markets. Moreover, this study investigates whether the predictive power of the volatility

forecasting models can be further improved by comprising the information variables from the

option markets.

4. Empirical Results

4.1. Summary Statistics

Table 1 summarizes the descriptive statistics of the TAIEX daily returns (in Panel A)

and the vega-weighted net demand of volatility for different types of investors (in Panel B).

The mean daily return for the TAIEX is 0.014%, and the TAIEX daily return displays a

left-skewed and leptokurtic pattern. The Augmented Dickey-Fuller (ADF) test statistics are

measured to test the stationary tendencies in the time series. The null hypothesis of a unit

root is rejected at the 1% level of significance. The vega-weighted net demand of volatility

for foreign institutions and individual investors has a positive mean, while the mean is

negative for domestic institutions and market makers. The statistics imply that, on average,

the foreign institutions and individual investors have long volatility positions, whereas the

domestic institutions and market makers tend to have short volatility positions. The

vega-weighted net demand of volatility for domestic institutions has the smallest standard

deviation.

4.2. Evaluation of the Forecasting Performance of the Time-Series Models

18

4.2.1. In-sample Forecasting Performance

The in-sample forecasting performance of the ARLS, historical volatility, GARCH, and

GJR-GARCH models is investigated and the results are presented in Table 2. The forecast

horizons consist of 10, 20, 40, 80, and 120 trading days.8 For comparison, the means and

standard deviations of the annualized realized volatility of returns over the periods are also

provided. For each forecast horizon, the model with the lowest RMSFE is specified by the

shaded area.

As shown in Table 2, the ARLS model has the lowest in-sample RMSFEs for all

forecast horizons. Moreover, across all models and forecast horizons, the ARLS model for

the 120-day forecast horizon yields the lowest in-sample RMSFE. As for the in-sample

forecasting performance of the historical volatility, GARCH, and GJR-GARCH models, the

results indicate that the GARCH and GJR-GARCH models generally have lower in-sample

RMSFEs than the historical volatility model.

4.2.2. Out-of-Sample Forecasting Performance

Moreover, each model is estimated using 750 daily return observations (approximately

three years of daily data) to create the out-of-sample volatility forecasts. Following the

estimation procedure of Ederington and Guan (2005, 2010b), J=200 is assumed in Equation

(8). The models are first estimated using the observations 201 through 950 (t), and the

parameter estimates are used to form volatility forecasts for the period t+1 (950+1) through

t+s (950+s), including a horizon of s days for RV(s)950+1 to RV(s)950+s (s = 10, 20, 40, 80, and

120 trading days). The return observations 202 through 951 (t+1) and the parameter

estimates are used to create volatility forecasts for the period t+2 (951+1) through t+s+1

(951+s), and so on, so that the volatility forecasts are generated over the subsequent period,

8 Many different sample period lengths are considered in the paper, including the time horizons of 10, 20,

40, 80, and 120 trading days. The ten-day period is a popular horizon for VaR measures. The other horizons are used to cover the expiration dates of the more heavily traded options.

19

starting from RV(s)950+s+1. The estimation process is reiterated everyday over the next

estimation period until all the observations are used up.9

The out-of-sample forecasting performance of the ARLS, historical volatility, GARCH,

and GJR-GARCH models is examined and the results are displayed in Table 3. As

demonstrated in Table 3, the ARLS model for the 120-day forecast horizon still has the

lowest out-of-sample RMSFE, while the historical volatility model based on the standard

deviation of past returns has the lower RMSFE for the 80-day forecast horizon. For the

out-of-sample volatility forecasting, the ARLS model generally outperforms the GARCH and

GJR-GARCH models, consistent with the results of the in-sample volatility forecasting.

4.3. Information Content of Volatility Demand

Furthermore, the volatility demand, based on the vega-weighted net demand for

volatility, is measured by the intraday transaction data of Taiwan stock index options

provided exclusively by TAIFEX. The trading information for the different types of

investors in the option markets is used to measure the information variables of volatility

demands for the foreign institutional investors, domestic institutional investors, and

individual investors. Consequently, this study further explores whether the volatility

forecasting ability can be improved by including the volatility demand with the information

content from option markets as well as the time-series volatility forecasts for the various

forecast horizons. The in-sample volatility forecasting results of the regression models

incorporating the information variables of volatility demands and the time-series volatility

forecasts are provided in Table 4 through Table 7. The out-of-sample volatility forecasting

results are reported in Table 8 through Table 11. Since the overlapping sample is used to

generate the volatility forecasting, the parameters of the regression models are estimated by

the generalized method of moments, with the t-statistics adjusted for the potential time-series

9 The standard errors of parameter estimates for the overlapping forecast horizons are adjusted for the

potential time-series correlation in the forecast errors.

20

autocorrelation by using the Newey and West (1987) method.

4.3.1. In-sample Forecasting Performance with Information Variables

As shown in Table 4 through Table 7, the coefficients of the time-series volatility

forecasts (derived from the ARLS, historical volatility, GARCH, and GJR-GARCH models,

respectively) in the four models are all statistically significant at the 1% level for each

forecast horizon. Although the coefficients of the volatility demands for the different types

of investors in each model are insignificant for shorter forecast periods (10-, 20-, and 40-day

forecast horizons), the coefficients of the volatility demands for the foreign institutions,

domestic institutions, and individual investors become significant for longer forecast periods

(80- and 120-day forecast horizons). For the shorter forecast periods, the regression model

including the volatility forecast from the GJR-GARCH model (for 10- and 20-day forecast

horizons) or GARCH model (for 40-day forecast horizon) performs slightly better than the

corresponding regression model containing the ARLS volatility forecast. Nevertheless, for

the longer forecast periods, the regression model consisting of the volatility forecast from the

ARLS model and the information variables of volatility demands has the highest Adj-R2

(33.58% and 31.82% for 80- and 120-day forecast horizons, respectively) and thus dominates

all the other regression models (comprising the volatility forecasts from the historical

volatility, GARCH, and GJR-GARCH models). These results are generally in agreement

with those of the prior studies showing the existence of long memory in the financial market

volatility (Granger and Ding, 1996; Ederington and Gun, 2005, 2010a). When the property

of long memory in financial markets is encountered, the ARLS model, compared with the

GARCH and GJR-GARCH models, places more weight on the more distant past observations

and accordingly may have a superior performance in forecasting the future volatility

(Ederington and Guan, 2005).

4.3.2. Out-of-Sample Forecasting Performance with Information Variables

21

Moreover, the out-of-sample volatility forecasting results of the regression models

incorporating the time-series volatility forecasts with the information variables of volatility

demands are displayed in Table 8 through Table 11. Overall, the out-of-sample volatility

forecasting results are generally consistent with the empirical findings of the in-sample

volatility forecasting. For each forecast period, the coefficients of the time-series volatility

forecasts (from the ARLS, historical volatility, GARCH, and GJR-GARCH models) in the

four models are still statistically significant. While the explanatory power of the

information content of volatility demands seems weaker for the shorter volatility forecast

periods (10- and 20-day forecast horizons), the importance of the trading information from

the different types of investors in the option markets grows substantially in the longer

volatility forecast periods (40- and 120-day forecast horizons). For 120-day forecast period,

the regression model including the information variables of volatility demands and the

volatility forecast from the ARLS or historical volatility model performs better than the other

regression models (comprising the volatility forecasts from the GARCH and GJR-GARCH

models). More specifically, the trading information from the foreign and domestic

institutional investors in the option markets seems relatively more important than the

information provided by the individual investors, as shown in Table 9 for the longer (120-day)

forecast period. Although lots of the trading volume of Taiwan’s financial markets is

contributed by the individual investors, parts of the transactions of individual investors may

arise from the noise trading or herding behavior, and thus convey less determinant

information to the market. Consequently, as the rapid globalization of the Taiwan’s markets

and the professional expertise of the institutional investors, the trading information provided

by the foreign and domestic institutions may seem more influential than that provided by the

individual investors in volatility forecasting.

Table 12 further provides the rankings to analyze the model comparisons of the

in-sample and out-of-sample volatility forecasting performance, based on the model adj-R2

22

from Table 4 through Table 11, to summarize the research findings. Regardless of the

in-sample or out-of-sample forecasting performance, the regression models composed of the

volatility forecasts from the ARLS model and the information variables of volatility demands

seem to perform better than the other models. As suggested by Ederington and Guan (2005),

the ARLS model, based on the past absolute return innovations, may provide the better

forecasts for the future volatility. Furthermore, this study also finds that the volatility

demands of investors from option markets contain useful information about the future

volatility of the underlying assets. There are positive relationships between the realized

volatility and the information variables of volatility demands. In fact, our empirical results

show that the information content of volatility demands extracted from the trading volume of

option markets influences the volatility of the underlying stock markets, especially for the

longer forecast horizon.

5. Conclusions

Volatility forecasting plays an essential role in investment decision-making and risk

management. This research provides additional contributions to the volatility forecasting

literature and also extends the studies of Ederington and Guan (2005, 2010a, 2010b) and Ni

et al. (2008) in two important ways. First, this study examines the volatility forecasting

performance of the conventional time-series models (historical volatility, GARCH, and

GJR-GARCH models) and the Absolute Restricted Least Squares (ARLS) model developed

by Ederington and Guan (2005, 2010a, 2010b) using the evidence from Taiwan’s stock and

option markets over a variety of time horizons. Overall, the empirical results of our study

indicate that the ARLS model, based on the past absolute return innovations, dominates the

GARCH and GJR-GARCH models, based on the past squared return deviations, in predicting

the future volatility of Taiwan’s stock market. Second, we further construct the volatility

forecasting models with the information variables of the vega-weighted volatility demands, as

presented by Ni et al. (2008), from different types of investors to extract the information

23

contained in the option markets and to determine which types of option participants possess

the volatility information in Taiwan’s stock market. Our research data are exclusively

provided by the Taiwan Futures Exchange, which contain the comprehensive transaction

records of intraday options trading. Investors’ volatility demands are measured to explore

the occurrence of volatility information trading by different types of investors, including the

foreign institutional investors, domestic institutional investors, and individual traders in the

option market. Our empirical findings demonstrate that the volatility demands derived from

the option trading volumes of different types of investors do contain important information

for predicting the future stock market volatility. Moreover, the model that incorporates both

the volatility forecasts from the ARLS model and the volatility demands of different types of

investors is able to generate better forecasts for the future stock market volatility, especially

for the longer forecast horizon. The results also reveal that although lots of the trading

volume of Taiwan’s financial markets is contributed by the individual investors, the trading

information provided by the foreign and domestic institutions seems more influential than

that provided by the individual investors in volatility forecasting for Taiwan’s stock market.

In sum, the results of our research suggest that the information from option markets can be

viewed as an important explanatory factor when predicting the future dynamics of stock

market volatility. As pointed out by Poon and Granger (2005), whether the volatility

forecasting ability can be further improved by using the exogenous variables is an interesting

and worthwhile research area.

Acknowledgements

The authors gratefully acknowledge the valuable non-public data set exclusively

provided by the Taiwan Futures Exchange, which contains the comprehensive transaction

records of intraday options trading and makes the conduct of this research possible.

24

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Table 1 Summary Statistics of the TAIEX Returns and the Vega-weighted Net Demand of Volatility for Different Types of Investors

Panel A: TAIEX Returns

Variables Mean Std. Dev. Median Max Min Skewness Kurtosis ADF

Rt 0.00014 0.01271 0.00056 0.06525 -0.06912 -0.2983 6.1893 -58.041

Panel B: Vega-weighted Net Demand of Volatility for Different Types of Investors

Variables Mean Std. Dev. Median Max Min

FIVD 71891.42 149916.72 33528.17 1988942 -391724

DIVD -3627.65 53748.36 -3419.26 685158 -247463

IIVD 16953.18 235774.15 16617.93 1917274 -1481992

MMVD -85236.29 236853.84 -45503.91 1743702 -2023158 Note: Rt is the daily return of Taiwan Stock Exchange Capitalization-Weighted Stock Index (TAIEX). FIVD, DIVD, IIVD, and MMVD denote the vega-weighted net demand of volatility for foreign institutional investors, domestic institutional investors, individual investors, and market makers, respectively. ADF is the Augmented Dickey-Fuller statistic of unit root test.

27

Table 2 In-sample Root Mean Squared Forecast Error (RMSFE) of Different Volatility Forecasting Models

Forecast Periods (n) Models 10 Days 20 Days 40 Days 80 Days 120 Days

HV(n) 0.05609 0.05167 0.05241 0.05119 0.05126 ARLS 0.04835 0.04516 0.04509 0.04375 0.04225 GARCH 0.05106 0.04774 0.04924 0.05081 0.05116 GJR-GARCH 0.05087 0.04845 0.05062 0.05239 0.05376 RV μ 0.19084 0.19247 0.19273 0.19359 0.18877

Σ 0.08915 0.07966 0.07096 0.06367 0.05475 Note: HV(n) represents the historical volatility (standard deviation of returns) over the past n days. ARLS denotes the volatility forecast derived from the absolute restricted least squares model (Ederington and Guan, 2005). GARCH and GJR-GARCH stand for the volatility forecasts obtained from the GARCH(1,1) and GJR-GARCH(1,1) models, respectively. The mean (μ) and standard deviation (σ) of the annualized realized volatility (RV) of returns over the forecast period are also reported. All volatility forecasts are annualized and transferred to standard deviation in calculating the root mean squared forecast error (RMSFE). For each forecast period, the model with the lowest RMSFE is specified by the shaded area. Table 3 Out-of-Sample Root Mean Squared Forecast Error (RMSFE) of

Different Volatility Forecasting Models

Forecast Periods (n) Models 10 Days 20 Days 40 Days 80 Days 120 Days

HV(n) 0.06231 0.06047 0.06332 0.05219 0.05248 ARLS 0.05469 0.05236 0.05574 0.05303 0.04621 GARCH 0.05977 0.06100 0.06564 0.07067 0.05398 GJR-GARCH 0.05659 0.05588 0.05966 0.06185 0.05667 RV μ 0.19369 0.19388 0.19359 0.19573 0.18580

Σ 0.09452 0.08292 0.07122 0.06339 0.05666 Note: HV(n) represents the historical volatility (standard deviation of returns) over the past n days. ARLS denotes the volatility forecast derived from the absolute restricted least squares model (Ederington and Guan, 2005). GARCH and GJR-GARCH stand for the volatility forecasts obtained from the GARCH(1,1) and GJR-GARCH(1,1) models, respectively. The mean (μ) and standard deviation (σ) of the annualized realized volatility (RV) of returns over the forecast period are also reported. All volatility forecasts are annualized and transferred to standard deviation in calculating the root mean squared forecast error (RMSFE). For each forecast period, the model with the lowest RMSFE is specified by the shaded area.

28

Table 4 In-Sample Volatility Forecasting Results of the Regression Models Including the Historical Volatility Forecast and the Information Variables of Volatility Demand from Different Types of Investors in the Option Markets Forecast Period

C HV(n) FIVD DIVD IIVD R2 Adj-R2 F

n=10 0.0805*** 0.5683*** 0.0017 0.0029 0.0008 0.4127 0.4117 399.14 (16.91) (26.17) (1.27) (1.01) (1.12)

n=20 0.0852*** 0.5516*** -0.0012 0.0030 0.0010 0.4096 0.4086 392.33 (17.44) (24.61) (-0.97) (1.10) (1.48)

n=40 0.1008*** 0.4674*** 0.0009 0.0014 0.0011 0.3041 0.3029 244.93 (19.42) (19.42) (0.77) (0.50) (1.57)

n=80 0.1097*** 0.4246*** 0.0028*** 0.0051** 0.0008* 0.2619 0.2606 195.33 (21.16) (17.59) (2.60) (2.20) (1.92)

n=120 0.1112*** 0.4047*** 0.0031*** 0.0060** 0.0012** 0.2274 0.2260 159.09 (19.96) (15.28) (2.80) (2.47) (2.02)

Note: This table reports the in-sample results for the regression models of the realized volatility of TAIEX returns on the historical volatility forecast and the volatility demand from different types of investors in the option markets. HV(n) represents the historical volatility (standard deviation of returns) over the past n days. FIVD, DIVD, and IIVD denote the volatility demands of the foreign institutional investors, domestic institutional investors, and individual investors, respectively. The values in parentheses are the t-statistics adjusted for the potential time-series autocorrelation by using the Newey and West (1987) method. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

Table 5 In-Sample Volatility Forecasting Results of the Regression Models Including the ARLS

Volatility Forecast and the Information Variables of Volatility Demand from Different Types of Investors in the Option Markets Forecast Period

C ARLS FIVD DIVD IIVD R2 Adj-R2 F

n=10 -0.0016 1.0091*** -0.0008 0.0027 0.0008 0.4335 0.4325 434.65 (-0.22) (29.58) (-0.65) (0.98) (1.04)

n=20 -0.0023 1.0119*** -0.0012 0.0029 0.0009 0.4281 0.4271 423.31 (-0.32) (28.47) (-1.03) (1.13) (1.39)

n=40 -0.0012 1.0038*** 0.0011 0.0023 0.0010 0.3625 0.3614 318.72 (-0.15) (23.87) (0.98) (0.90) (1.63)

n=80 -0.0087 1.0402*** 0.0028*** 0.0048** 0.0013* 0.3068 0.3055 243.64 (-0.84) (20.03) (2.65) (2.10) (1.95)

n=120 -0.0140 1.0743*** 0.0031*** 0.0055*** 0.0014** 0.2812 0.2799 211.45 (-1.23) (18.70) (3.11) (2.60) (2.32)

Note: This table reports the in-sample results for the regression models of the realized volatility of TAIEX returns on the ARLS volatility forecast and the volatility demand from different types of investors in the option markets. ARLS represents the volatility forecast derived from the absolute restricted least squares model. FIVD, DIVD, and IIVD denote the volatility demands of the foreign institutional investors, domestic institutional investors, and individual investors, respectively. The values in parentheses are the t-statistics adjusted for the potential time-series autocorrelation by using the Newey and West (1987) method. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

29

Table 6 In-Sample Volatility Forecasting Results of the Regression Models Including the GARCH Volatility Forecast and the Information Variables of Volatility Demand from Different Types of Investors in the Option Markets Forecast Period

C GARCH FIVD DIVD IIVD R2 Adj-R2 F

n=10 0.0310*** 0.7905*** 0.0018 0.0028 0.0005 0.4214 0.4204 413.68 (4.90) (27.47) (1.34) (0.96) (0.75)

n=20 0.0521*** 0.7031*** -0.0015 0.0024 0.0007 0.4065 0.4055 387.32 (8.90) (26.24) (-1.22) (0.89) (1.08)

n=40 0.0718*** 0.6007*** 0.0011 0.0020 0.0010 0.3639 0.3628 320.65 (12.73) (23.07) (0.99) (0.81) (1.55)

n=80 0.1017*** 0.4538*** 0.0024** 0.0038* 0.0011* 0.2896 0.2883 224.42 (19.57) (18.86) (2.26) (1.68) (1.65)

n=120 0.1103*** 0.4042*** 0.0029*** 0.0056*** 0.0010* 0.2670 0.2656 196.88 (22.69) (17.85) (2.87) (2.64) (1.72)

Note: This table reports the in-sample results for the regression models of the realized volatility of TAIEX returns on the GARCH volatility forecast and the volatility demand from different types of investors in the option markets. GARCH represents the volatility forecast derived from the GARCH(1,1) model. FIVD, DIVD, and IIVD denote the volatility demands of the foreign institutional investors, domestic institutional investors, and individual investors, respectively. The values in parentheses are the t-statistics adjusted for the potential time-series autocorrelation by using the Newey and West (1987) method. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

Table 7 In-Sample Volatility Forecasting Results of the Regression Models Including the GJR-GARCH Volatility Forecast and the Information Variables of Volatility Demand from Different Types of Investors in the Option Markets Forecast Period

C GJR-

GARCH FIVD DIVD IIVD R2 Adj-R2 F

n=10 0.0322*** 0.7801*** 0.0019 0.0028 -0.0006 0.4408 0.4398 447.74 (5.34) (28.37) (1.44) (0.98) (-0.87)

n=20 0.0573*** 0.6712*** -0.0018 0.0021 0.0008 0.4311 0.4301 428.52 (10.12) (25.87) (-1.45) (0.79) (1.21)

n=40 0.0842*** 0.5542*** 0.0011 0.0018 0.0011* 0.3513 0.3501 303.54 (15.32) (21.73) (0.96) (0.72) (1.70)

n=80 0.1136*** 0.4007*** 0.0024** 0.0047** 0.0013* 0.2572 0.2559 190.61 (22.05) (16.73) (2.23) (1.98) (1.73)

n=120 0.1174*** 0.3882*** 0.0025** 0.0059*** 0.0010* 0.2196 0.2182 152.09 (24.57) (17.46) (2.48) (2.72) (1.78)

Note: This table reports the in-sample results for the regression models of the realized volatility of TAIEX returns on the GJR-GARCH volatility forecast and the volatility demand from different types of investors in the option markets. GJR-GARCH represents the volatility forecast derived from the GJR-GARCH(1,1) model. FIVD, DIVD, and IIVD denote the volatility demands of the foreign institutional investors, domestic institutional investors, and individual investors, respectively. The values in parentheses are the t-statistics adjusted for the potential time-series autocorrelation by using the Newey and West (1987) method. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

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Table 8 Out-of-Sample Volatility Forecasting Results of the Regression Models Including the Historical Volatility Forecast and the Information Variables of Volatility Demand from Different Types of Investors in the Option Markets Forecast Period

C HV(n) FIVD DIVD IIVD R2 Adj-R2 F

n=10 0.0842*** 0.5694*** -0.0018 0.0048 0.0013 0.3362 0.3345 192.71 (11.67) (17.85) (-0.96) (0.63) (1.18)

n=20 0.0963*** 0.5218*** 0.0026 0.0078 0.0016 0.2672 0.2653 137.83 (12.33) (14.69) (1.45) (1.13) (1.51)

n=40 0.1004*** 0.5027*** 0.0030* 0.0124* 0.0018* 0.2004 0.1983 93.48 (11.89) (12.60) (1.80) (1.78) (1.76)

n=80 0.0903*** 0.5586*** 0.0037*** 0.0096* 0.0014* 0.2863 0.2843 145.62 (12.37) (15.64) (2.73) (1.70) (1.66)

n=120 0.0836*** 0.6392*** 0.0039*** 0.0097* 0.0015* 0.2594 0.2573 123.64 (9.68) (13.74) (3.07) (1.88) (1.81)

Note: This table reports the out-of-sample results for the regression models of the realized volatility of TAIEX returns on the historical volatility forecast and the volatility demand from different types of investors in the option markets. HV(n) represents the historical volatility (standard deviation of returns) over the past n days. FIVD, DIVD, and IIVD denote the volatility demands of the foreign institutional investors, domestic institutional investors, and individual investors, respectively. The values in parentheses are the t-statistics adjusted for the potential time-series autocorrelation by using the Newey and West (1987) method. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

Table 9 Out-of-Sample Volatility Forecasting Results of the Regression Models Including the ARLS

Volatility Forecast and the Information Variables of Volatility Demand from Different Types of Investors in the Option Markets Forecast Period

C ARLS FIVD DIVD IIVD R2 Adj-R2 F

n=10 0.0287*** 0.8986*** -0.0017 0.0054 0.0011 0.3284 0.3266 186.06 (2.81) (17.58) (-0.90) (0.69) (1.04)

n=20 0.0429*** 0.8216*** 0.0034* 0.0087 0.0016 0.3016 0.2998 163.24 (4.21) (16.01) (1.93) (1.16) (1.56)

n=40 0.0681*** 0.7437*** 0.0035** 0.0125* 0.0018* 0.2292 0.2271 110.91 (6.22) (13.20) (2.01) (1.88) (1.78)

n=80 0.0724*** 0.7112*** 0.0031** 0.0109* 0.0017* 0.2730 0.2710 136.31 (6.90) (13.00) (2.09) (1.79) (1.72)

n=120 0.0417*** 0.8438*** 0.0042*** 0.0112** 0.0017* 0.2712 0.2691 131.36 (3.49) (12.10) (3.11) (2.01) (1.95)

Note: This table reports the out-of-sample results for the regression models of the realized volatility of TAIEX returns on the ARLS volatility forecast and the volatility demand from different types of investors in the option markets. ARLS represents the volatility forecast derived from the absolute restricted least squares model. FIVD, DIVD, and IIVD denote the volatility demands of the foreign institutional investors, domestic institutional investors, and individual investors, respectively. The values in parentheses are the t-statistics adjusted for the potential time-series autocorrelation by using the Newey and West (1987) method. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

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Table 10 Out-of-Sample Volatility Forecasting Results of the Regression Models Including the GARCH Volatility Forecast and the Information Variables of Volatility Demand from Different Types of Investors in the Option Markets

Forecast Period

C GARCH FIVD DIVD IIVD R2 Adj-R2 F

n=10 0.0576*** 0.7249*** -0.0020 0.0045 0.0015 0.2487 0.2467 125.96 (5.02) (13.02) (-0.97) (0.54) (1.18)

n=20 0.0924*** 0.5611*** 0.0030 0.0093 0.0019 0.2246 0.2225 109.49 (7.31) (8.73) (1.56) (1.17) (1.64)

n=40 0.1046*** 0.5073*** 0.0034* 0.0109 0.0020* 0.1872 0.1850 85.91 (9.38) (8.98) (1.86) (1.46) (1.83)

n=80 0.1106*** 0.4631*** 0.0027* 0.0106* 0.0017* 0.1979 0.1957 89.56 (12.07) (10.18) (1.74) (1.66) (1.68)

n=120 0.1275*** 0.4507*** 0.0033** 0.0098* 0.0015* 0.1716 0.1693 73.12 (8.82) (6.40) (1.98) (1.74) (1.70)

Note: This table reports the out-of-sample results for the regression models of the realized volatility of TAIEX returns on the GARCH volatility forecast and the volatility demand from different types of investors in the option markets. GARCH represents the volatility forecast derived from the GARCH(1,1) model. FIVD, DIVD, and IIVD denote the volatility demands of the foreign institutional investors, domestic institutional investors, and individual investors, respectively. The values in parentheses are the t-statistics adjusted for the potential time-series autocorrelation by using the Newey and West (1987) method. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

Table 11 Out-of-Sample Volatility Forecasting Results of the Regression Models Including the

GJR-GARCH Volatility Forecast and the Information Variables of Volatility Demand from Different Types of Investors in the Option Markets

Forecast Period

C GJR-

GARCH FIVD DIVD IIVD R2 Adj-R2 F

n=10 0.0478*** 0.8098*** -0.0014 0.0076 0.0009 0.3058 0.3040 167.61 (4.87) (16.55) (-0.73) (0.97) (1.03)

n=20 0.0746*** 0.6783*** 0.0025 0.0096 0.0017 0.2702 0.2683 139.95 (8.01) (14.40) (1.40) (1.31) (1.62)

n=40 0.1092*** 0.5161*** 0.0032* 0.0098 0.0018* 0.2109 0.2088 99.69 (11.32) (10.24) (1.79) (1.43) (1.75)

n=80 0.1187*** 0.4710*** 0.0028* 0.0108* 0.0017* 0.2374 0.2353 113.00 (13.15) (9.80) (1.72) (1.69) (1.71)

n=120 0.1203*** 0.4429*** 0.0029** 0.0104* 0.0015* 0.1358 0.1334 55.47 (15.44) (10.72) (2.07) (1.70) (1.68)

Note: This table reports the out-of-sample results for the regression models of the realized volatility of TAIEX returns on the GJR-GARCH volatility forecast and the volatility demand from different types of investors in the option markets. GJR-GARCH represents the volatility forecast derived from the GJR-GARCH(1,1) model. FIVD, DIVD, and IIVD denote the volatility demands of the foreign institutional investors, domestic institutional investors, and individual investors, respectively. The values in parentheses are the t-statistics adjusted for the potential time-series autocorrelation by using the Newey and West (1987) method. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively.

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Table 12 Rankings for the Model Comparisons of the In-Sample and Out-of-Sample Volatility Forecasting Performance with Information Variables of Volatility Demand

Forecast horizons

HV(n) + VD ARLS + VD GARCH + VD GJR-GARCH + VD

In-sample forecast 10 days 4 2 3 1 20 days 3 2 4 1 40 days 4 2 1 3 80 days 3 1 2 4 120 days 3 1 2 4 Total 17 8 12 13

Out-of-sample forecast 10 days 1 2 4 3 20 days 3 1 4 2 40 days 3 1 4 2 80 days 1 2 4 3 120 days 2 1 3 4 Total 10 7 19 14

Note: The rankings are based on the Adj-R2 of the regression models for the realized volatility of TAIEX returns on the volatility forecasts from different time-series models with the information variables of volatility demand. HV(n), ARLS, GARCH, and GJR-GARCH represent the regression models using the volatility forecasts derived from the historical volatility model, the absolute restricted least squares model, the GARCH(1,1) model, and the GJR-GARCH(1,1) model, respectively. VD stands for the volatility demand from different types of investors in the option markets.