DATA

14 The TAIFEX introduced the European style TXO, written on the TAIEX, on December 24, 2001. The contract matures on the third Wednesday of the delivery month. The contract months involve five contracts with different maturities in the nearby month, the next two calendar months, and the following two quarterly

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price of less than 0.1, the minimum tick size, are excluded. These prices cannot reflect true option value. Second, due to the potential liquidity concerns, the options with less than five trading days remaining to maturity are eliminated. Third, the options violating the put–call parity boundary conditions are deleted. These options are significantly undervalued and have negative Black–Scholes implied volatilities.

Table 2 presents the results of the parameter estimation for the realized volatility forecast based on the VecHAR model in Equation (3). The procedure of a daily rolling window generates 927 estimations for every parameter during the sample period. Table 2 reports the average. The mean coefficients for CV, the first elements in the B1 andB22

matrices, are significantly positive, indicating an own persistence in the CV component.

There exist dynamically asymmetric dependencies between CV, nJV, pJV, and NV. For instance, CV is lagged to nJV as shown by the significant estimates for the second elements in the B1 matrices whereas nJV is only lagged to nJV. Therefore, all four volatility components are included in the forecasting of realized volatility.

Table 2 Parameter estimates for the VecHAR model

Notes. This table presents the estimating results of parameters for realized volatility forecast based on a vector autoregressive (VecHAR) model in Equation (3):

^{22 0 1 1 5 5 22 22 22},

( ) '.

t t t t t

t t t t t

Z B B Z B Z B Z

Z CV nJV pJV NV

+ = + − + − + − +ε+

= (3)

The expected realized volatility is estimated using the moving window data of past 800 days. The realized variation measures underlying the estimate are based on 5-minute high-frequency data from January 1, 2002 to December 31, 2009 inclusively. The procedure of a daily rolling window generates 927 estimations for each parameter during the sample period. Table 2 reports the average. In Equation (3), B₀ is a vector of the intercept term. B₁, B₅, and B₂₂ are matrices for the regression coefficients, in which the first column, second column, third column, and fourth column in each matrix correspond to the parameters of the four volatility components, respectively. A four-dimensional vector is included in the VecHAR model, involving continuous volatility (CV), negative jump volatility (nJV), positive jump volatility (pJV), and overnight volatility (NV). In addition, Newey–West standard errors are used to calculate the t-values of the estimated parameters. Coeff. indicates the regression coefficient. ***, **, and * indicate that t-values are significant at the 0.01, 0.05, and 0.1 level, respectively.

Figure 1 exhibits the plot of the time-series for model-free implied volatility (IV) and expected realized volatility (RV_E) in the top panel and VRP in the bottom panel. A visual inspection reveals that both the implied volatility and expected realized volatility track closely. Overall, the IV is slightly above the RV_E by 162 basis points, indicating a positive VRP (The means of IV and RVE are 0.2320 and 0.2158, respectively).

Figure 1. Time series plots of implied volatility, expected realized volatility, and volatility risk premium. The volatility risk premium (VRP) is quantified as the model-free implied volatility (IV) less the expected realized volatility (RV_E). The model-free method proposed by Jiang and Tian (2005, 2007) is adopted to extract the implied volatility, and a vector heterogeneous autoregressive (VecHAR) model is used to estimate the expected

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The second panel of Figure 1 shows that the time-series VRP ranges from –0.2883 to 0.2245 during the period of 2005–2009 and has a mean 0.0162. The 1.62% volatility spread provides evidence to support the finding of Bollen and Whaley (2004) and Gârleanu et al.

(2009) that market makers who provide liquidity to the buy side are compensated for accepting risk. However, when the market is more volatile, market makers also face substantial risk of losses. In the period of financial crisis in 2008, a negative VRP, also shown in Todorov (2010) and Bollerslev, Gibson, Zhou (2011), occurs frequently. That is, market makers providing liquidity to the buy side suffer trading losses. In addition, the VRP is stationary time series according to the results of the Dickey–Fuller test with test statistic of -44.6.

Panels A and B of Table 3 respectively report the summary statistics of option order imbalances measured by the number of trades (#OIB) and traded dollar amount ($OIB).

#DdAllRisk1, #DdVolRisk1, and #DdJpRisk1 (#DdAllRisk2, #DdVolRisk2, and #DdJpRisk2) indicate option demand, volatility demand, and jump demand in the near (second) month, in which all are measured by the number of trades. Similarly, $DdAllRisk1, $DdVolRisk1, and

$DdJpRisk1 ($DdAllRisk2, $DdVolRisk2, and $DdJpRisk2) are option demands in the near (second) month measured by the dollars $OIB. The results show that all the option order imbalances are slightly negative, negative skewness, and leptokurtic. For instance, the DdAllRisk1, DdVolRisk1, and DdJpRisk1 measured by #OIB ($OIB) in the near month average –0.0058, –0.0284, and –0.0055 (–0.0127, –0.0379, and –0.0125), respectively. In addition, the augmented Dickey–Fuller (ADF) unit root tests significant reject the hypothesis of one unit root for every individual series, indicating that these demand variables are stationary. The correlation coefficients between option order imbalances in near- and second-month for #DdAllRisk, #DdVolRisk, and #DdJpRisk ($DdAllRisk,

$DdVolRisk, and$DdJpRisk) are 0.09, 0.06, and 0.09 (0.18, 0.22, and 0.15), respectively. The correlation coefficients range from 0.06 to 0.22, showing a low correlation between these option demand variables in the near- and second-month.

Table 3 Summary statistics for order imbalances

obs. Mean Std Min p5 p50 p95 Max Skew Kurt ADF

Panel A: Order imbalances measured by number of trades (#OIB)

#DdAllRisk₁ 927 –0.0058 0.0324 –0.3271 –0.0577 –0.0055 0.0451 0.0946 –0.9921 13.20 -569 Notes. This table presents summary statistics for daily option order imbalances in the near and second months. Panel A and Panel B report the statistics of order imbalances measured by number of trades (#OIB) and dollars ($OIB), respectively. #DdAllRisk_1, #DdVolRisk_1, and#DdJpRisk₁ (#DdAllRisk_2, #DdVolRisk_2, and#DdJpRisk₂) indicate option demand, volatility demand, and jump demand in the near (second) month, in which order imbalances are measured by the number of trades. Similarly, $DdAllRisk_1, $DdVolRisk_1, and $DdJpRisk₁ ($DdAllRisk_2,

$DdVolRisk_2, and$DdJpRisk₂) are option demands in the near (second) month, in which they are measured by the dollars $OIB. ADF is the augmented Dickey–Fuller unit root test.