CHAPTER 2 THE IMPACT OF ORDER IMBALANCE IN OPTIONS ON VOLATILITY
4. EMPIRICAL RESULTS
4.3. Robustness Tests on Option Demand Pressure Effect on VRP
Two robustness checks are conducted to further verify the finding of a positive effect of demand pressure on VRP. First, a liquidity indicator of options is included into the regression model to control the probable influence on the VRP. Second, an alternative measure of realized volatility is used to re-examine whether the result of demand pressure effect on the VRP is robust. They are specified as follows.
First, option liquidity is likely to affect the effect of demand pressure on VRP. Brenner, Eldor, and Hauser (2001) and Chou, Chung, Hsiao, and Wang (2011) find that option liquidity impacts its implied volatility (price) associated with the estimation of the VRP, the implied volatility less expected realized volatility. Therefore, a liquidity indicator, the daily aggregate option liquidity (QSPR), is incorporated into the regression model as a control variable for potential bias due to liquidity in the option market.15
The QSPR averages daily percentage quoted spread of options in the near and second
15 For conciseness, only the effect of option demand pressure on VRP is examined by controlling on the interaction between market-maker hedged profits and option net demand, daily realized volatility, daily index return, lag VRPs, and option liquidity.
months. For daily option percentage quoted spread in each contract month, the average of percentage quoted spread of call and put options is first calculated in every five-minute interval and then averaged across intervals in a day, in which the percentage quoted spread in calls (and puts) is equally weighted across all individual call (put) options with different exercise prices. As for the percentage quoted spread of individual option, it is calculated as the difference between ask and bid prices dividing the mid-quote.
The results are reported in Table 7. The coefficient of β4 picks up the effect of option liquidity on VRP. Table 7 continues to show that a significant and positive effect of demand pressure on VRP persists after controlling for liquidity in options, consistent with the results in Table 5. In addition, the insignificant coefficients for liquidity indicator (β4) indicate that option demand pressure in contrast to its liquidity explains the time-varying VRP well.
Table 7 The effect of option demand pressure on VRP by controlling on option liquidity
DdAllRisk DdVolRisk DdJpRisk
Coeff. t Coeff. t Coeff. t
Panel A: Demand measured by number of trades (#OIB)
φ1 0.0851 1.84* 0.0747 1.39 0.0821 1.77*
φ2 0.0687 3.01*** 0.0396 2.39** 0.0708 2.90***
β1 -0.0005 -4.88*** -0.0004 -4.58*** -0.0004 -5.41***
β2 -0.0117 -1.04 -0.0108 -0.98 -0.0123 -1.11
β3 -0.3800 -3.19*** -0.3988 -3.35*** -0.3760 -3.18***
β4 -0.0455 -0.88 -0.0599 -1.16 -0.0454 -0.88
Adj.R2 0.8842 - 0.8831 - 0.8846 -
Panel B: Demand measured by traded dollars ($OIB)
φ1 0.0890 2.42** 0.0943 2.37** 0.0838 2.24**
φ2 0.0630 2.86*** 0.0272 1.91* 0.0674 2.84***
β1 -0.0004 -3.90*** -0.0004 -5.07*** -0.0004 -5.30***
β2 -0.0126 -1.13 -0.0145 -1.31 -0.0140 -1.26
β3 -0.3945 -3.34*** -0.4302 -3.62*** -0.3939 -3.37***
β4 -0.0489 -0.96 -0.0798 -1.52 -0.0501 -0.99
Adj.R2 0.8846 - 0.8844 - 0.8852 -
Note. This table presents the results of option demand pressure on volatility risk premium (VRP) by controlling on the
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(RV), daily index return (IR), option liquidity (QRSP), and lag VRPs. The coefficient of β4 picks up the effect of option liquidity on the VRP. Two types of option order imbalance are used to measure the option net demand, one in number of trades (#OIB) and the other in dollars ($OIB). The results are reported in Panel A and Panel B, respectively. For each type of order imbalance measure, three order imbalance variables are calculated separately weighted by aggregate risk, volatility risk, and jump risk and are used to proxy, respectively, for option demand (DdAllRisk), volatility demand (DdVolRisk) and jump demand (DdJpRisk). They are individually included in the regression model to investigate the demand pressure effect on VRP. QSPR is the daily ×liquidity in the option market. The VRP is quantified as the implied volatility less expected realized volatility. OIB and1 OIB denote the 2 daily option order imbalances in the near and second months. RV is daily realized volatility, and IR is the daily index return. MD is a Monday dummy. The VRPt-j’s are lagged volatility risk premiums. Moreover, Newey-West standard errors are used to calculate the t-statistics of the estimated parameters. For brevity, this table does not report theα⌢ ,0 α⌢ and m w⌢j’s. The Adj. R2 denotes the adjusted R2 for the regression. ***, **, and * indicate that t-values are significant at the 0.01, 0.05, and 0.1 level, respectively.
Second, an alternative measure of realized volatility is used to examine whether our results of the demand effect are robust under different measures. Many empirical studies find positive autocorrelation between high-frequency index returns. As reported in Andersen et al. (2001), the serial autocorrelation in high-frequency returns may bias the estimation of realized volatility, measured by summing up the squared intraday returns. This bias likely leads to an inaccurate estimate of VRP and can subsequently result in an improper conclusion from our analysis.
Andersen et al. (2001) suggest that the intraday returns should be cleaned up using an MA(1) filter before computing realized volatility. The de-meaned MA(1)-filtered returns can reduce serial correlation and are better suited for the calculation of realized volatility.
Thus, this study follows their suggestion by applying the MA(1) filter to the 5-minute returns. Using the filtered series, the related variables are recalculated such as the expected realized volatility, VRP, and the detection of jumps and re-examine the effect of demand pressure on the VRP.
Table 8 The demand effect of option based on the MA(1)-filtered returns
DdAllRisk DdVolRisk DdJpRisk
Coeff. t Coeff. t Coeff. t
Panel A: Demand measured by number of trades (#OIB)
φ1 0.0241 1.12 –0.0001 0.00 0.0232 1.10
φ2 0.0563 2.98*** 0.0316 1.78* 0.0549 2.59***
ψ1 0.3590 3.10*** 0.4160 2.78*** 0.3346 3.33***
Notes. This table presents the results for the regression model, shown in Equation (6), of option demand pressure on the volatility risk premium (VRP) based on MA(1)-filtered returns:
0 1 1, 2 2, 1 1, 2 2, 1 2
An MA(1) filter is used to remove the serial autocorrelation in high-frequency 5-minute returns. Subsequently, the filtered returns are used to recalculate related variables in the regression model. Two types of option order imbalance are used to measure the option net demand, one in number of trades (#OIB) and the other in dollars ($OIB). The results are reported in Panel A and Panel B, respectively. For each type of order imbalance measure, three order imbalance variables are calculated separately weighted by aggregate risk, volatility risk, and jump risk and are used to proxy, respectively, for option demand (DdAllRisk), volatility demand (DdVolRisk) and jump demand (DdJpRisk). They are individually included in the regression model to investigate the demand pressure effect on VRP. VRP is quantified as the implied volatility less expected realized volatility. OIB 1 andOIB denote the daily option order imbalances in the near and second months, respectively. D2 t, a jump dummy variable, is equal to 1 if a price jump occurs during the daily trading time period on day t, and zero otherwise. The price jumps are identified by a nonparametric test proposed by Lee and Mykland (2008).
IntDdP&L is the interaction between market-maker hedged profits and option net demand. RV is daily realized volatility, and IR is the daily index return. MD is a Monday dummy. VRPt-j are lagged volatility risk premiums.
Newey–West standard errors are used to calculate the t-statistics of the estimated parameters. For brevity, this table does not report α⌢ ,0 α⌢ ,m α⌢ , and d w⌢j. ***, **, and * indicate that t-values are significant at the 0.01, 0.05, and 0.1 level, respectively.
The results of a positive demand pressure effect on VRP are similar to those in Tables 4, 5, and 6. For brevity, only the result of demand pressure on VRP with jumps is illustrated in Table 8. Panels A and B continue to show highly significant t-values of ψ1 for all three demand variables, indicating that jumps generate a larger impact of demand pressure on
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VRP. A positive and larger coefficients ψ1 relative to φ1 for volatility demand at time of jump occurrence suggests that time-varying risk aversion is driven by market jumps. In sum, it is thus concluded that higher (lower) VRP is more likely to be the result of the positive (negative) demand pressure effect rather than the serial autocorrelation in high-frequency returns and liquidity effect.