摘要
本文在高頻架構下探討波動度交易活動的資訊內容，並著關注於VIX 期貨與選擇權交易。我們的分析表明，VIX 期貨與選擇權的委託單失衡與VIX市場的報酬率顯著相關。值得注意的是，在VIX 市場不確定性升高、流動性減少以及總體經濟宣告期間，這種報酬率的可預測性會增加。我們也進一步發現，無論是價內、價平還是價外的選擇權委託單失衡皆有顯著的報酬預測力。此外，本研究提供的實證證據表明，VIX 期貨的高頻資訊交易遵循反向交易模式，而VIX 選擇權交易則呈現動能交易模式。進一步的，我們的結果表明，VIX 期貨在一個交易日內的資訊交易量呈現 U 型模式，VIX 選擇權的資訊交易主要集中在開盤附近的交易區間內。最後，研究結果表明，只有VIX 選擇權的資訊交易活動包含有關 VIX 市場的波動度訊息。整體而言，我們的實證結果指出當投資人具有市場報酬率資訊時，他們從期貨或選擇權市場進行交易，而當具有波動度資訊時，則集中於選擇權市場交易。

Abstract
This paper examines the informational content of volatility trading activities within a high-frequency framework, focusing on VIX futures and options trading.
Our analysis indicates that the order imbalance of VIX futures and options is significantly correlated with the subsequent- returns in the VIX market. Notably, the returns predictability increases during periods of heightened market uncertainty,reduced liquidity, and macroeconomic announcements. We further find that the significant predictability of order imbalances in VIX options persists across all moneyness levels. Furthermore, empirical evidence provided by this study suggests that high-frequency trading of VIX futures follows a contrarian trading pattern, while VIX options trading exhibits a momentum trading pattern. Additionally, our findings demonstrate that the intraday trading volume of VIX futures displays a Ushaped pattern, with the informational trading of VIX options primarily concentrated near the opening trading interval. Lastly, empirical results reveal that only the informational trading activities of VIX options contain volatility signals about the VIX market. Overall, our results are supportive of the view that futures contracts tend to attract investors who have information about market returns, whereas options are more appealing to those with insights into volatility and direction of returns.

論文審定書........................................................................................................................ i
摘要....................................................................................................................................ii
Abstract ............................................................................................................................ iii
1. Introduction .................................................................................................................. 1
2. Literature review ......................................................................................................... 10
3. Data and methodology ............................................................................................... 18
3.1 VIX futures and options data .................................................................................... 18
3.2 Variable definitions ................................................................................................... 20
3.3 Regression settings.................................................................................................... 22
3.3.1 The Return predictability of the VIX futures and options .................................... 22
3.3.2 The VIX market return predictability of the VIX derivatives under different market conditions. ...................................................................................................................... 26
4. Results ......................................................................................................................... 28
4.1 Information content in the VIX futures and options ................................................ 28
4.2 Information content in the VIX futures and options across different levels of VIX market uncertainty ......................................................................................................... 29
4.3 Information content in the VIX futures and options across different levels of VIX market illiquidity............................................................................................................. 31
4.4 Information content around the macroeconomic announcement ........................ 33
4.5 Drivers of the order imbalance of VIX futures and options ......................................35
4.6 When Does Order Imbalance in VIX Options Occur in A Day? ................................. 38
4.7 Robustness results .................................................................................................... 42
4.7.1 Robustness results across different trading measure and various time intervals .......................................................................................................................................... 42
4.7.2 The informed trading in VIX options across various moneyness levels .............. 44
4.7.3 Information on VIX market volatility in VIX futures and options ......................... 45
4.7.4 Vector Autoregression (VAR) Results ..................................................................... 47
5. Conclusion .................................................................................................................. 48
References ...................................................................................................................... 55

List of Figure
Figure 1. The intraday pattern of order imbalance in VIX futures ................................ 61
Figure 2. The intraday pattern of order imbalance in VIX options ............................... 62

List of Table
Table 1. Summary statistics of trading volume in the VIX futures and options markets across different time intervals.......................................................................................62
Table 2. Summary statistics of trading measures in the VIX futures and options markets across different time intervals..........................................................................63
Table 3. Correlation coefficients of variables in the VIX futures and options markets across different time intervals.........................................................................................64
Table 4. Autocorrelation test of variables in the VIX futures and options markets across different time intervals....................................................................................................66
Table 5. Order Imbalance in VIX Futures and Corresponding Returns Across Various Frequencies......................................................................................................................68
Table 6. Order Imbalance in VIX Options and Corresponding Returns Across Various Frequencies......................................................................................................................70
Table 7. Order Imbalance in VIX Futures and Corresponding Returns on Different Levels of VIX Market Uncertainty.....................................................................................72
Table 8. Order Imbalance in VIX Options and Corresponding Returns on Different Levels of VIX Market Uncertainty.....................................................................................74
Table 9. Order Imbalance in VIX Futures and Corresponding Returns on Different Levels of VIX Market Volatility..........................................................................................76
Table 10. Order Imbalance in VIX Options and Corresponding Returns on Different Levels of VIX Market Uncertainty.....................................................................................78
Table 11. Order Imbalance in VIX Futures and Corresponding Returns on Different Levels of VIX Market Illiquidity.........................................................................................80
Table 12. Order Imbalance in VIX Options and Corresponding Returns on Different Levels of VIX Market Illiquidity.........................................................................................82
Table 13. Order Imbalance in VIX Futures and Corresponding Returns on Different Levels of VIX Market Liquidity..........................................................................................84
Table 14. Order Imbalance in VIX Options and Corresponding Returns on Different Levels of VIX Market Liquidity..........................................................................................86
Table 15. Order Imbalance in VIX Futures and Corresponding Returns around Macroeconomic Announcement Date.............................................................................88
Table 16. Order Imbalance in VIX Options and Corresponding Returns around Macroeconomic Announcement Date.............................................................................90
Table 17. Causes of Order Imbalance of VIX Futures......................................................92
Table 18. Causes of Order Imbalance of VIX Options......................................................94
Table 19. When Does Order Imbalance in VIX Futures Occur in A Day?.........................96
Table 20. When Does Order Imbalance in VIX Options Occur in A Day?.........................98
Table 21. Robustness Test of the Order Imbalance of VIX Futures Using Alternative Trading Activity Measures Across Different Time Intervals..........................................100
Table 22. Robustness Test of the Order Imbalance of VIX Options Using Alternative Trading Activity Measures Across Different Time Intervals..........................................102
Table 23. The Return Predictability of Order Imbalance in VIX Options Across Various Moneyness.....................................................................................................................104
Table 24. Order Imbalance in VIX Futures and Corresponding Volatility Across Various Frequencies....................................................................................................................106
Table 25. Order Imbalance in VIX Options and Corresponding Volatility Across Various Frequencies....................................................................................................................108
Table 26. VAR Results of Order Imbalance in VIX Futures and Corresponding Returns Across Various Frequencies...........................................................................................110
Table 27. Var Results of Order Imbalance in VIX Options and Corresponding Returns Across Various Frequencies...........................................................................................112
Appendix 1. Unit root test of variables..........................................................................114
Appendix 2. Order Imbalance in VIX Futures and Options and Corresponding Returns Across Various Frequencies...........................................................................................115
Appendix 3. Order Imbalance in VIX Futures and Corresponding Returns during the COVID-19 Pandemic.......................................................................................................117

Admati, A. R., & Pfleiderer, P. (1998). A theory of intraday patterns: Volume and price
variability. Review of Financial Studies, 1(1), 3–40.
Ahn, H. J., Kang, J., & Ryu, D. (2008). Informed trading in the index option market:
The case of KOSPI 200 options. Journal of Futures Market, 28(12), 1118-1146.
Amihud, Y. (2002). Illiquidity and stock returns: Cross-section and time series effects.
Journal of Financial Market, 5(1), 31–56.
Aslan, H., Easley, D., Hvidkjaer, S., & O'hara, M. (2011). The characteristics of
informed trading: Implications for asset pricing. Journal of Empirical Finance,
18(5), 782-801.
Back, K. (1993). Asymmetric information and options. Review of Financial Studies, 6,
435–472.
Bae, K. H., & Dixon, P. (2018). Do Investors use Options and Futures to Trade on
Different Types of Information? Evidence from an Aggregate Stock Index.
Journal of Futures Markets, 38, 175–198.
Bernile, G., Hu, J., & Tang, Y. (2016). Can information be locked up? Informed trading
ahead of macro-news announcements. Journal of Financial Economics, 121,
496–520.
Black, F. (1975). Fact and Fantasy in the Use of Options. Financial Analysts Journal,
31, 36–41.
Blittlingmayer, G. (1998). Output, stock volatility, and political uncertainty in a natural
experiment: Germany, 1880–1940. Journal of Finance, 53, 2243–2257.
Brogaard, J., & Hendershott, T. (2014). High-frequency trading and price discovery.
Review of Financial Studies, 27(8), 2267–2306.
54
Busse, J., Green, C., & Jegadeesh, N. (2012). Buy-side trades and sell-side
recommendations: interactions and information content. Journal of Financial
Markets, 15 , 207-232.
Cao, H. H., & Ou-Yang, H. (2009). Differences of opinion of public information and
speculative trading in stocks and options. Review of Financial Studies, 22, 299–
335.
Cespa, G., & Foucault, T. (2013). Sale of price information by exchanges: does it
promote price discovery? Management Science, 60(1), 148–165.
Chan, K. (1992). A further analysis of the lead-lag relationship between the cash market
and stock index futures market. Review of Financial Studies, 5(1), 123–152.
Chakravarty, S., Gulen, H., & Mayhew, S. (2004). Informed trading in stock and option
markets. Journal of Finance, 59, 1235–1257.
Chordia, T., Roll, R., & Subrahmanyam, A. (2001). Market liquidity and trading
activity. Journal of Finance, 56(2), 501–530.
Chordia, T., Roll, R., & Subrahmanyam, A. (2002). Order imbalance, liquidity, and
market returns. Journal of Financial Economics, 65, 111–130.
Chordia, T., Roll, R., & Subrahmanyam, A. (2008). Liquidity and market efficiency.
Journal of Financial Economics, 87(2), 249–268.
Chordia, T., Kurov, A., Muravyev, D., & Subrahmanyam, A. (2021). Index option
trading activity and market returns. Management Science, 67(3), 1758–1778.
Cushing, D., & Madhavan, A. (2000). Stock returns and trading at the close. Journal of
Financial Market, 3(1), 45–67.
De Jong, C., Koedijk, K. G., & Schnitzlein, C. R. (2006). Stock market quality in the
presence of a traded option. Journal of Business, 79, 2243–2274.
55
Easley, D., Engle, R. F.,O’Hara, M.,and Wu, L. (2008). Time-varying arrival rates of
informed and uninformed trades. Journal of Financial Econometrics, 6(2), 171–
207.
Easley, D., López de Prado, M. M. & O'Hara, M. (2012). Flow toxicity and liquidity in
a high-frequency world. Review of Financial Studies, 25(5), 1457-1493.
Easley, D., & O'Hara, M. (1987). Price, trade size, and information in securities markets.
Journal of Financial Economics, 19(1), 69-90.
Easley, D., & O'Hara, M. (2010). Liquidity and valuation in an uncertain world. Journal
of Financial Economics, 2010, 97(1), 1-11.
Easley, D., O'Hara, M., & Srinivas, P. S. (1998). Option volume and stock prices:
Evidence on where informed traders trade. Journal of Finance, 53, 431–465.
Easley, D., O'Hara, M., & Yang, L. (2016). Differential access to price information in
financial markets. Journal of Financial and Quantitative Analysis, 51(4), 1071
– 1110.
Ederington, L. H., & Lee, J. H. (1996). The creation and resolution of market
uncertainty: The impact of information releases on implied volatility. Journal of
Financial and Quantitative Analysis, 31, 513–539.
Ferreira, M. A., Matos, P., Pereira, J. P., & Pires, P. (2017). Do locals know better?: A
comparison of the performance of local and foreign institutional investors.
Journal of Banking and Finance, 82, 151–164.
Foucault, T., Hombert, J., & Roşu, I. (2016). News trading and speed. Journal of
Finance, 71(1), 335–382.
Foucault, T., Kadan, O., & Kandel, E. (2005). Limit order book as a market for liquidity.
Review of Financial Studies. 18(4), 1171–1217.
56
Foster, F. D., & Viswanathan, S. (1994). Strategic trading with asymmetrically
informed traders and long-lived information. Journal of Financial and
Quantitative Analysis, 29(4), 499-518.
Gallant, A., Rossi, P., & Tauchen, G. (1992). Stock prices and volume. Review of
Financial Studies, 5, 199–242.
Gao, L., Han, Y., Li, S. Z., & Zhou, G. (2018). Market intraday momentum. Journal of
Financial Econometrics, 192 (2), 394–414.
Glosten, L. R., & Milgrom, P. R. (1985). Bid, ask and transaction prices in a specialist
market with heterogeneously informed traders. Journal of Financial Economics,
14(1), 71-100.
Guo, H., & Qiu, B. (2016). A Better Measure of Institutional Informed Trading.
Contemporary Accounting Research, 33(2), 815-850.
Heston, S., C. Jones, M. Khorram, S. Li and H. Mo, 2023, Option Momentum, Journal
of Finance, 78 (6), 3141-3192.
Ho, T. S., &Stoll, H. R. (1983). The dynamics of dealer markets under competition.
Journal of Finance, 38(4), 1053-1074.
Holden, C. W., & Subrahmanyam, A. (1992). Long‐lived private information and
imperfect competition. Journal of Finance, 47(1), 247-270.
Hong, H., & Stein, J. C. (1999). A unified theory of underreaction, momentum trading,
and overreaction in asset markets. Journal of Finance, 54(6), 2143-2184.
Hu, X., Pan J., Wang, J. (2013). Early peek advantage?, Massachusetts Institute of
Technology, Cambridge, MA. Unpublished working paper
Huang, H. G., Tsai, W. C., Weng, P. S., & Wu, M. H. (2021). Volatility order imbalance
of various types of institutional traders and expected asset returns: Evidence
from Taiwan. Journal of Financial Markets, 52, 100546.
57
Huang, H. G., Tsai, W. C., Weng, P. S., & Yang, J. J. (2023). Intraday momentum in
the VIX futures market. Journal of Banking and Finance, 148, 106746.
Iati, R. (2009). High-frequency Trading Technology. TABB Group.
Karpoff, J. M. (1987). The relation between price changes and trading volume: A
survey. Journal of Financial and Quantitative Analysis, 22(1), 109-126.
Kang, J., & Park, H. (2008). The information content of net buying pressure: Evidence
from the KOSPI 200 index option market. Journal of Financial Markets, 11, 36–
56.
Kim, O., & Verrecchia, R. E. (1994). Market liquidity and volume around earnings
announcements. Journal of Accounting and Economics, 17, 41–67.
Kyle, A. (1985). Continuous auctions and insider trading. Econometrica, 53,1315–1336.
Love, R., & Payne, R. (2008). Macroeconomic news, order flows, and exchange rates.
Journal of Financial and Quantitative Analysis, 43(2), 467-488.
Muravyev, D. (2016). Order flow and expected option returns. Journal of Finance, 71(2),
673-708.
Newey, W. K., & West, K. D. (1987). Hypothesis testing with efficient method of
moments estimation. International Economic Review, 777-787.
O'Hara, M. (2015). High frequency market microstructure. Journal of Financial
Economics, 116(2), 257-270.
Pan, J., & Poteshman, A. M. (2006). The information in option volume for future stock
prices. Review of Financial Studies, 19, 871–908.
Rogers, J., Skinner, D., & Zechman, S. (2014). Run EDGAR run: SEC dissemination
in a high-frequency world, University of Chicago, Chicago, IL. Unpublished
working paper
Ryu, D., Kang, J., & Suh, S. (2015). Implied pricing kernels: An alternative approach
for option valuation. Journal of Futures Markets, 35(2),127-147.
58
Sim, M., Ryu, D., & Yang, H. (2016). Tests on the monotonicity properties of KOSPI
200 options prices. Journal of Futures Markets, 36(7), 625-646.
Spiegel, M. and A. Subrahmanyam, 1995, On intraday risk premia. Journal of Finance
50 (1), 319-339.
Stoll, H., 1978, The Supply of Dealer Services in Securities Markets, Journal of Finance,
33(4), 1133-1151.
Weng, P. S., Wu, M. H., Chen, M. L., & Tsai, W. C. (2017). An empirical analysis of
the dynamic probability of institutional informed trading: evidence from the
Taiwan futures exchange. Journal of Futures Markets, 37(9), 865–891.
Wood, R. A., McInish, T. H., & Ord, J. K. (1985). An Investigation of Transaction Data
for NYSE Stocks. Journal of Finance, 40(3), 723–741.