Trade duration, informed trading, and option moneyness

Kee H. Chunga, Seongkyu “Gilbert” Parkb, and Doojin Ryuc,* a School of Management, State University of New York at Buffalo, Buffalo, NY, United States b School of Accounting and Finance, Hong Kong Polytechnic University, Hong Kong c College of Economics, Sungkyunkwan University, Seoul, Republic of Korea

Acknowledgements The authors thank Hee-Joon Ahn, Farida Akhtar, Jose Da Fonseca, Da Hea Kim, David Sun, Jaeram Lee, Lars Norden, Heejin Yang, and Robert I. Webb.

* Corresponding Author (D. Ryu). College of Economics, Sungkyunkwan University, 25-2, Sungkyunkwan-ro, Jongno-gu, Seoul 03063, Republic of Korea; Tel: +82-2-760-0429; Fax: +82-2- 760-0950; E-mail: [email protected].

Abstract This study shows the relationship between the price impact of a trade and the duration between trades by extending a trade indicator microstructure model. Using the intraday transaction data from the KOSPI 200 options market, one of the most famous and actively traded derivatives markets in the world, we find that the price impact is greater when the trade duration is shorter for in-the-money (ITM) options, while the correlation is opposite for out-of-the-money (OTM) options. Our finding that fast trading indicates informed (noisy) trading in the ITM (OTM) options remains unchanged despite controlling for the effects of trade volume, market liquidity, and intraday time periods. There are indications that the different compositions of informed and uninformed traders in terms of option moneyness cause this result. We also find that the information content of trade duration becomes greater when informed trading is more concentrated, liquidity is lower, option maturities are longer, and the market is more volatile.

JEL Classifications: G10, G15 Keywords: Informed trading; Intraday trades; Market microstructure model; Liquidity; Option moneyness; Price impact

Highlights • We devise a trade indicator microstructure model to study trade duration effects. • The price impact of a trade decreases (increases) with trade duration for OTM (ITM) options.

1 • Our result is robust despite controlling for volume, liquidity, and intraday effects. • The information content of trade duration varies across options trading traits.

1. Introduction What causes the different behavior of price movements? This paper examines an issue studied by various researchers in the field of financial economics, namely, the possible reasons for the differences in the relationship between the price impacts of trades and the inter-transaction times measured by durations between trades. Dufour and Engle (2000) find that “times when markets are most active are times when there is an increased presence of informed traders,” thus showing that the price impact of a trade decreases with trade duration. While subsequent studies such as those by Chen, Li, and Cai (2008), Furfine (2007), Liu and Maheu (2012), Ryu (2015b), Spierdijk (2004), and Xu, Chen, and Wu (2006) also arrive at the same conclusion, Beltran-Lopez, Grammig, and Menkveld (2012) and Grammig, Theissen, and Wünsche (2011) and report that the price impact increases with trade duration. These contrasting results may be caused by the different approaches/methodologies used by the authors and/or the different datasets employed to incorporate/describe the varying market environments being studied. Our research contributes to the debate by proposing that the difference in the degree of information asymmetry may explain these varied results. When it is highly likely that the trading counterparty will be informed, informed traders will not risk submitting orders that can earn profits but have less execution probability; rather, they will submit orders close to the fundamental value. Thus, the price may converge faster and fewer trades may be executed. However, the existence of more noise traders in the market ensures that informed traders can time their trades to maximize their profits. In other words, with less competition among informed traders, and if noise trading activity varies, informed traders can time their orders when there are more noise traders in the market and increase their profits. This paper relates to the strategic decisions of informed traders depending on the market structure and environment.1 Our research explains the different correlations between the price impact of a trade and the trade duration in terms of how informed traders change their trading behavior depending on the chances of the trading counterparty being informed. Motivated by this understanding and the inconsistent results in the previous literature, we hypothesize that the price effects and information roles of trade duration can differ depending on the

1 Lee, Eom, and Park (2013) show that investors spoof more frequently for stocks with higher volatility. Obizhaeva and Wang (2013) find that the optimal trade execution strategy relies on the market’s dynamic properties, such as the speed taken by the supply/demand to recover and return to its steady state.

2 traits and proportions of investors, or more specifically, the different compositions of informed and uninformed investors participating in the market. In particular, this study examines whether the trade duration plays different roles across options with varying degrees of information asymmetry on the same underlying asset. We posit that the trading environment and degree of informed trading significantly differ across option moneyness.2 To test this, we study the KOSPI 200 options market, wherein it is well known that the participation rates and compositions of investors significantly differ by option moneyness. More specifically, the proportion of informed versus that of uninformed investors in out-of-the-money (OTM) options exhibits clear distinct patterns compared to that in in- the-money (ITM) options. The KOSPI 200 options market provides an ideal setting for analyzing the information content of trade duration because all contracts are traded under the similar trading condition and environment (e.g., the same trading mechanism, underlying asset, and information source).3 More importantly, a strand of empirical studies, including Ahn, Kang, and Ryu (2008, 2010), Guo, Han, and Ryu (2013), Kang and Park (2008), Kim and Ryu (2012), Ryu (2011), Ryu, Kang, and Suh (2015), and Sim, Ryu, and Yang (forthcoming), consistently report that individual traders who are primarily utilitarian (or futile traders) account for a large volume in the KOSPI 200 OTM options trading, while

2 Prior research suggests that the extent of informed trading varies with option moneyness (Biais and Hillion, 1994). Though the previous studies agree that the option moneyness metric, which determines the degree of leverage effect and the option delta value, explains the cross-sectional distribution of the degree of informed trading, they disagree as to which option moneyness attracts informed trading to a larger extent. Textbook cases and classical studies on developed options markets, including Chakravarty, Gulen, and Mayhew (2004), Lee and Yi (2001), Pan and Poteshman (2006), and Stoll and Whaley (1990), explain that out-of-the-money (OTM) options provide higher leverage effect for options traders; therefore, informed investors attempting to maximize their profits by exploiting this leverage effect prefer investing in OTM options. In contrast, Ahn, Kang, and Ryu (2008, 2010), Kim and Ryu (2012), Ryu (2011), Ryu, Kang, and Suh (2015), and Sim, Ryu, and Yang (forthcoming) find that the information content of OTM options is quite low in an options market that is highly liquid but with speculative and noisy trading. They find that informed trading is more concentrated on in-the- money (ITM) options in this market and attribute this finding to the relatively high participation rates of experienced investors (e.g., foreign institutions) in ITM options trading. In an experimental setting, De Jong, Koedijk, and Schnitzlein (2006) also argue that ITM options can attract a higher portion of informed trading than other options because ITM options have high delta and sensitivity values, and as a result, they are the most highly related to underlying price changes. Johnson and So (2012) suggest some empirical predictions and conditions where high leverage (i.e., ITM) options have more information content than lower leverage (i.e., OTM) options. Analyzing the dataset of the Chicago Board Options Exchange (CBOE) options market, Kaul, Nimalendran, and Zhang (2004) claim that at-the-money (ATM) options, which have relatively higher liquidity and lower transaction costs, provide an optimal environment for informed trading. 3 We provide more details on the KOSPI 200 options market and fully explain why we focus on this index options market in Sections 2 and 3.

1 foreign institutional investors who are more experienced, and thus better informed, actively trade in the ITM options market.4 Thus, this qualitative difference between the OTM and ITM options trading allows us to analyze how the degree of information asymmetry affects the relationship between the price impacts of trades and their durations. In agreement with the reviewed literature, we observe that investor composition differs by option moneyness. Then, we analyze how our results differ by option moneyness after controlling for other considerations of options trading, such as trade volume, market liquidity, and intraday time periods. We find that the price impact of a trade decreases with trade duration (i.e., fast trading indicates informed trading) for OTM options, whereas it increases with trade duration (i.e., fast trading indicates uninformed and/or noisy trading) for ITM options. Our result may be attributed to the variation in the strategy of informed investors in the market environment. The varied characteristics of OTM and ITM options result in different trading environments, namely, the changing compositions of informed versus uninformed investors. These indicate that, when an investor decides to submit orders, her counterparty can differ by option moneyness. For the OTM options market, where the counterparty is likely to be a noise trader, an informed investor can wait until the market is active to maximize her profit, as in Admati and Pfleiderer (1988). Thus, the information content of a trade is more likely to exist when the market is active. The empirical results are also consistent with those of Easley and O’Hara (1992), who argue that informed traders split their trades, thus leading to frequent trades in the presence of information content. Recently, Collin- Dufresne and Fos (2014) use a variant of Kyle’s (1985) model to show that informed traders time their trades when noise trading activity is higher, and thus, more private information gets revealed. Collin- Dufresne and Fos (2015) also provide empirical evidence that activist investors time their trades when market liquidity is higher. In contrast, for the case of ITM options, it is more probable for the trading counterparty to be an informed trader. In an informational event, any submitted order placed far from the new value of the option is unlikely to be executed. Thus, orders that were already placed may be cancelled or revised because of the shift in the fundamental value of the option, and we may observe price discovery with less number of trades executed. Since the price impact of a trade (quote revisions and cancellations are not counted as trades) is measured when the transaction occurs, the time between two consecutive trades may be longer than the times when there are less revisions in quotes. In this

4 Utilitarian traders trade for non-informational reasons. They obtain benefits besides trading profits from trading. Futile traders believe that they are informed but fail to make trading profits because they have no informational advantages that would make them profitable traders (Harris, 2002). Based on these considerations, we assume that the trading of individuals is orthogonal to information, and thus, it does not vary with informed trading.

2 case, we achieve a positive correlation between the price impact and trade duration. The no-trade theorem by Milgrom and Stokey (1982) is an extreme case, wherein all traders are fully informed. Our empirical findings for the ITM options are also consistent with those of Parlour (1998), who shows that the crowding out of limit orders causes frequent trades but with less price impact. Our study also contributes to the literature by extending the trade indicator (structural microstructure) model of Madhavan, Richardson, and Roomans (1997) (hereafter, the MRR model) to examine the relationship between the price impacts of trades and their duration. The majority of studies that find a negative association between the price impact and trade duration depend on the vector autoregression (VAR) framework of Dufour and Engle (2000) or extended VAR models (e.g., Chen, Li, and Cai, 2008; Furfine, 2007; Xu, Chen, and Wu, 2006). The results of these studies might be contaminated because of the arbitrary trade event filtering process under the VAR models. Indeed, Grammig, Theissen, and Wünsche (2011) argue that the negative relationship between the price impact and the trade duration reported in previous studies is an artifact of the VAR models, and instead, they find a positive relationship between the two variables using a structural model framework. The models used by Dufour and Engle (2000) and the other related VAR models employ the midquote as the price, whereas the MRR model uses actual transaction prices. Changes in the midquote may occur without trade events, and filtered observations based on midquote changes in the VAR models can cause selection bias.5 Our extended model also effectively measures the information content of trade duration after controlling for trade volume and liquidity effects, which are normally overlooked in the previous literature. By estimating the market microstructure models using the high-quality transaction dataset of the KOSPI 200 options, we clearly observe that the information role of the trade duration differs by option moneyness, indicating that the different compositions of the informed and uninformed investors determine the price effect of trade duration. Our results continue to hold after controlling for the intraday time periods. More importantly, our conclusions remain unchanged under the extended structural model, which considers the different liquidity levels and order sizes in each option moneyness. The additional regression analysis also indicates that the information content of trade duration is greater when informed trading is more concentrated, liquidity is lower, option maturities are longer, and the market is more volatile. The rest of the paper is organized as follows. Section 2 discusses the characteristics of the KOSPI 200 options market and explains why it provides an optimal experimental environment to examine the issues raised in this study. Section 3 presents our study sample and the descriptive statistics as well as explains our methodology and provides the empirical findings. Section 4 presents

5 See Grammig, Theissen, and Wünsche (2011) for a detailed discussion on using midquote price and actual price changes.

3 the intraday analysis and shows how the information content of the duration between trades is related to various options market attributes. Section 5 concludes this study.

2. The KOSPI 200 options market The KOSPI 200 options market is one of the most active and liquid index options markets in the world. Until recently, its trading volume has been the largest in the world (https://fia.org). The KOSPI 200 options market has solidified its status as a leading options market partly through the synergistic effect of combined trading with the KOSPI 200 futures product, one of the most liquid index futures in the world.6 Panel A of Table 1 shows that the KOSPI 200 options dominate many other derivatives in terms of trading volume for each year from 2003 to 2005.

[Table 1 here]

Another interesting fact about the KOSPI 200 index options is that individual investors’ trades comprise a substantial portion of the trading volume in the options market.7 Panel B of Table 1 shows the trading volume of the KOSPI 200 options by investor types (i.e., domestic individuals, domestic institutions, and foreigners) for the sample period from January 2003 to June 2005. As shown in Panel B of Table 1, domestic individuals account for more than half the total trading volume (51%) during the sample period. This is in stark contrast with the summary statistics of other developed derivatives markets in which institutional investors dominantly trade. The KOSPI 200 options market is a purely order-driven market without a designated market maker. All orders are executed in a centralized electronic limit order book (CLOB) according to price and time priority rules. On a normal trading day, the KOSPI 200 options market opens at 09:00 and closes at 15:15. During the last 10 minutes of trading (from 15:05 to 15:15) and the hour-long pre- opening session (from 08:00 to 09:00), standing orders are matched and executed according to the uniform pricing rule. For the remaining intraday periods (from 09:00 to 15:05), submitted orders are either executed immediately or consolidated into the limit order book. Options traders can trade four

6 Practically, the KOSPI 200 futures serve as underlying assets of the KOSPI 200 options (Lee, Kang, and Ryu, 2015; Ryu, 2011; Sim, Ryu, and Yang, forthcoming). Since it is costly to construct a stock portfolio consisting of 200 underlying stocks, most professional investors use the futures as hedging and/or speculative tools related to options trading. In practice, many derivatives traders in the Korean market take positions in both the KOSPI 200 futures and the options markets, resulting in high co- movements between the two markets. 7 The dominant role of domestic individual investors is also common to the KOSPI 200 futures. Individual investors are known to be highly speculative and noisy in Korea’s index derivatives markets (Han, Hwang, Ryu, 2015; Kim, Ryu, and Seo, 2015).

4 different options contracts with varying maturities. The maturity dates are the second Thursdays of three consecutive near-term months and the month nearest to each quarterly cycle (March, June, September, or December). However, among the four contracts, only the nearest maturity contracts are actively traded. The basic quoting unit of the KOSPI 200 options market is the “point.” One point corresponds to 100,000 Korean Won (KRW). An analysis of the KOSPI 200 options market is likely to provide less contaminated results compared to those from other markets because the market has little friction and can absorb almost all the trading needs of derivatives investors. Bid-ask spreads are quite narrow, usually only a tick during the trading periods, and as the market depths are large, there exists enough liquidity for execution. Given the features of options contracts, short-sale constraints do not exist. If there is a short-sale constraint, negative information would be only partially reflected in the price because informed investors cannot freely submit sell orders if they do not own the assets (Basak and Makarov, 2011; Diamond and Verrecchia, 1987; Easton, Pinder, and Uylangco, 2013; Jones and Lamont, 2002; Lim, 2011; Le and Zurbruegg, forthcoming). As a result, under the short-sale restriction, the information content of trade duration would be lower. For instance, a long duration between trades under the short-sale constraint could result from either no information or negative information. The KOSPI 200 index options market provides an ideal setting to study the role of duration between trades for informational reasons as well. The market uses the CLOB system, and thus, we do not need to consider dark pools. Also, the analysis of informed trading in the index options market relies on more macroeconomic (market-wide) events, and hence the definition of informed trading is slightly different from the firm-specific information. The accuracy and speed of analyzing information is more related (Chung, Elder, and Kim, 2013; Ryu, 2015a) and the market is less related to firm- specific events where the results may be driven by asset- or firm-specific features. Furthermore, unlike the NYSE or NASDAQ, there are neither designated market makers nor upstairs markets in the KOSPI 200 options market, which ensures trader anonymity, and as a result, combined with the ample liquidity, informed investors implement their trading strategies with less market friction and obstacles. Most importantly, to test our hypothesis that the information content of trade duration differs by the composition of informed and uninformed investors participating in each market, we choose the KOSPI 200 options market because it has long been reported that investor participation rates significantly differ by option moneyness. Meanwhile, options with different moneyness values share the same underlying asset, their trading is based on the same information sources (i.e., the same macroeconomic sources and market-wide news), and their trading environments (e.g., transaction fees and taxes) are quite similar. Thus, the different implications of trading different moneyness options possibly originate from their liquidity and investor participation rates. In other words, domestic individuals, who are regarded as uninformed and noisy traders, actively trade the KOSPI 200 OTM options, which are highly speculative and liquid, whereas foreign institutions, which are regarded as

5 sophisticated and better-informed investors, tend to focus more on the less liquid ITM options. These patterns are not observed in the dataset of other developed derivatives markets, which do not even provide the needed information. Under this situation, if we appropriately control for option market characteristics such as market liquidity, we can attribute our finding that fast trading means informed (noisy) trading in the OTM (ITM) options to the different proportions of informed versus uninformed investors in the OTM and ITM options markets, and test our hypothesis using the high-quality dataset of the KOSPI 200 options.

3. Study sample and descriptive statistics We analyze the trade and quote (TAQ) data for the KOSPI 200 options from January 2003 to June 2005.8 The data contain information on transaction price and size, bid/ask spread, market depth, transaction time, initiating investor type, and whether the trade is initiated by a buyer or a seller. The richness of the data allows us to differentiate the composition of each investor group by option moneyness. This is not possible in most of the other options markets because of the lack of data concerning market participants in terms of option moneyness. Our ability to make these distinctions enables us to analyze how the different compositions of market players affect the information effects of duration between trades under a similar market condition. We define the option moneyness metric of call (put) options as S/K (K/S), where S is the current spot price and K is the exercise price. We exclude options contracts with moneyness metric values lower than 0.88 or higher than 1.12 because they have poor liquidity. We include all trades and quotes recorded during the continuous trading session of each day in the study sample and exclude trades and quotes during the pre-opening and closing sessions from the study sample. We also include only the intraday transaction data of the nearest maturity contracts in the sample because the liquidity of longer term maturity options is extremely low, which indicates that speculative and short-term trading prevail in the KOSPI 200 options market. Finally, for each trading day, we exclude option contracts from the sample if there are fewer than 10 transactions during that day. The KOSPI 200 options have a monthly maturity cycle whereas the KOSPI 200 futures, which are not only closely related to the options but also serve as their underlying assets, have a quarterly maturity cycle. Investor behavior may exhibit somewhat different patterns around maturity

8 After the sample period, the trading environment and properties of the KOSPI 200 options market remain unchanged. The options market is still highly liquid, market friction is relatively low, individual trades explain a substantial portion of the options trading, and the properties and trading motives of individual investors are not changed. Therefore, we believe that our baseline case applies to more recent periods too. Another reason for choosing our sample period is that there were no trading halts and hardly any missing data during the period, conditions that are required for the reliable estimation of our structural model.

6 dates of derivatives (Chang and Lin, 2015). To eliminate the possible maturity effects and obtain reliable estimation results, we construct 10 options series, each covering a three-month period. The first options series covers January to March of 2003, the second series spans from April to June of 2003, and so on. For each options series, we define six moneyness categories: 0.88-0.93 (M1, the most deep-out-of-the money options), 0.93-0.96 (M2), 0.96-0.98 (M3), 0.98-1.0 (M4), 1.0-1.04 (M5), and 1.04-1.12 (M6, the most deep-in-the-money options). Table 2 shows the mean values of the number of trades (Trade), number of contracts (Contract), weighted average transaction prices (Price), average duration between trades (Duration), market depth (Depth), and the fraction of trades initiated by each investor group (the domestic individual investor group, domestic institutional investor group, or foreign institutional investor group) for each moneyness category across the 10 options series.9 Price is measured in points and Duration is measured in seconds. Depth is measured as the sum of all orders on the best five outstanding bids and asks immediately before each transaction. Panels A and B of Table 2 show the results for call options and put options, respectively. For both call and put options, the trade duration is the shortest and the number of transactions is the largest in slightly OTM options with moneyness between 0.98 and 1.0 (i.e., M4). Similarly, trading volume measured as the number of contracts is the highest in OTM options with moneyness between 0.93 and 0.96 (i.e., M2). These results indicate that OTM options are generally more liquid than ATM (at-the-money) and ITM options in the KOSPI 200 options market. Not surprisingly, nominal option prices monotonically increase with option moneyness. We confirm that there are more foreign institutional investors and relatively fewer individual investors in the ITM options than the OTM options. Considering that previous studies, including Ahn, Kang, and Ryu (2008, 2010), Kang and Park (2008), Kim and Ryu (2012), Ryu (2012, 2015a), and Sim, Ryu, and Yang (forthcoming), analyze a similar microstructure dataset (i.e., the TAQ dataset of the KOSPI 200 index derivatives) and show that the fraction of investor types is highly and directly related to the degree of informed trading, we conjecture that informed trading is more concentrated in the ITM options than in the OTM options in the KOSPI 200 options market.

[Table 2 here]

We posit that the proportions of investors differ for the following reasons. Most individuals are short-term investors and day traders, and they are characterized as futile and speculative investors. Individual investors in the KOSPI 200 options market generally do not use index derivatives as

9 The number of trades reported in Table 2 is slightly smaller than the actual number of transactions because we exclude all transaction records for a given day from the sample if there are defects in the raw data on that day.

7 hedging tools or trading vehicles for long-term portfolio management (Ryu, 2011, 2015a). The extremely high leverage effect provided by the OTM options can attract these speculative but noisy investors. Since only short-term (i.e., less than a month) maturity options are actively traded in the KOSPI 200 options market, OTM options are less likely to become in-the-money before the maturity dates, and thus, their nominal prices are very low. Noisy individuals prefer investing in OTM options, which they view as similar to buying a lottery. These speculative, and somewhat irrational, characteristics of individual investors (also seen in Table 2) cause them to heavily trade the OTM options. In contrast, the high sensitivity of ITM options due to their high delta values can attract informed investors because the ITM options and underlying assets show similar movements (De Jong, Koedijk, and Schnitzlein, 2006; Johnson and So, 2012). Institutional trades are related to hedging, profit-making, and portfolio management intentions, which lead institutional (normally, better- informed) investors to trade in ITM options, which are more sensitive to the underlying asset price movements than OTM options. Meanwhile, the high nominal prices of ITM options act as an effective barrier for individual investors with less wealth and trading experience. These aspects make the investor compositions in the ITM and OTM options significantly different, thus motivating us to investigate the different price behaviors by option moneyness.

4. Methodology and empirical findings 4.1. Methodology The structural MRR model assumes that an incoming trade influences asset price changes in two ways: the permanent price impact due to informed trading and the temporary price effect due to uninformed and/or liquidity trading. Most structural models, such as that of Huang and Stoll (1997), are built on the notion that market makers set up their bid and ask prices to recover various market- making costs (e.g., inventory-holding, order-processing, and adverse-selection costs). However, the MRR framework is flexible and does not explicitly consider these costs. Therefore, the MRR model and its extensions could be applied to any market, including order-driven markets where there is no designated market maker. Another advantage of the MRR model is its robustness. The MRR model yields quite reliable estimates as long as the trade direction (i.e., buy or sell) is correctly specified.10

10 For these reasons, many empirical studies on market microstructure, such as Ahn, Kang, and Ryu (2008, 2010), Angelidis and Benos (2009), Bessembinder, Maxwell, and Venkataraman (2006), Chakravarty, Jaon, Upson, and Robert (2012), Green (2004), Gregoriou (2015), Hagströmer, Henricsson, and Nordén (2012), Han and Zhou (2014), and Ryu (2011, 2013a, 2013b), adopt the structural MRR model framework. Since the estimates of the MRR model critically depend on the trade direction (i.e., whether an incoming trade is buyer- or seller-initiated), the model is classified as a trade indicator model. Our dataset provides the exact and explicit buy/sell classification code for

8 In addition, the MRR model uses the generalized method of moments (GMM) technique, which is free from distributional assumptions and robust to heteroskedasticity and serial correlation in the error term. We use the following duration-dependent MRR (D-MRR) model, in which changes in the fundamental value of an asset depend on the trade duration, unexpected portion of incoming trades, and updates to public information:

μt – μt–1 = (α0 + α1ln(Tt))(xt – E[xt|xt–1]) + εt, (1)

where xt is equal to 1 for buyer-initiated trades and –1 for seller-initiated trades, μt is the post-trade expected fundamental value of the asset, εt is a serially independent error term that represents innovation in public beliefs, and Tt is the duration between two consecutive trades at time t–1 and time t. In Equation (1), α0+α1ln(Tt) represents the permanent price impact of an incoming trade at time t, which measures the degree of informed trading. For this permanent price impact of the trade at time t, α0 is the portion that is independent of trade duration, α1ln(Tt) is the portion that is dependent on trade duration, and α1 captures the information content of trade duration, which is our main interest. A positive α1 implies that, as the duration between trades becomes longer, the permanent price impact of the trade becomes larger. If α1 is negative, it implies that, as the duration between trades becomes shorter, the price impact of the trade becomes larger. The larger the absolute value of α1, the greater the impact. The value of the conditional expectation, E[xt|xt–1], is equal to ρxt–1, where ρ is the serial correlation of the trade indicator variable.

The transaction price, Pt, is determined by the post-trade fundamental asset value (μt), the temporary price effect component of the incoming trade ((β0+β1ln(Tt))xt), and the residual (ξt):

Pt = μt + (β0 + β1ln(Tt))xt + ξt. (2)

In Equation (2), β0+β1ln(Tt) measures the temporary price effect of the trade at time t, which is independent of changes in the fundamental value. If a trade were not made by an informed trader or if the information quality of the trade is low, the trade-induced price change will be temporary. The price will soon return to the fundamental value. For this temporary price effect of the trade at time t,

β0 is the portion independent of trade duration, β1ln(Tt) is the portion dependent on trade duration, and

β1 captures the effect of trade duration on the temporary price. The residual ξt captures the effects of rounding errors from price discreteness and discontinuity of the quoting unit. From Equations (1) and

each trade, which enables an exact estimation of the model.

9 (2), we obtain the following equation:

Pt – Pt–1 = (α0 + β0)xt – (ρα0 + β0)xt–1 + (α1 + β1)xtln(Tt) – β1xt–1ln(Tt–1) – ρα1xt–1ln(Tt) + υt,

where υt = εt + ξt – ξt–1. (3)

Combining Equation (3) and the information regarding the serial correlation in the trade indicator variable, we set up the following moment equations for the GMM estimation.

푥푡−1(푥푡 − 휌푥푡−1) 휐 − 휐 푡 0 푥 (휐 − 휐 ) 푡 푡 0 E 푥푡−1(휐푡 − 휐0) = 0. (4) 푥푡푙푛푇푡(휐푡 − 휐0) 푥푡−1푙푛푇푡−1(휐푡 − 휐0) [ 푥푡−1푙푛푇푡(휐푡 − 휐0) ]

We estimate five model parameters (α0, β0, α1, β1, and ρ) simultaneously using these moment equations, where υ0 is a constant drift term. The first equation shows the information on the serial correlation in the trade indicator variables. The second equation reflects that the constant drift term is set to the average pricing error. The next five normalizing equations are constructed from the ordinary least squares (OLS) residuals implied by Equation (3).

4.2. Empirical findings Panel A (B) of Table 3 shows the estimation results for call (put) options in each moneyness category. The table reports the mean values of estimated parameters (α0, α1, β0, β1, and ρ) across the 10 options series and their t-statistics. The table also reports the mean values of the permanent price

impact as a percentage of the underlying option price (PIi), the temporary price effect as a percentage of the corresponding option price (TE={(β0+β1푙푛푇)/Price}×100), the implied spread as a percentage of the corresponding option price (ISi=2(PIi+TE)), and the relative magnitude of the permanent price impact (γi=PIi/(PIi+TE)×100). 푙푛푇 denotes the average trade duration in each sample, and Price denotes the weighted average value of options prices.

[Table 3 here]

The permanent price impact, PIi, is measured in two ways depending on whether it is adjusted by the estimates for ρ (i=A) or not (i=U). We note the role of the serial correlation, ρ, of the trade indicator variables and the equation, E[xt|xt–1] = ρxt –1. Let p be the probability that the current

10 period’s direction of trade is the same as the previous trade’s. Then, E[xt|xt–1] = pxt–1– (1 – p)xt–1; so, we have p = (1 + ρ)/2. From this equation and Equation (1), we show that the price impact incurred by the incoming trade, (α0 + α1ln(Tt))(xt – E[xt|xt–1]), becomes (α0 + α1ln(Tt))(1 – ρ) when the direction of trade is the same as that of the previous trade, and (α0 + α1ln(Tt))(1 + ρ) otherwise. Since the price impact should be the weighted average of the two, p(α0 + α1ln(Tt))(1 – ρ) + (1 – p)(α0 + α1ln(Tt))(1 + ρ)

= (α0 + α1ln(Tt))(1 – ρ)(1 + ρ). In Table 3, we report the price impact in two ways, i) when i=U

(Unadjusted), PIU={(α0+α1푙푛푇)/Price}×100, ignoring the effect of ρ, and ii) when i=A (Adjusted), the

ρ-adjusted permanent impact PIA={(α0+α1푙푛푇)(1–ρ)(1+ρ)/Price}×100. We also present the implied spread and its relative portion explained by the informed trading (i.e., γ) using both measures of price impact.

Except for the values of α0 for the most deep-in-the-money ITM option (M6), all the model parameter estimates are statistically significant. For example, in the case of call options for which moneyness ranges from 0.96 to 0.98 (see column M3 in Panel A of Table 3), the average estimates of

α0, α1, β0, and β1 are 0.00055, –0.00011, 0.00334, and 0.00014 points, respectively. On average, the unadjusted permanent price impact (PIU) equals 0.072%, or with adjustment (PIA), 0.056% of the option price, and the temporary price effect (TE) is equal to 0.658% of the option price. The model implied spread (IS) is 1.460%, or 1.427% of the option price, and the values of γ indicate that about 10% and 7.9% of the implied spread is due to informed trading without and with adjustment, respectively. Similar to the findings of Ahn, Kang, and Ryu (2008, 2010) and Ryu (2011), we note a monotonically increasing pattern across option moneyness for almost every parameter (Table 3). The estimated parameters are directly affected by options prices, the relative proportion of informed trading, and liquidity, all of which exhibit monotonic patterns across the option moneyness. The estimates related to informed trading (i.e., γ and PI) generally increase with options moneyness, which reflects the increasing portion of informed trading as options approach the in-the-money direction. The higher estimates in the ITM options are also consistent with results seen in the experimental setting of De Jong, Koedijk, and Schnitzlein (2006) and in developed markets (Johnson and So, 2012); notably, they are exactly consistent with the findings of previous research on market microstructure using the KOSPI 200 options data (Ahn, Kang, and Ryu, 2008, 2010; Kim and Ryu, 2012; Ryu, 2011; Ryu, Kang, and Suh, 2015; and Sim, Ryu, and Yang, forthcoming), which report that the information content of OTM (ITM) options is relatively low (high) and attribute this finding to the higher participation rates of experienced investors in ITM options trading. The findings that the permanent price impact (PI) and the relative portion of permanent price impact in the implied spread (γ) of ITM options are greater than those of OTM options indicate that the percentage of trades made by informed traders (institutional and foreign investors) increases, rather than decreases, with option moneyness. This contrasts with other studies (e.g., Pan and Poteshman, 2006) using the US options market data, which argue that informed traders are more

11 likely to trade OTM options than ITM options. The results in the KOSPI 200 options market reflect the market lore that while OTM options traders are speculative, they are normally noisy, uninformed, and myopic, which when aligned with the findings in Table 2, support our earlier conjecture that the informed trading is relatively more concentrated in the ITM options trading than in the OTM options trading. We also find that the implied spread (IS) monotonically decreases with option moneyness, indicating that the relative spread accounts for a substantial portion of transaction costs in trading OTM options, considering the small nominal prices of the OTM options. Also, it indicates that the effect of moneyness on the temporary price effect outweighs the corresponding effect on the permanent price impact.

Importantly, the results show that the estimates for α1 are highly significant in all option moneyness categories, which means that incorporating the trade duration into the model is an effective way to estimate the permanent price impacts and to measure the information content of trades. The size of the estimates for α1 increases monotonically with option moneyness, indicating that the information content of trade duration increases with option moneyness. In particular, the estimates are negative and significant for OTM options (see columns M1, M2, M3, and M4 in Table 3), but positive and significant for ITM options (see columns M5 and M6 in Table 3). In contrast to the estimates for α1, those for β1 are significantly positive across all option moneyness categories, indicating that the temporary price effect of a trade increases with duration between trades. Considering that the long duration indicates illiquidity, this result should not come as a surprise because the non-informational cost of trading decreases with the increase of liquidity (Demsetz, 1968).

The negative and significant estimates for α1 in the OTM options indicate that liquidity providers make a larger price adjustment after a trade (denoting the larger price impact of a trade) when OTM options are more actively traded. In contrast, the positive and significant estimates for α1 in the ITM options indicate that liquidity providers make a larger price adjustment after a trade when ITM options are less actively traded. The different compositions of traders in the OTM and ITM options explain why the relationship between the trades and the price impact of a trade differs for these options. As we introduced, previous studies on market microstructure using the KOSPI 200 options data report that individual investors, who are largely regarded as futile or utilitarian traders, account for a large portion of OTM options trading. In contrast, they also report that institutional and foreign investors dominate ITM options trading in Korea. We find a similar pattern of the composition of traders (see Table 2), and our findings may be summarized as follows: fast trading means informed trading in OTM options and noisy and/or uninformed trading in ITM options. Our findings for the ITM options can be interpreted in the following way. Now consider that each investor type has a certain level of trading activity during the non-information event period. Assume that an information event occurs at time t. Because individual investors are mostly futile or

12 utilitarian traders, their trading is orthogonal to information. For the other types of investors, suppose that some (“better-informed”) investors can interpret the value implication of the new information for an event better than other (“less-informed”) investors.11 To fully exploit this information advantage, informed investors try to trade more. However, knowing that they could lose to better-informed investors, the less-informed investors may stop trading if the probability of trading with better- informed (e.g., foreign institutional) investors is higher than the probability of trading with domestic individual (i.e., uninformed futile or utilitarian) investors. As noted above, institutional investors dominate in ITM options trading, and thus, these investors are more likely to trade with other institutional investors than with individual investors. Hence, some of these investors may stop trading for fear of losing to better-informed investors, or their orders may not get executed if their bid (ask) orders are underpriced (overpriced) compared to the fundamental value. In this scenario, trading volume during the information event period could be smaller than that during the non-event period. Simultaneously, the price impact of a trade during the information event period would be greater than that during the non-event period because of the informed trading triggered by the information event at time t. These considerations suggest a larger price impact in less active markets, as we observe in the ITM options trading. In contrast, domestic individual investors dominate in the OTM options trading, and thus, when institutional investors trade, they are more likely to trade with individual traders than with other institutional (especially, foreign institutional) investors. Knowing that their trading counterparties are most likely to be futile or utilitarian traders, institutional investors may trade more after the information event to fully exploit their information advantage. In this scenario, the trading volume during the information event period could be larger than that during the non-event period. At the same time, the price impact of a trade during the information event period would be greater than that during the non-event period because of the informed trading triggered by the information event at time t. In addition, informed investors may choose to trade during high activity periods to reduce the price impact of their trades by camouflaging their trading (Admati and Pfleiderer, 1988). These considerations suggest a larger price impact in more active markets, as we observe in the OTM options. The large temporary price effect (TE) of OTM options provides another potential explanation for the negative relationship between the price impact and trade duration. Suppose that informed investors in OTM options trade less when TE is large to minimize trading costs. It implies that informed traders are more likely to trade OTM options (and the price impact is likely to be greater)

11 Alternatively, some traders are aware about both the occurrence of the information event and its value implication, while other traders do not know the value implication of the event (even though they know that the information event has occurred).

13 when the trade duration is shorter (i.e., α1<0) because the trade duration increases with TE (i.e., β1>0). This explanation may not apply to ITM options because TE is much smaller (or even negative) for ITM options. Kim and Verrecchia (1994) maintain that public information disclosures (e.g., earnings announcements) provide information that allows some traders to make better judgments about a firm’s performance than other traders, increasing the degree of information asymmetry among traders during the disclosure period.12 The authors also predict that greater informed trading during the disclosure period may lead to an increase in trading volume despite the reduction in liquidity. This line of argumentation applies only to a market in which either a) all informed traders are considered homogeneous or b) informed traders are more likely to trade with uninformed traders than with better- informed traders (e.g., the OTM options market in Korea). Once we allow for heterogeneously informed traders, the arrival of new information may lead to both lower liquidity and smaller trading volume (e.g., the ITM options market in Korea).

4.3. Controlling for volume and liquidity The composition of traders is not the only difference between different moneyness in options. Normally, the levels of market liquidity substantially differ by option moneyness, and the KOSPI 200 options market is no exception. Further, market liquidity affects the strategic decision making process for investors (Arakelyan, Rubio, and Serrano, 2015; Capuano, 2006), and liquidity is one of the major considerations for options traders in choosing their trading vehicle (Kaul, Nimalendran, and Zhang, 2004). Thus, we control for the liquidity effect, which exhibits different patterns by option moneyness, as seen in Table 2. While the quoted bid-ask spread may be a useful measure in other financial markets, in the KOSPI 200 options market, trading is highly active and most of the observed spreads are equal to the minimum tick size in the majority of the periods, which indicates that the observed spreads are not an appropriate measure for market liquidity in the options market. Accordingly, to control for the market liquidity, we incorporate alternative measures for liquidity into the D-MRR model. To consider the liquidity effect, we control for market depth in our analysis. As shown in Table 2, the market depth monotonically decreases by moneyness. Our results from the D- MRR model may be attributed to this issue rather than the difference in the proportions of investors.

We calculate the market depth (Deptht-) as the total sum of orders in the five best bids and asks on the limit order book just before each trading time t and incorporate it into our structural model.

12 Subsequent studies, such as Lee, Mucklow, and Ready (1993), Coller and Yohn (1997), Yohn (1998), and Bhat and Jayaraman (2009), find evidences that are generally consistent with the prediction of Kim and Verrecchia (1994).

14 We also acknowledge that prior research suggests that the information content of a trade varies with trade volume. Some studies find that large trades have greater information content than small trades (Easley and O’Hara, 1987; Easley, Kiefer, and O’Hara, 1997a, 1997b; Holthausen, Leftwich, and Mayers, 1987, 1990; Lin, Sanger, and Booth, 1995). Others argue that informed traders fragment their trades to camouflage their trading motives and reduce the price impact (Alexander and Peterson, 2007; Barclay and Warner, 1993; Chakravarty, 2001; Chou and Wang, 2009; Chung, Chuwonganant, and Jiang, 2008; Huang and Masulis, 2003; Kyle, 1985; Lin, 2014). As these two competing findings suggest, informed investors could trade a large number of contracts in a given period of time by submitting either a large number of small orders or a small number of large orders. If informed traders were to consider trade volume as their main decision variable, the trade duration per se would be just a by-product of their trade volume decision. Hence, it is possible that the duration effect reported in the previous section may simply reflect the (inverse) impact of trade volume on price. Thus, we also control for the volume effect by using the extended model. Further, we provide additional evidence on whether larger trades exert a greater or smaller impact on price. By incorporating the depth measure as well as trade volume into the D-MRR model, we construct the following extended model (Equations (5) to (8)) and examine the role of trade duration on the price discovery process after controlling for the liquidity effects through this extended model.

Δμt = μt – μt-1 = (α0 + α1ln(Tt) + α2√Vt + α3Deptht-)(xt – E[xt|xt–1]) + εt, (5)

where Vt is the trade volume of an incoming order at time t, (α0+α1ln(Tt)+α2√Vt+α3Deptht-) measures the permanent price impact of the trade at time t, and all other variables are the same as previously defined in Equation (1). For the permanent price impact, α0 is the portion that is independent of trade duration and trade volume, α1ln(Tt) is the portion that depends on trade duration, α2√Vt is the portion

13 that depends on trade volume, and α3Deptht- is the part that depends on market depth. The time subscript (t-) of the depth measure indicates that it is measured immediately before the incoming trade

13 Although earlier studies (e.g., Glosten and Harris, 1988; Kyle, 1985) suggest that price impact is linear in volume, we capture the trade volume effect by a square root function following the recent empirical studies of Ahn, Kang, and Ryu (2010) and Angelidis and Benos (2009), which show that the price impact functions are best described by the square root function. We can further extend the model by incorporating the quoted spread (Spreadt-) into it. However, as we explained earlier, adding the observed spread has some empirical defects. Further, the computational burden of including an additional variable is quite high whereas its empirical implication is not significant. The estimated result of the extended model with observed bid-ask spreads provides the same conclusion about the role of trade duration. For brevity, we do not report the result in this paper. The results are available upon request.

15 at time t. The temporary price effect consists of four parts: the duration- and volume-independent portion (β0), the duration-dependent portion (β1ln(Tt)), the volume-dependent portion (β2√Vt), and the depth-dependent portion (β3Deptht-):

Pt = μt + (β0 + β1ln(Tt) + β2√Vt + β3Deptht-)xt + ξt. (6)

Combining Equations (5) and (6), we obtain the following expression for price changes:

ΔPt = (α0 + β0)xt – (ρα0 + β0)xt–1 + (α1 + β1)xtln(Tt) – β1xt–1ln(Tt–1) – ρα1xt–1ln(Tt)

+ (α2 + β2)xt√Vt – β2xt–1√Vt-1 – ρα2xt–1√Vt

+ (α3 + β3)xtDeptht- – β3xt–1Deptht–1 – ρα3xt–1 Deptht- + υt, (7)

where υt = εt + ξt – ξt-1. We call this extended MRR model including the trade duration, volume, and liquidity measured by the depth as the DVL-MRR model. The GMM estimation equations of the DVL-MRR model are given in Equation (8).

푥푡−1(푥푡 − 휌푥푡−1) 휐 − 휐 푡 0 푥 (휐 − 휐 ) 푡 푡 0 푥푡−1(휐푡 − 휐0) 푥푡푙푛푇푡(휐푡 − 휐0) 푥푡−1푙푛푇푡−1(휐푡 − 휐0) 푥푡−1푙푛푇푡(휐푡 − 휐0) E = 0. (8) 푥 √푉 (휐 − 휐 ) 푡 푡 푡 0 푥푡−1√푉푡−1(휐푡 − 휐0)

푥 √푉 (휐 − 휐 ) 푡−1 푡 푡 0 푥푡퐷푒푝푡ℎ푡−(휐푡 − 휐0) 푥푡−1퐷푒푝푡ℎ푡−1−(휐푡 − 휐0) [ 푥푡−1퐷푒푝푡ℎ푡−(휐푡 − 휐0) ]

Table 4 presents the results of the DVL-MRR model by option moneyness. The table reports the mean values of the estimated parameters (α0, α1, α2, α3, β0, β1, β2, β3, and ρ) across the 10 options series and their t-statistics. All parameter estimates shown in Table 4 are statistically significant. The table also reports the mean values of the permanent price impact as a percentage of the underlying option price, the temporary price effect as a percentage of the underlying option price, the implied spread as a percentage of the underlying option price, and the proportion (in %) of the permanent price impact in the implied spread.

16

[Table 4 here]

Table 4 shows that the estimates for α1, which capture the information effects of trade duration in the DVL-MRR model, exhibit the same patterns across option moneyness as those shown in Table 3, indicating that the information role of trade duration remains the same after controlling for the effects of trade volume and liquidity. The results show that the estimates for α2, which capture the information content of trade volume, are significantly positive across all option moneyness categories, indicating that large trades are more informed than small trades. We can interpret this result as follows. In a highly liquid market, such as the KOSPI 200 options market, investors tend to submit large orders without fragmenting them because they do not have to worry about adverse price movements which often arise for large orders under the deficiency of liquidity. Unlike in illiquid markets, where informed investors split their orders to camouflage their identity and reduce adverse price movements, the KOSPI 200 options traders can make large trades by enjoying the ample liquidity provided by the market. This can make large trades more informed than smaller trades in the options market. We also find that the estimates for β2 are all negative, which reflects the possible effect of economies of scale in the temporary price effect component. The DVL-MRR model, which considers liquidity effects, provides more reliable results than the D-MRR model. For example, while some estimates for α0 are somewhat counterintuitively negative for the D-MRR model, the DVL-MRR model yields significant and positive estimates for α0 for all option moneyness and types. The price impact estimates from the DVL-MRR model also exhibit similar patterns of the relative proportion of trades by foreign institutional investors who have the information advantage in the KOSPI 200 options market. The findings that the price impacts (proxy for the degree of informed trading) and participation rates of foreign institutional investors (who are normally better-informed investors than individual investors) exhibit similar variations across option moneyness also support the informativeness of foreign institutions, which is consistent with the previous findings of research pertaining to market microstructure data on the KOSPI 200 options market, as we have previously documented. Through the estimation of the adjusted DVL-MRR model (i.e., the DV-MRR model or DL- MRR model), we confirm that our conclusions on the information content of trade duration continue to hold when we control either the trade volume or the market depth. We find that the estimates for α1 show the same pattern even when we control for only trade volume or only market liquidity measured by depth. For brevity, we do not include our results here. Furthermore, we see consistent results even

17 when we include the model-implied spread in Equations (9) and (10).14 It shows that our contention of differing price impacts depending on the degree of information asymmetry still holds after controlling for market liquidity as well as trade volume.

5. Further analysis 5.1. Intraday analysis Prior studies (e.g., Chung, Van Ness, and Van Ness, 1999; Mclnish and Wood, 1992) find strong intraday patterns in market microstructure variables (e.g., the bid-ask spread and the size of the price impact). This section provides further evidence on the information content of trade duration from intraday analysis. Table 5 reports the mean values of the permanent price impact parameter α1 and the temporary price effect parameter β1 and their t-statistics across 17 intraday trading intervals within each moneyness category.15 Panels A and B show the results for call and put options, respectively. We divide the trading sessions into 30-minute intervals except for the beginning and ending intervals, which are set shorter considering that informed trading and/or liquidity provision can be concentrated in these intervals (Admati and Pfleiderer, 1988; Ahn, Cai, Hamao, and Ho, 2002; Angelidis and Benos, 2009; Chang, Hsieh, and Lai, 2013; Huang, 2004; Huang and Stoll, 1997; Madhavan, Richardson, and Roomans, 1997; Ryu, 2011).

[Table 5 here]

The results in Table 5 show that within each intraday interval, most of the estimates for α1 and β1 are significant and exhibit patterns across moneyness categories that are similar to those reported in Tables 3 and 4, indicating that the variation in the information content of trade duration across moneyness categories is similar throughout the trading day. Although we do not find systematic intraday patterns for the estimates for α1 in the deep OTM and ITM options (columns M1, M2, and M6), the estimates during closing intervals, which begin at 14:45, are much larger than the corresponding figures during other earlier intraday intervals in other moneyness categories (see columns M3, M4, and M5), which are more liquid. We find similar results for the permanent price impact (PI) and the relative portion of the permanent price impact (γ).16 A possible interpretation of

14 As noted earlier, quoted spreads in this market are not a meaningful indicator since the sizes of the bid-ask spreads mostly equal the minimum tick. Thus, we use the model-implied spread we obtain from the (extended) MRR model. 15 For brevity, we only report duration-related parameters (α1 and β1) from the D-MRR model. The results are qualitatively identical when we use the DVL-MRR model. 16 For brevity, we do not include the tables containing these estimates in our paper. They are available from the authors upon request.

18 these results is that informed traders trade more actively before the market closes to fully exploit their informational advantage for the day.

We also find that the estimates for β1 during the closing intraday intervals (beginning at 14:45) are mostly larger than the corresponding figures during the earlier intraday intervals in the moneyness categories of M3, M4, M5, and M6. These results indicate that, during the closing market period when uninformed investors actively trade, and trades’ unwinding daily positions dominate, the temporary effect of trades becomes more important; specifically, the effect of trade duration on the temporary effect spread component tends to increase. We argue that informed and uninformed trader clustering before the market closes supports the U-shaped intraday trading volume behavior of Jain and Joh (1988). We do not observe high trading volume during market opening hours because standing orders are matched and executed according to the uniform pricing rule from 8:00 and 9:00. Admati and Pfleiderer (1988) show that the concentrated trading volume is a result of liquidity trading and induced informed trading activity. Since the individual traders tend to clear their positions before the market closes, they supply liquidity, and this induces informed traders to trade near closing hours as well.

5.2. Informativeness of the duration between trades and options market variables

The previous subsection shows that the estimates for α1 and β1 exhibit intraday patterns, suggesting that the information content of trade duration may be related to other market microstructure variables with similar intraday patterns. In this subsection, we examine which option market variables explain the information content of trade duration and whether our findings remain consistent after controlling these variables. Accordingly, we construct one-hour-long intraday trading intervals for each trading day, pooling option types (calls or puts), and option moneyness to estimate the D-MRR model for each intraday interval. In each interval, the estimated D-MRR model’s results and collected option market variables yield various observations such as moneyness, trade duration and its information content, price impact, trade volume, time to maturity, and volatility. Excluding option series or intervals that do not show convergence leaves us with 6,209 observations for the regression analysis. Using these variables and the observations collected from the intraday intervals, we estimate the following regression model:

Ii = δ0 + δ1Moneynessi + δ2Durationi + δ3PIi + δ4Volumei + δ5TTMi + δ6Volatilityi + δ7Intrai + εi, (9) where i denotes the ith one-hour-long intraday trading interval of each trading day in the pooling sample. Moneyness denotes the moneyness category, Duration is the average log trade duration

(ln(푇̅)), PI is the average permanent price impact (i.e., PI = α0+α1ln(푇̅)), Volume is the square root of the average trade volume (sqrt(푉̅)), TTM is the time to maturity, Volatility is the realized return

19 volatility calculated using five-minute log returns, and Intra denotes the intraday dummy variable, which equals 1 if the i-th observations are included in the current one-hour-long intraday interval and

0 otherwise. δ0 is a constant, and ε denotes the error term. Motivated by Chen, Li, and Cai (2008) and Furfine (2007), we define the measure for the information content of trade duration as I, which is determined by the dispersion of trade duration and captures the relative information content from fast

10th 90th trading to slow trading. The dependent variable I is defined as (α0+α1lnT ) – (α0+α1lnT ), where T10th and T90th denote the 10th and 90th percentile values of trade duration in each interval.17 Table 6 shows the estimated regression result. Overall, the liquidity variables (Duration and Volume) and the informed trading proxy (PI) significantly explain the information content of trade duration. The explanatory power of trade duration remains consistent after controlling for the option market variables, including liquidity and informed trading measures. The negative and significant coefficients on Moneyness indicate that the information content of trade duration is greater for the OTM options than for the ITM options, which is consistent with our finding that fast trading means informed trading in the OTM options and noisy trading in the ITM options. The significantly positive coefficient on Duration indicates that the information content of trade duration is larger for infrequently traded options. The negative coefficient on Volume indicates that the trade duration contains more information for low-volume options. The signs of the estimated coefficients for these two liquidity measures, Duration and Volume, reflect that the trade duration carries relatively little information when the market is already highly liquid (i.e., fast trading and large trades dominate markets). The coefficient on PI is positive and significant, which indicates that trade duration conveys more information for options with greater informed trading.

[Table 6 here]

We include the variable Volatility into the model because market volatility affects the price discovery process in informed trading (Wang, Chang, and Lee, 2013). The coefficient on Volatility is significantly positive, meaning that the information content of trade duration is greater when the market is more volatile. The significance of the estimate coefficient on TTM reflects that investor behavior may exhibit somewhat different patterns depending on the remaining maturities of derivatives (Chang and Lin, 2015). The coefficient on TTM is also positive, which indicates that the trade duration sheds information as the maturity date approaches. This finding is plausible in that, as

17 Whether we use unadjusted or adjusted price impact measures (i.e., PIU or PIA), the regression analysis provides similar results and interpretations. The measure I captures the relative information content from fast trading to slow trading. The manner in which the trade durations are dispersed directly affects its information content.

20 opposed to information-based trading, other trading motives such as unwinding and closing positions govern options trading just before the maturity dates.

6. Summary and concluding remarks We examine the information content of the duration between trades by analyzing the intraday data of the KOSPI 200 options. We develop trade indicator models that include both the duration between trades and trade volume as key variables, and analyze how the price impact of a trade varies with these variables. Our empirical results show that for OTM options, the price impact of a trade decreases with the duration between trades. For ITM options, however, we find that the price impact increases with the duration between trades. We interpret these results as evidence that whether the price impact of a trade is greater in fast or slow markets depends on the composition of informed and uninformed traders and the distribution of informed traders across information quality. We also find that the information content of the duration between trades is greater when informed trading is concentrated, liquidity is lower, the maturity date is further away, and the market is more volatile. Our results have important implications for both investors and regulators. For uninformed individual traders, the different information contents of trade duration between ITM and OTM options suggest that they may avoid trading OTM and ITM options during high and low activity periods, respectively, to minimize their loss to informed traders (i.e., domestic and foreign institutional investors). Recently, the Korean government and the Korea Exchange (KRX) have attempted to regulate Korea’s index derivatives market to address concerns about excessive trading by individual investors. The majority of individual investors are known to be net losers in Korea’s derivatives markets. To protect them from predatory informed investors (mainly foreign professional investors), the Korean government and KRX have been devising new market regulations and trader guidelines. However, the current regulatory system relies only on the price movement of the derivatives asset to determine whether the market is overheated. The results of our study suggest that the trade duration and its different implications in the OTM and ITM options could be additional useful parameters that market regulators should consider to better protect uninformed individual traders in the Korean index options market.

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26 Table 1 Global derivatives exchanges by rank and trading volume by investor type in the KOSPI 200 options Panel A shows the 10 most active derivative contracts and their exchanges, measured in millions of contracts, from 2003 to 2005. Contracts are ordered based on their trading volume in 2005. Source: Futures Industry Association (https://fia.org/) . Panel B shows the trading volume of the KOSPI 200 options by investor type (domestic individuals (Individuals), domestic institutions (Institutions), and foreigners (Foreign)) for the sample period from January 2003 to June 2005. The trading volume of each investor type is measured in the number of options contracts traded.

Panel A. Trading volumes of worldwide derivatives exchanges Rank Contracts and Exchanges 2003 2004 2005 1 KOSPI 200 options, Korea Exchange 2837.7 2521.6 2535.2 2 Eurodollar Futures, CME 208.8 297.6 410.4 3 Euro-Bund Futures, Eurex 244.4 239.8 299.3 4 10-year T-Note futures, CBOT 146.5 196.1 215.1 5 E-mini S&P 500 Index Futures, CBOT 161.2 167.2 207.1 6 Eurodollar Options, CME 100.8 130.6 188.0 7 Euribor Futures, Euronext.liffe 137.7 157.8 166.7 8 Euro-Bobl Futures, Eurex 150.1 159.2 158.3 9 Euro-Schatz Futures, Eurex 117.4 122.9 141.2 10 DJ Euro Stoxx 50 Futures, Eurex 116.0 121.7 140.0

Panel B. Trading volume by investor types in the KOSPI 200 options market Total Call options Put options In contracts % In contracts % In contracts % Individuals 6,584,231,687 51.21 3,447,844,525 51.54 3,136,387,162 50.85 Institutions 4,733,585,562 36.82 2,472,848,244 36.97 2,260,737,318 36.65 Foreign 1,539,585,921 11.97 768,370,039 11.49 771,215,882 12.50 Total 12,857,403,170 100.00 6,689,062,808 100.00 6,168,340,362 100.00

27 Table 2 Summary statistics of the options data This table shows the mean values of the number of trades (Trade), number of contracts (Contract), contract-weighted average transaction prices (Price), average duration between two consecutive trades (Duration), market depth (Depth), and percentage fraction of trades initiated by each investor group (domestic individuals (Individuals), domestic institutions (Institutions), or foreign institutions (Foreign)) for each moneyness category across the 10 options series, where each option series covers a three-month period. Price is presented in points. Duration is presented in seconds. Depth is defined as the sum of all submitted orders on the best five outstanding bid and ask prices and measured immediately before each incoming trade. M1, M2, M3, M4, M5, and M6 denote options for which moneyness values are 0.88-0.93 (most out-of-the-money), 0.93-0.96, 0.96-0.98, 0.98-1.0, 1.0-1.04, and 1.04-1.12 (most in-the-money), respectively. We define the moneyness metric of call (put) options as S/K (K/S), where S is the stock price and K is the exercise price. Panels A and B depict the results for the call options and put options, respectively.

Panel A. Call options M1 M2 M3 M4 M5 M6 Trade 497,375 906,927 1,054,136 1,105,556 863,130 62,231 Contract 54,015,373 84,943,161 79,889,291 63,829,049 25,929,733 786,350 Price 0.184 0.359 0.545 0.750 1.507 5.937 Duration 6.21 2.04 1.15 1.04 2.45 60.38 Depth 128,584 57,922 32,774 16,580 3,703 2,541

Number of contracts (in percentiles) Individuals 51.3 44.3 42.3 43.4 44.6 15.8 Institutions 27.0 38.4 42.5 42.7 34.6 12.8 Foreign 21.6 17.2 15.1 13.9 20.8 71.3

Trading value (in percentiles) Individuals 47.4 38.3 38.6 42.0 42.2 15.0 Institutions 31.7 43.8 43.0 37.7 28.7 12.2 Foreign 20.8 17.8 18.3 20.3 29.0 72.7

Panel B. Put options M1 M2 M3 M4 M5 M6 Trade 723,867 928,516 859,614 1,032,075 747,659 53,105 Contract 64,648,952 69,701,237 58,657,497 57,937,917 18,657,816 728,810 Price 0.271 0.454 0.569 0.708 1.575 6.106 Duration 4.49 1.82 1.28 1.10 2.96 73.43 Depth 65,081 33,334 26,227 15,281 2,856 2,339

Number of contracts (in percentiles) Individuals 46.4 41.5 41.7 45.4 46.1 13.5 Institutions 31.9 39.9 42.0 40.8 29.7 9.9 Foreign 21.6 18.6 16.2 13.7 24.1 76.5

Trading value (in percentiles)

28 Individuals 42.1 38.1 39.5 44.4 42.7 12.8 Institutions 36.5 41.6 40.0 34.8 23.3 9.3 Foreign 21.3 20.2 20.4 20.7 33.9 77.9

29 Table 3 Estimation results of the duration dependent (D-MRR) model This table reports the mean values of the permanent-impact-related estimates (the duration- independent parameter α0 and duration-related parameter α1), the temporary-effect-related estimates (the duration-independent parameter β0 and duration-related parameter β1), and the autocorrelation parameter estimate (ρ) across the 10 options series and their t-statistics (in parenthesis). The table also reports the mean values of the permanent price impact as a percentage of the underlying option price (PIU, PIA), the temporary price effect as a percentage of the underlying option price (TE), the model- implied spread as a percentage of the underlying option price [ISi=2(PIi+TE)], and the relative magnitude of the permanent price impact [γi=PIi/(PIi+TE)×100]. Subscript i becomes U for an unadjusted measure and A for a ρ-adjusted measure (i.e., PIA=PIU (1+ρ)(1–ρ)) for each PI, IS, and γ. M1 to M6 denote options for which moneyness values are 0.88-0.93 (most out-of-the money), 0.93- 0.96, 0.96-0.98, 0.98-1.0, 1.0-1.04, and 1.04-1.12 (most in-the-money), respectively. We define the moneyness metric of call (put) options as S/K (K/S), where S is the stock price and K is the exercise price. Panels A and B show the results for call options and put options, respectively, in each moneyness category.

Panel A. Call options M1 M2 M3 M4 M5 M6

α0 (Coefficient × 100) 0.044 0.049 0.055 0.076 0.117 -0.112 (53.3) (79.2) (88.0) (86.8) (49.3) (-1.4)

α1 (Coefficient × 100) -0.014 -0.013 -0.011 -0.004 0.057 0.458 (-43.1) (-52.5) (-36.6) (-12.4) (24.8) (20.5)

β0 (Coefficient × 100) 0.381 0.349 0.334 0.324 0.258 -0.372 (234.3) (303.0) (309.5) (260.5) (103.8) (-5.0)

β1 (Coefficient × 100) 0.011 0.013 0.014 0.014 0.033 0.048 (55.4) (75.0) (65.9) (46.0) (32.4) (4.6)

ρ 0.670 0.574 0.484 0.397 0.302 0.303 (235.2) (280.6) (255.7) (228.2) (174.2) (49.2)

PIU 0.067 0.065 0.072 0.094 0.144 0.338 TE 3.108 1.128 0.658 0.464 0.211 -0.020

ISU 6.349 2.386 1.460 1.117 0.710 0.635

γU 3.3 6.3 10.0 17.1 40.5 107.1

PIA 0.037 0.045 0.056 0.079 0.130 0.306

ISA 6.289 2.345 1.427 1.087 0.684 0.572

γA 2.1 4.6 7.9 14.8 38.2 108.4

Panel B. Put options M1 M2 M3 M4 M5 M6

α0 (Coefficient × 100) 0.053 0.061 0.068 0.084 0.141 -0.174 (70.9) (81.3) (77.1) (83.9) (46.3) (-2.0)

α1 (Coefficient × 100) -0.014 -0.013 -0.008 -0.001 0.061 0.538 (-51.0) (-42.5) (-24.4) (-10.0) (22.5) (20.0)

β0 (Coefficient × 100) 0.333 0.313 0.311 0.317 0.231 -0.471 (226.9) (244.5) (230.2) (230.0) (75.4) (-5.4)

β1 (Coefficient × 100) 0.013 0.015 0.014 0.014 0.033 0.036 (68.7) (70.0) (52.2) (37.9) (28.0) (3.0)

30 ρ 0.617 0.521 0.458 0.385 0.286 0.328 (268.7) (256.6) (222.8) (216.8) (156.6) (47.7)

PIU 0.081 0.081 0.095 0.116 0.163 0.383 TE 1.627 0.788 0.594 0.477 0.188 -0.045

ISU 3.417 1.740 1.378 1.185 0.702 0.677

γU 6.1 10.2 14.1 19.4 46.3 113.4

PIA 0.050 0.060 0.076 0.099 0.149 0.341

ISA 3.354 1.696 1.339 1.152 0.675 0.592

γA 4.1 7.8 11.6 17.1 44.1 116.1

31 Table 4 Estimation results of the duration, volume, and liquidity dependent (DVL-MRR) model This table reports the mean values of the permanent-impact-related estimates (the duration- and volume-independent parameter α0, duration-related parameter α1, volume-related parameter α2, and depth-related parameter α3), the temporary-effect-related estimates (the duration- and volume- independent parameter β0, duration-related parameter β1, volume-related parameter β2, and depth- related parameter β3), and the autocorrelation parameter estimate (ρ) across the 10 options series and their t-statistics (in parenthesis). The table also reports the mean values of the permanent price impact as a percentage of the underlying option price (PIU, PIA), the temporary price effect as a percentage of the underlying option price (TE), the model-implied spread as a percentage of the underlying option price [ISi=2(PIi+TE)], and the relative magnitude of the permanent price impact [γi=PIi/(PIi+TE)×100]. Subscript i changes to U for an unadjusted measure and A for a ρ-adjusted measure (i.e., PIA=PIU(1+ρ)(1–ρ)) for each PI, IS, and γ. M1 to M6 denote options for which moneyness values are 0.88-0.93 (most out-of-the money), 0.93-0.96, 0.96-0.98, 0.98-1.0, 1.0-1.04, and 1.04-1.12 (most in- the-money), respectively. We define the moneyness metric of call (put) options as S/K (K/S), where S is the stock price and K is the exercise price. Panels A and B show the results for call options and put options, respectively, in each moneyness category.

Panel A. Call options M1 M2 M3 M4 M5 M6

α0 (Coefficient × 100) 0.005 0.017 0.032 0.066 0.179 1.032 (4.9) (12.6) (22.8) (37.1) (34.5) (5.1)

α1 (Coefficient × 100) -0.006 -0.007 -0.006 0.001 0.060 0.463 (-20.7) (-25.5) (-19.0) (-4.0) (25.3) (21.3)

α2 (Coefficient × 100) 0.007 0.009 0.011 0.014 0.032 0.119 (55.6) (90.4) (97.4) (93.3) (82.4) (9.8)

α3 (Coefficient × 100) 0.000 0.000 0.000 -0.001 -0.004 -0.032 (-19.5) (-32.4) (-38.3) (-39.8) (-49.3) (-9.3)

β0 (Coefficient × 100) 0.341 0.330 0.311 0.291 0.110 -0.402 (120.1) (179.2) (189.2) (136.1) (20.1) (-2.0)

β1 (Coefficient × 100) 0.008 0.010 0.012 0.014 0.030 0.052 (43.2) (60.5) (57.9) (44.2) (30.3) (4.7)

β2 (Coefficient × 100) -0.004 -0.005 -0.007 -0.010 -0.022 -0.066 (-63.9) (-99.4) (-103.1) (-98.3) (-71.0) (-7.0)

β3 (Coefficient × 100) 0.000 0.000 0.000 0.001 0.004 0.004 (34.9) (46.5) (52.7) (45.3) (49.7) (1.9)

ρ 0.649 0.567 0.473 0.386 0.294 0.302 (232.3) (288.1) (262.0) (231.0) (172.8) (49.1)

PIU 0.308 0.171 0.130 0.135 0.164 0.341 TE 3.164 1.161 0.649 0.446 0.199 -0.026

ISU 6.943 2.664 1.559 1.161 0.725 0.631

γU 10.4 13.5 16.9 23.5 45.2 109.0

PIA 0.160 0.111 0.100 0.115 0.150 0.309

ISA 6.648 2.546 1.499 1.120 0.697 0.568

γA 6.4 9.6 13.6 20.7 42.9 110.4

Panel B. Put options

32 M1 M2 M3 M4 M5 M6

α0 (Coefficient × 100) 0.012 0.029 0.042 0.076 0.148 1.176 (8.8) (18.0) (23.6) (37.4) (23.4) (4.9)

α1 (Coefficient × 100) -0.007 -0.006 -0.005 0.002 0.065 0.541 (-24.4) (-19.8) (-14.8) (-3.7) (23.6) (19.9)

α2 (Coefficient × 100) 0.009 0.012 0.012 0.015 0.037 0.109 (79.9) (98.2) (86.4) (91.6) (65.2) (8.0)

α3 (Coefficient × 100) 0.000 0.000 0.000 -0.001 -0.003 -0.036 (-26.4) (-32.9) (-32.3) (-37.9) (-32.3) (-8.8)

β0 (Coefficient × 100) 0.293 0.287 0.289 0.283 0.097 -0.471 (123.1) (140.4) (144.0) (119.9) (16.1) (-2.1)

β1 (Coefficient × 100) 0.010 0.013 0.013 0.013 0.030 0.032 (55.2) (60.7) (49.6) (37.1) (26.5) (2.6)

β2 (Coefficient × 100) -0.005 -0.008 -0.008 -0.011 -0.024 -0.076 (-89.6) (-106.7) (-93.1) (-93.4) (-53.4) (-6.5)

β3 (Coefficient × 100) 0.000 0.001 0.001 0.001 0.005 0.004 (44.8) (46.0) (43.2) (41.4) (41.6) (1.7)

ρ 0.601 0.512 0.453 0.376 0.282 0.328 (268.2) (263.9) (229.2) (219.1) (155.0) (47.5)

PIU 0.232 0.165 0.147 0.156 0.182 0.391 TE 1.669 0.789 0.579 0.454 0.183 -0.056

ISU 3.802 1.907 1.452 1.220 0.729 0.670

γU 13.8 18.3 20.6 25.6 49.7 117.3

PIA 0.141 0.120 0.116 0.134 0.167 0.348

ISA 3.621 1.817 1.390 1.176 0.700 0.584

γA 9.4 14.2 17.0 22.8 47.6 120.5

33 Table 5 Intraday analysis This table reports the mean values of the duration-related permanent impact parameter, α1, and temporary effect parameter, β1, across the 10 options series for 17 intraday trading intervals by moneyness category. M1 to M6 denote options for which moneyness values are 0.88-0.93 (most out-of-the money), 0.93-0.96, 0.96-0.98, 0.98-1.0, 1.0-1.04, and 1.04-1.12 (most in-the-money), respectively. Most of estimates are significantly estimated at the 5% significance level. We define the moneyness metric of call (put) options as S/K (K/S), where S is the stock price and K is the exercise price. Panels A and B show the results for call options and put options, respectively, in each moneyness category.

Panel A. Call options

α1 (Coefficient × 100) β1 (Coefficient × 100) Interval M1 M2 M3 M4 M5 M6 M1 M2 M3 M4 M5 M6 09:00-09:15 -0.0142 -0.0122 -0.0056 0.0161 0.1452 0.5306 0.0131 0.0142 0.0157 0.0198 0.0565 0.0785 09:15-09:30 -0.0136 -0.0117 -0.0044 0.0169 0.1487 0.5873 0.0134 0.0144 0.0159 0.0196 0.0548 0.0671 09:30-10:00 -0.0140 -0.0117 -0.0062 0.0146 0.1399 0.5912 0.0135 0.0145 0.0159 0.0192 0.0485 0.0748 10:00-10:30 -0.0142 -0.0118 -0.0054 0.0157 0.1491 0.6382 0.0139 0.0145 0.0162 0.0193 0.0487 0.0974 10:30-11:00 -0.0141 -0.0114 -0.0042 0.0169 0.1543 0.6068 0.0142 0.0145 0.0162 0.0198 0.0499 0.0909 11:00-11:30 -0.0139 -0.0112 -0.0027 0.0185 0.1599 0.6425 0.0142 0.0145 0.0162 0.0200 0.0503 0.0874 11:30-12:00 -0.0146 -0.0113 -0.0023 0.0200 0.1653 0.6777 0.0144 0.0147 0.0162 0.0202 0.0536 0.0928 12:00-12:30 -0.0143 -0.0111 -0.0022 0.0208 0.1694 0.6612 0.0143 0.0148 0.0165 0.0209 0.0531 0.1132 12:30-13:00 -0.0139 -0.0112 -0.0025 0.0208 0.1679 0.6151 0.0142 0.0148 0.0165 0.0209 0.0528 0.1001 13:00-13:30 -0.0142 -0.0114 -0.0024 0.0218 0.1640 0.6619 0.0143 0.0148 0.0164 0.0207 0.0490 0.0693 13:30-14:00 -0.0143 -0.0114 -0.0021 0.0222 0.1618 0.6127 0.0144 0.0148 0.0164 0.0210 0.0508 0.0770 14:00-14:30 -0.0145 -0.0115 -0.0029 0.0221 0.1628 0.6368 0.0143 0.0148 0.0164 0.0207 0.0504 0.0726 14:30-14:45 -0.0141 -0.0112 -0.0007 0.0263 0.1824 0.6909 0.0144 0.0150 0.0165 0.0221 0.0562 0.1039 14:45-14:50 -0.0145 -0.0106 0.0042 0.0408 0.2222 0.4835 0.0148 0.0154 0.0172 0.0248 0.0729 0.0620 14:50-14:55 -0.0149 -0.0113 0.0048 0.0400 0.2227 0.7685 0.0150 0.0157 0.0168 0.0249 0.0814 0.1037 14:55-15:00 -0.0146 -0.0109 0.0047 0.0406 0.2176 0.5374 0.0150 0.0156 0.0173 0.0251 0.0803 0.1766 15:00-15:05 -0.0145 -0.0115 0.0014 0.0354 0.2080 0.6694 0.0149 0.0152 0.0166 0.0236 0.0756 0.1831

34 Panel B. Put options

α1 (Coefficient × 100) β1 (Coefficient × 100) Interval M1 M2 M3 M4 M5 M6 M1 M2 M3 M4 M5 M6 09:00-09:15 -0.0139 -0.0107 0.0008 0.0207 0.1581 0.6351 0.0139 0.0161 0.0189 0.0219 0.0521 0.1345 09:15-09:30 -0.0137 -0.0100 0.0027 0.0213 0.1594 0.6634 0.0144 0.0162 0.0192 0.0213 0.0526 0.1822 09:30-10:00 -0.0139 -0.0105 0.0005 0.0173 0.1465 0.6689 0.0143 0.0164 0.0186 0.0211 0.0442 0.1139 10:00-10:30 -0.0137 -0.0103 0.0016 0.0198 0.1500 0.6647 0.0146 0.0168 0.0193 0.0218 0.0459 0.1320 10:30-11:00 -0.0137 -0.0102 0.0020 0.0202 0.1537 0.6944 0.0147 0.0168 0.0193 0.0216 0.0455 0.1638 11:00-11:30 -0.0134 -0.0103 0.0025 0.0223 0.1556 0.6869 0.0146 0.0166 0.0195 0.0217 0.0470 0.1607 11:30-12:00 -0.0132 -0.0100 0.0025 0.0222 0.1603 0.7114 0.0143 0.0164 0.0194 0.0225 0.0477 0.1534 12:00-12:30 -0.0132 -0.0097 0.0021 0.0216 0.1661 0.6793 0.0144 0.0167 0.0200 0.0226 0.0484 0.1662 12:30-13:00 -0.0133 -0.0100 0.0023 0.0218 0.1630 0.7558 0.0146 0.0170 0.0192 0.0222 0.0456 0.1283 13:00-13:30 -0.0134 -0.0100 0.0024 0.0208 0.1561 0.7047 0.0148 0.0171 0.0193 0.0225 0.0477 0.1442 13:30-14:00 -0.0134 -0.0099 0.0019 0.0202 0.1602 0.7004 0.0146 0.0168 0.0191 0.0217 0.0463 0.1745 14:00-14:30 -0.0134 -0.0100 0.0011 0.0203 0.1567 0.7031 0.0147 0.0168 0.0188 0.0222 0.0478 0.1227 14:30-14:45 -0.0129 -0.0097 0.0035 0.0255 0.1715 0.6341 0.0143 0.0165 0.0200 0.0232 0.0570 0.1958 14:45-14:50 -0.0141 -0.0067 0.0125 0.0371 0.2065 0.5266 0.0144 0.0175 0.0226 0.0286 0.0661 0.3301 14:50-14:55 -0.0138 -0.0071 0.0140 0.0381 0.2181 0.5495 0.0139 0.0177 0.0217 0.0292 0.0702 0.3427 14:55-15:00 -0.0136 -0.0068 0.0139 0.0395 0.2160 0.5379 0.0141 0.0175 0.0224 0.0289 0.0716 0.4107 15:00-15:05 -0.0133 -0.0078 0.0101 0.0350 0.2042 0.4686 0.0137 0.0170 0.0214 0.0265 0.0655 0.2623

35 Table 6 Informativeness of the duration between trades and options market variables

In each one-hour-long intraday interval, we estimate the D-MRR model and calculate various options market variables including the option moneyness, trade duration, price impact, trade volume, time to maturity, and volatility. Using these variables, we estimate the following regression model: Ii = δ0 + δ1Moneynessi + δ2Durationi + δ3PIi + δ4Volumei + δ5TTMi + δ6Volatilityi + δ7Intrai + εi, where i denotes the ith one-hour-long trading interval of each trading day in the pooling sample. Moneyness denotes moneyness category, Duration is average log trade duration, PI is the average permanent price impact, Volume is the square root of average trade volume, TTM is the time to maturity, Volatility is the realized return volatility calculated using five-minute log returns, and Intra denotes the intraday dummy variable, which equals 1 if the i-th observations are included in the current one- hour-long intraday interval and 0 otherwise. δ0 is a constant and ε denotes the error term. The dependent variable I is the information content of the trade duration, which is defined as 10th 90th 10th 90th th th (α0+α1lnT )–(α0+α1lnT ), where T and T denote the 10 and 90 percentile values of the trade duration in each interval.

Coefficient t-statistics Constant 1.5E-02 (19.00) Moneyness -1.7E-02 (-20.39) Duration 1.4E04 (4.78) PI 6.1E-03 (78.49) Volume -6.7E-05 (-7.99) TTM 3.2E-05 (11.94) Volatility 8.3E-05 (19.30) Intra 1.9E-05 (3.59) Number of observations 6,209 Adjusted R2 0.659

36