Information Effects of Trade Size and Trade Direction: Evidence from the KOSPI 200 Index Options Market*

Authors


  • *

    Acknowledgments: The authors are grateful for the helpful comments from an anonymous referee, Kazuhiko Ohashi, and seminar participants at the Asian Finance Association 2009 International Conference. Ryu acknowledges support from the Hankuk University of Foreign Studies (HUFS) Research Fund.

Corresponding author: Doojin Ryu, Department of International Business, Hankuk University of Foreign Studies, Yongin-si, Gyeonggi-do, Korea. Tel: +82 31 330 4609, Fax: +82 31 330 3074, email: sharpjin@hufs.ac.kr.

Abstract

In the present study, we examine two important issues related to the information content of a trade in option markets: (i) whether trade size is related to information content; and (ii) whether buy and sell transactions carry different information content. Our analysis is based on comprehensive market microstructure data on the KOSPI 200 options, the single most actively traded derivative securities in the world. We use two structural models modified from the Madhavan et al. [Review of Financial Studies 10 (1997) 1035–1064] model, the size-dependent model (SDM), and the dummy variable model (DVM). The SDM incorporates trade size in the model to estimate the magnitude of the information content of a trade. The DVM separately estimates information contents for buyer- and seller-initiated trades using a dummy variable. Our SDM analysis reveals that large trades are in general more informative than small trades. The results from the DVM analysis indicate that buyer-initiated trades generally have greater information content than seller-initiated trades. A further analysis using investor-type information shows that the asymmetry in information content between buy and sell trades is mostly attributable to the orders submitted by foreign and domestic institutional investors.

1. Introduction

The present paper examines two important issues related to the information content of a trade in option markets: (i) whether trade size is related to information content; and (ii) whether buy and sell transactions carry different information content. The two issues have been investigated extensively in equity markets. However, relatively few studies have been conducted on the information effects of trade size and trade direction in option markets. We examine these two issues using rich market microstructure data on the KOSPI 200 options, the single most actively traded derivative securities in the world. In the year 2006 alone, the number of contracts traded in the KOSPI 200 options was 2.41 billion. In the same year, the aggregate volume of the rest of the top-10 derivatives products in the world totaled 2.40 billion contracts.

In the framework of standard asset pricing theories like the capital asset pricing model, trade size per se is irrelevant in determining security prices. Every market participant is a price taker and has the same access to information. However, if some investors are more informed than others, the uninformed will face the problem of adverse selection in trading (Bagehot, 1971; Glosten & Milgrom, 1985). The price effects of asymmetric information are theoretically modeled in several key papers, including Kyle (1985) and Easley & O’Hara (1987).

One common thread in the models of Kyle (1985) and Easley & O’Hara (1987) is that trade size affects the information content of a trade. In Easley & O’Hara (1987), informed investors prefer to trade in large volumes to maximize their trading profits. Hence, a large order is more likely to be information driven than a small order. In Kyle’s (1985) framework, however, informed investors strategically spread their trades over time to hide their intentions. Although Kyle’s paper itself does not provide a definite prediction about the relationship between order size and information, one can easily infer that an informed investor will strategically break up a suboptimally large order into a few smaller ones and spread them over time.

Empirical evidence on the link between trade size and information is abundant. From earlier papers such as that of Holthausen et al. (1987) to more recent ones such as those of Barclay & Warner (1993), Easley et al. (1997), Dufour & Engle (2000), and Chakravarty (2001), there is plentiful empirical evidence that trade size is significantly related to information content. However, these studies offer two completely different pictures with respect to how trade size relates to information content. According to Holthausen et al. (1987), Easley et al. (1997), and Dufour & Engle (2000), the larger a trade, the more likely the trade is initiated by an informed trader. However, Barclay & Warner (1993) present evidence that trades in the medium-sized category have the most price impact. They explain the result using the so-called “stealth trading hypothesis”, which holds that trading in medium-sized orders is optimal for informed investors for camouflaging their intent and, therefore, minimizing adverse price movements. Chakravarty (2001) reinforces the stealth trading hypothesis by finding evidence that orders from institutions cause the large price contribution of medium-sized trades.

The controversial findings presented above suggest that more research is needed to improve our understanding of the link between trade size and information content. Furthermore, most existing studies that focus on this link look at equity markets only. Little is known about this issue in option markets. The only study so far that examines the direct link between the two variables is Anand & Chakravarty (2007) on equity options markets. No study has investigated how informed investors strategically choose their trade size in index option markets. To our knowledge, this is the first study that examines the link between information and trade size in an index option market.

We study the index option market because of the importance that index products have in derivatives trading. Index derivatives are usually the most actively traded products in any derivatives market. Moreover, in emerging markets, often index derivatives form the only practical conduit of derivative-based arbitrages or hedging. In many of these markets, individual equity options do not exist, or, if they do exist, trading is extremely infrequent.1

In markets that are semi-strong form efficient, the source of informed trading is private, firm-specific information. In this line of logic, one needs to look at individual equity option data to find traces of informed trading in option markets.2 Unlike in equity option markets, however, price changes in index option markets are driven by public information about macroeconomic factors, not by private information. Hence, one might argue that information asymmetry does not play a role in index option trading. Nevertheless, recent studies indicate that informed trading is also active in markets for index derivatives (Schlag & Stoll, 2005; Erenburg et al., 2006; Ahn et al., 2008; Kang & Park, 2008). Possible explanations for the information advantages of certain investors in index derivatives markets include superior skills of processing macroeconomic information, faster access to the market, and/or superior trading abilities.

The next issue that we examine in the present paper is whether buy/sell trade directions have different information effects in index option trading. Several published studies report the evidence of systematic buy/sell asymmetry in information effects in equity markets (Kraus & Stoll, 1972; Miller, 1977; Figlewski, 1981; Figlewski & Webb, 1993; Chan & Lakonishok, 1993, 1995; Ahn et al., 2005). Little is known about whether similar asymmetry exists in option markets, where the trading mechanism is markedly different from that of equity markets.

In a complete market, as with the case of trade size, there is no reason why a buyer-initiated trade should contain more information than a seller-initiated trade, and vice versa in a systematic way. However, prior studies find that various factors related to incompleteness in equity markets could create a systematic tendency of stock purchases carrying more information than sales. One such factor is short sale restrictions. Short sale restrictions shut some pessimists out of the market, causing stock prices to under-represent negative information (Miller, 1977; Figlewski, 1981; Figlewski & Webb, 1993; Ahn et al., 2005). Another example is the stock selection feature of portfolio managers reported by Chan & Lakonishok (1993, 1995). According to Chan and Lakonishok, institutional purchases are likely to convey more information than institutional sales. Their logic is that a portfolio manager’s choice of a particular issue to sell out of a limited set of securities in a portfolio is not necessarily information motivated. On the contrary, the choice to buy a specific issue out of the numerous alternatives in the market is likely to carry favorable information about the issue.

The abovementioned frictions, of course, are not applicable to index option markets. The asymmetric information effect created by portfolio managers’ purchases and sales would not apply to index option trading because in index option markets investors trade a single asset, an index option. The asymmetry induced by short sale restrictions is not applicable, either, because option traders do not need short selling. Instead, they can simply buy put options.

However, buy/sell information asymmetry could still exist in option markets, albeit for different reasons. In option markets, investors can always choose between call and put options, and this could create asymmetric information effects in the buy/sell order flow. Suppose an investor in an option market has a negative signal on the future value of an asset. The investor can either sell a call naked or buy a put option.3 Of the two choices, the latter will be preferred for the following reasons. When the investor sells a naked call, the maximum future loss is unbounded, while the maximum gain is only the option premium. However, if the investor buys a put, the potential gain could be substantial, with the maximum loss limited just at the option premium. A naked sale of a call also adds the non-trivial burden of maintaining margin requirements, which could often be substantial. A similar reasoning applies to the case of an investor with positive information: buying a call option will be a superior strategy to selling a put option. These considerations suggest a systematic pattern in option markets that buy transactions carry more information than sell transactions.

As an extension of the buy/sell asymmetry-related issue, we examine whether the asymmetry between buy and sell transactions is linked to investor type. It is a street lore that institutions are more informed than individuals. Chakravarty (2001) and Barber et al. (2009) find evidence that supports this claim. There is also a growing but controversial literature on whether domestic investors have information advantages over foreigners or vice versa. Choe et al. (2005), Hau (2001), and Dvorak (2005) report evidence that foreigners underperform domestic investors. On the contrary, Grinblatt & Keloharju (2000), Froot et al. (2001), and Froot & Ramadorai (2008) find that foreign investors are more informed than their domestic counterpart. There is also a group of studies that report foreign investors’ information advantages in Korea equity markets.4 As long as the buy/sell asymmetry in option markets is caused by informed trading and a certain type of investor is more accountable for informed trading than others, we should see a systematic link between the asymmetry and investor type. In our analysis, to answer this question, we differentiate the orders of institutional investors from the orders of individuals and also the orders of foreign institutions from those of domestic institutions.

We use two structural models that extend the spread decomposition model proposed by Madhavan et al. (1997) (the MRR model). In the MRR model, information asymmetry is captured by estimated adverse selection costs, which we use as a proxy for the information content of a trade. Our first model is the size-dependent model (SDM). We use this model in our analysis of the information effects of trade size. An innovation of the SDM is that the model conveys the idea that trade size can affect adverse selection costs. More specifically, the model estimates the extra price impact of the volume of a trade separately from the impact of the direction of the trade. For our analysis of buy/sell asymmetry, we introduce the dummy variable model (DVM). The DVM separately estimates the information contents of buyer- and seller-initiated trades using a dummy variable. The model is also used when we examine the effects of investor type on buy/sell asymmetry.

The index option data set we use in the present study is extremely rich in terms of its coverage of details. The data set contains an information set that is usually unavailable in the data from other markets: for example, it contains information on investor type (in total, 17 types). The trader type information is essential in our analysis that examines the effects of institutional trading.

The rest of the paper is organized as follows. The next section describes the KOSPI 200 options market and explains the data set. Section 3 proposes the two structural models and the motivation for using these models. Section 4 discusses the main empirical findings. Section 5 concludes the paper.

2. Data

2.1. KOSPI 200 Options Market

The KOSPI 200 options are based on the KOSPI 200 index, which is composed of the 200 most representative stocks of the Korea Exchange (KRX). The options are by far the most actively traded derivatives in the world. Table 1 presents the trading volume in millions of contracts for the top-10 derivatives in the world between 2001 and 2006. The table clearly shows that the KOSPI 200 options have maintained a dominant number one spot during the entire 6-year span. In 2006 alone, its trading volume was more than 2.41 billion contracts, which is greater than the cumulative volume from the rest of the top-10 derivatives of the world (2.40 billion contracts).5

Table 1.   The world’s top-10 derivative contracts
The world’s 10 most active derivative contracts, measured in millions of contracts from the year 2001 to the year 2006, are shown. The rank is determined based on the trading volume of the year 2005 because the Tasa de Interés Interbancaria de Equilibrio (TIIE) 28-Day Interbank Rate Futures, which is ranked fifth in 2006, is ranked below 20th before 2002.
RankContract200120022003200420052006
 1KOSPI 200 options, KRX823.31889.82837.72521.62535.22414.4
 2Eurodollar Futures, CME184.0202.1208.8297.6410.4502.1
 3Euro-Bund Futures, Eurex178.0191.3244.4239.8299.3319.9
 410-year T-Note Futures, CBOT57.695.8146.5196.1215.1255.6
 5E-mini S&P500 Index Futures, CBOT39.4115.7161.2167.2207.1257.9
 6Eurodollar Options, CME88.2105.6100.8130.6188.0269.0
 7Euribor Futures, Euronext.liffe91.1105.8137.7157.8166.7202.1
 8Euro-Bobl Futures, Eurex99.6114.7150.1159.2158.3167.3
 9Euro-Schatz Futures, Eurex92.6108.8117.4122.9141.2165.3
10DJ Euro Stoxx 50 Futures, Eurex37.886.4116.0121.7140.0213.5

In addition to the extreme abundance of liquidity, the KOSPI 200 options market has another unique characteristic: a high participation rate of individual investors. In most of the derivative markets in developed countries, institutional investors form the majority of the market participants. In the KOSPI 200 options market, however, individuals are the major participants. For example, in our sample year, 2002, individual investors account for 66% of the total trading volume, which almost doubles the combined trading volume by all institutions.

2.2. Microstructure of the KOSPI 200 Options Market

KOSPI 200 options are European options. The options have a contract size of KRW100 000 times the level of the KOSPI 200 index price. Four different option series with varying maturities are traded in the options market. The maturity months are three consecutive near-term months and one nearest month from the quarterly cycle of March, June, September, or December. Nine different exercise prices are set for the three consecutive near-term contracts and five different exercise prices for the next quarterly month contract. The options use two different tick sizes. If the quotation price is three points or higher, the tick size is 0.05 points (i.e. KRW5000); otherwise, the tick size is 0.01 points (KRW1000).

The market is purely order driven. All limit orders are consolidated into the central electronic limit order book, where they are crossed with the incoming market orders.6 The market adopts two trading systems: call and continuous auctions. Before the market opens, a pre-opening call auction, which sets the initial price of the day at 09:00 hours, takes place. A regular continuous double auction follows it. The continuous auction lasts until 15:05 hours, at which point once again the market switches to a call auction before it closes at 15:15 hours.

2.3. Data and the Sample Period

We use the historical trade and quote data of the KOSPI 200 options provided by the KRX. The data set is unique in that it provides a rich set of information about each order and trade. This includes not only the usual information, such as the transaction price, trade size, and time of an each order, but also detailed information about the type of investor who submits the order. The investor type flag in the data set is given in 11 domestic and six foreign investor groups. We can also make exact identifications of the trade directions (whether a trade is initiated by a buyer or a seller), by keeping track of the fine time stamp provided by the data, which records every trade and quote at 100th of a second.

The sample period of this study is from 1 January to 31 December 2002. We choose this specific period because it does not contain any persistent upward or downward trends. Chiyachantana et al. (2004) demonstrate that market-wide bearishness or bullishness is an important factor to control for in research that examines buy/sell asymmetry in transaction costs. As one of the two main issues we examine in the present study is asymmetric information effects between buy and sell trades, we need to pick a market period that is neutral enough, belonging neither to a persistent bull market nor to a prolonged bear market. The market during the years prior to 2001 was severely bearish, whereas the period subsequent to 2002 is characterized by sturdy bullishness that continued until 2007. The markets in the years of 2001 and 2002 just fit the aforementioned specification. We choose 2002 because it is more recent.7 Another advantage of the 2002 data is that no trading halt occurs during the year. Trading halts are common in the other years.

We include only the nearest and second-nearest maturity options in our analysis because the other maturity options are barely traded. We use all trades and quotes recorded during the continuous trading session of every trading day, from 09:00 to 15:05 hours. This procedure results in 15.6 million transactions of call options and 12.8 million transactions of put options. In terms of trading volume, call options account for approximately one billion contracts and put options account for nearly 800 million contracts.

2.4. Option Delta

In our analysis, we separately examine call and put options. We further classify options by their delta values. This is somewhat in contrast to many existing studies on options, which use option moneyness for classification. Traditionally, moneyness is defined as the underlying asset’s price over the strike price. Option delta is a more comprehensive measure than this traditional metric in that it incorporates such information as the time to the maturity of the option and the volatility of the underlying asset value.8 This point is well demonstrated by Bollen & Whaley (2004).9

The use of option delta is justified in the following illustration. In the KOSPI 200 options market, the longest time to maturity of a nearest month option is usually fewer than 30 calendar days. This short maturity makes the traditional definition of option moneyness, such as the underlying price over the strike price (S/K), less meaningful for investors. For example, suppose there are two call option series with the same strike price at 100. Furthermore, suppose that one has 30 calendar days left until maturity, while the other has three calendar days left. Now assume that the level of the current underlying index is 95. Whereas both options have the same moneyness at 0.95, the 3-day option will trade out of the money and, conditional on the movement of the underlying market, the 30-day option could trade in the money because of its speculative value. Hence, using option moneyness for a grouping purpose is problematic in this case, leading to a potential error of treating two distinctively different options as identical. Of course, using option delta will alleviate such a problem.

The option delta (Δ) is calculated as follows:

image

where

image
image(1)

N(·) is the standard normal cumulative density function. St denotes the value of the KOSPI 200 index at time t. D stands for the present value of the dividends paid from time t until the expiration date, T. K is the option’s strike price. The term r is the continuously compounded risk-free interest rate, which is measured by the rates from 91-day Certificate of Deposit (CD). τ1 (τ2) is the ratio of the trading time in the number of minutes (in the number of calendar days) remaining until the option maturity to the total length of the trading time in the number of minutes (the number of calendar days) in a year. σ is the implied volatility of the underlying asset, as estimated from the midpoint of the bid and ask prices of the at-the-money option at time t.

2.5. Data Processing

We process our sample data in the following steps. Throughout the entire process, we handle put and call options separately. First, we partition each trading session into 15-min intraday intervals. Then, for each option series, we estimate the option delta for each 15-min interval. Then we sort the intervals by the respective delta estimates. Next, delta ranges are set using a grid of 0.05 (for put options, the absolute values of the delta estimates are used). The lowest range has delta values from 0 to 0.05. The highest range has delta values of 0.95 or greater. We then merge all 15-min interval data if their delta estimates belong to the same range. We discard the first two groups whose delta values are below 0.1 because of their extremely low prices, which are only a few times larger than the tick size. We also exclude the last two groups (delta values greater than 0.9) because trading in these ranges is extremely infrequent.

Table 2 presents the descriptive statistics of the sample by different delta ranges. We report the results on call (Panel A) and put options (Panel B) separately. The table shows that trading activity decreases monotonically with (absolute) delta values regardless of whether it is measured by the number of transactions, volume in number of contracts, or volume in monetary value. The pattern is also clearly present when we look at buys and sells separately. Liquidity is most plentiful with low delta options. It gradually decreases as the delta value increases. The contract-weighted average transaction prices increase with delta values because the greater the delta of an option, the deeper in the money the option goes.

Table 2.   Descriptive statistics
The descriptive statistics of the trading activity for the KOSPI 200 options throughout 16 groups classified by the option delta for 2002 are shown. Panel A shows the results for call options and Panel B shows the results for put options. The “Total” column shows the results for total value in each delta interval. The “Buy (Sell)” column shows results for the buyer (seller)-initiated trades. Presented are the number of transactions (in thousands), trading volume in thousand contracts, trading value in billion Korean Won (KRW), contract-weighted average price in points (one point is equivalent to 100 000 KRW), average trade size in contract, and average trade value in points. The last row (“All”) shows the statistics for the whole sample data.
|Δ|Number of transactions (in 1000)Trading volume (in 1000 contracts)Trading value (in billion KRW)Average price (in 100 000 KRW)Average trade size (in contract)Average trade value (in 100 000 KRW)
TotalBuySellTotalBuySellTotalBuySellTotalBuySellTotalBuySellTotalBuySell
Panel A: Descriptive statistics for call options
0.10–0.1520038991104176 89386 27890 6157758382839310.4390.4440.43488.396.082.138.7442.6035.60
0.15–0.2020049231081155 87676 06579 8119825484049840.630.6360.62577.882.473.849.0152.4346.10
0.20–0.251824838986116 72856 57160 1579309454947600.7980.8040.79164.067.561.051.0554.2948.29
0.25–0.30151670780974 95436 68138 2747144352236220.9530.960.94649.451.947.347.1249.8144.77
0.30–0.35131661969753 62126 18227 4396259308831711.1671.1791.15640.742.339.447.5749.8845.51
0.35–0.4097946251735 72617 39918 3284463218722761.2491.2571.24236.537.735.445.5947.3644.02
0.40–0.4590642647928 76614 04414 7224142204121011.441.4531.42731.833.030.745.7447.8943.83
0.45–0.5061428532917 992880491882913144014731.6191.6361.60329.330.927.947.4250.4844.76
0.50–0.5548222425813 390659967912432121712141.8161.8451.78827.829.526.350.4654.3547.08
0.55–0.6035816619290744425464919389689692.1352.1882.08525.326.624.254.1058.2350.51
0.60–0.6526612514171303511361915307647662.1462.1772.11626.828.025.757.4360.9154.33
0.65–0.70181869543042190211411215785422.6042.6412.56523.825.422.361.9367.0657.26
0.70–0.7512559662755137613798694424273.1543.2133.09622.023.120.969.2774.3864.66
0.75–0.8010550552312114511677553783773.2673.3013.23422.022.721.371.7574.9568.82
0.80–0.8581394217668878796223133093.5213.5273.51421.822.820.876.7280.5973.17
0.85–0.9070333714667507165582932653.8053.9073.69820.922.419.579.5487.6472.17
All12 83159436888702 754342 907359 84861 63830 45031 1880.8770.8880.86754.857.752.248.0451.2345.28
Panel B: Descriptive statistics for put options
0.10–0.15175079795314 052468 62271 9016537323633020.4650.4710.45980.386.175.537.3640.5934.65
0.15–0.201715798917118 46657 90460 5627738381539230.6530.6590.64869.172.666.145.1347.8142.80
0.20–0.25142366176278 54138 15840 3846457315932980.8220.8280.81755.257.753.045.3647.7843.27
0.25–0.30121656565153 64726 01927 6275265256826980.9810.9870.97644.146.042.443.2945.4441.41
0.30–0.3595444251236 50917 53918 9704247204921981.1631.1681.15938.339.737.144.5346.3342.97
0.35–0.4078836442525 44612 31813 1283526170318231.3861.3821.38932.333.930.944.7246.8242.92
0.40–0.4560327732617 493854389502817137814391.6111.6141.60829.030.927.546.7449.8044.15
0.45–0.5046821625313 351651868332329114811811.7441.7621.72828.530.227.149.7253.1746.76
0.50–0.5534515818798464793505217678858821.7951.8461.74628.530.427.051.2156.0547.13
0.55–0.6027713014784584212424615718037681.8581.9081.80830.532.528.856.7462.0452.09
0.60–0.651919010149292465246311115725392.2542.3222.18725.827.424.458.2063.6053.39
0.65–0.7014067743493171017839534714822.7292.7552.70524.925.624.367.9370.5165.60
0.70–0.7511956633113152515888374294082.6882.8132.56926.127.125.170.0876.3264.53
0.75–0.8077374115647777875973052923.8183.9253.71120.221.119.477.1282.9671.85
0.80–0.8557273011465495985292542754.6154.6234.60720.020.019.992.2492.6791.84
0.85–0.904320238093934164011952064.9534.9524.95418.819.318.493.1895.5991.02
All10 16847055464517 334252 046265 28846 68422 96923 7140.9020.9110.89450.953.648.645.9148.8243.40

3. Structural Models

3.1. Size-Dependent Model

We propose a structural model that accounts for trade size information when inferring the information content of a trade. There are two distinctively different opinions on how trade size relates to information content. Easley & O’Hara (1987) demonstrate that informed investors prefer to trade in large volume at any given price. The implication is that, in general, large trades convey more information than small trades. Lin et al. (1995) and Easley et al. (1997) find empirical evidence consistent with the prediction. On the contrary, Barclay & Warner (1993) propose that informed traders strategically split their large orders into smaller ones to camouflage their identity. According to this “stealth trading hypothesis,” it is medium-sized trades, not large trades, that have the largest price impact. Chakravarty (2001) also reports findings that confirm the hypothesis.

The original MRR model assumes a fixed order size. To accommodate the information effect of trade size, we modify the MRR approach by incorporating trade size as an independent variable in the estimation model. This model is the SDM. There are some advantages of adopting the structural model. First, we can examine the effect of trade size on the information content of a trade free from the arbitrariness of the discrete trade-size classification rules used by most existing studies. These rules usually use a grid in classifying trade size. For example, Huang & Stoll (1997) use a classification rule in their spread component estimation, which categorizes a trade as a small trade if its volume is fewer than 1000 shares, as a medium-sized trade if the size is between 1000 and 10 000 shares, and as a large trade if the size is greater than 10 000 shares. In our model, the volume of each trade itself is used as a direct input in the system. Second, the SDM also allows us to infer the effect of trade size on the temporary spread component or order-processing costs, another important transaction cost-related consideration for investors.

Now we describe the model. As in the MRR model, the post-trade value of an asset, μt, is defined as:

image(2)

In the above specification, xt and xt−1 are buy/sell indicators or trade initiation variables, taking the value of +1 for a buyer-initiated trade and −1 for a seller-initiated trade. The parameter α0 reflects the part of asymmetric information costs that are attributable to the trade direction itself. inline image is the square root of the volume of the trade at time t, measured in the number of contracts. The square root of volume instead of raw volume is used to accommodate the concave nature of the volume effect. α1 is the parameter in which we are interested and captures the trade size-related component of asymmetric information costs. The combined term inline image represents the permanent price effect of a trade made at time t. inline image is a surprise in the order flow. inline image can be interpreted as a change in investors’ belief about the asset value, reflecting the trade size in the order flow. ε is an independently and identically distributed (i.i.d.) error term with a zero mean that captures the innovation in public beliefs. The conditional expectation of xt given xt−1 is defined similar to the original MRR model:

image(3)

where ρ is the first-order autocorrelation in the order flow.

Meanwhile, the observed transaction price at time t, Pt, is defined as

image(4)

where β0 measures the part of order-processing costs attributable to trade direction, while β1 captures order-processing costs that are related to trade volume. inline image represents the temporary price effect of a trade made at time t. ξ is a rounding error due to price discreteness.

From Equations (2)–(4), we can express the price change at time t as

image(5)

We set up generalized method of moments (GMM) moment conditions and estimate the five parameters, α0, α1, β0, β1, and ρ:10

image(6)

We perform separate estimations for each of the 12 months in the sample year, as well as for the 16 different delta ranges. We use Hansen’s J-test to determine model fitness. All optimized function values are negligibly small and P-values are close to one. The coefficient that we are most interested in is α1, the sensitivity of adverse selection costs to trade size. If trade size is an important factor for informed trading, α1 should be positive and significant. In the meantime, a positive β1 implies that order-processing costs increase with trade size. A negative β1, by contrast, is consistent with economies of scale for order-processing costs.

The SDM is similar to the model proposed by Angelidis & Benos (2009) in their analysis on the market microstructure of the Athens stock market. They also extend the MRR model by including trade size as an independent variable. However, our model is slightly different from theirs in the following manner. Angelidis and Benos (2009) assume that the permanent spread component is proportional to the square root of trade size, while the temporary spread component has two parts: one that is dependent upon and the other that is independent of trade size. We allow both permanent and temporary components to be dependent upon as well as independent of trade size.

3.2. Dummy Variable Model

We describe the model used to analyze the asymmetric information effects between buy and sell trades. The model is also an extension of the MRR model. We call the structural model the dummy variable model (DVM) because it captures both permanent and temporary components of the spread, separately for buys and sells, using a dummy variable. Specifically, the DVM is the same as the original MRR model except that it contains a dummy variable on two OLS normal equations to separate the price effects of buyer- and seller-initiated trades. The moment conditions for the GMM estimation are set as

image(7)

In the above moment conditions, Dt denotes a dummy variable that indicates the initiating trade type. For each trade type (buy or sell), we separately estimate the three parameters α, β, and ρ using the GMM technique.11 For example, when we estimate adverse selection costs incurred by buys, if a specific trade at time t is buyer initiated, Dt takes the value of 1 and 0 otherwise. Similarly, for adverse selection costs incurred by sells, Dt becomes 1 if the trade at time t is seller initiated and 0 otherwise.

We apply a similar dummy variable technique to estimate the model parameters for our analysis of the information effects of buys and sells for different types of investors. In our data set, investors are classified into 17 types. We regroup these 17 types into three broad groups: domestic individuals, domestic institutions, and foreign institutions.

4. Empirical Results

4.1. Information Effect of Trade Size

4.1.1. Results from the Entire Sample

Tables 3 and 4 present the estimation results of the SDM. Both tables report the estimated values of α0, α1, β0, and β1, the estimated permanent price-effect component or adverse selection costs, inline image where inline image is the average volume of the trades during each estimation interval, and the estimated temporary price component or order-processing costs inline image The implied spread defined as

image

the proportion of adverse selection costs in the implied spread (γ), and the autocorrelation in the order flow (ρ) are also reported.

Table 3.   The monthly estimates of size-dependent model
The estimated parameters for the size-dependent version of the Madhavan, Richardson, and Roomans model (size-dependent model) for the KOSPI 200 options are shown. The estimation is carried out separately for each month. Panel A shows the results for call options and Panel B for put options. The reported coefficients are the trade size-independent and -dependent adverse selection components (α0 and α1 respectively), the spread component due to information asymmetry costs (α0 + α1inline image), the trade size-independent and -dependent order-processing components (β0 and β1 respectively), the spread component due to order-processing costs 01inline image), the proportion of the adverse selection component in the implied spread (γ), and the autocorrelation in the trade indicator variable (ρ). The t-statistics of the coefficient estimates are in parentheses. The last row shows the average values of the 12 monthly estimates.
Monthα0 (coefficient × 100)α1 (coefficient × 100)Adverse selectionβ0 (coefficient × 100)β1 (coefficient × 100)Order processingImplied spreadγ (%) (coefficient × 100)ρ (coefficient × 100)
Coefficient × 100Price (%)Coefficient × 100Price (%)Coefficient × 100Price (%)
Panel A: Estimation results for call options
 10.217 (25.99)0.012 (22.41)0.3000.2920.474 (139.92)–0.018 (–57.54)0.3450.3351.2901.25546.60.255 (159.23)
 20.161 (22.69)0.012 (26.31)0.2440.2570.442 (163.15)–0.015 (–65.07)0.3350.3541.1591.22242.10.280 (154.40)
 30.169 (24.82)0.015 (33.42)0.2690.2450.483 (138.89)–0.018 (–63.71)0.3610.3281.2611.14642.70.258 (168.75)
 40.187 (25.11)0.014 (25.62)0.2830.2850.472 (140.71)–0.019 (–57.90)0.3470.3491.2591.26844.90.255 (174.37)
 50.172 (28.29)0.012 (29.82)0.2580.2640.458 (144.94)–0.016 (–65.36)0.3450.3541.2061.23742.80.264 (170.35)
 60.161 (24.17)0.011 (23.68)0.2370.2750.431 (166.09)–0.016 (–64.52)0.3210.3731.1171.29642.50.278 (154.33)
 70.171 (29.44)0.011 (30.20)0.2520.2880.443 (184.99)–0.015 (–71.46)0.3310.3781.1651.33143.30.265 (176.45)
 80.129 (23.78)0.011 (32.53)0.2110.2390.420 (176.87)–0.015 (–65.79)0.3120.3541.0461.18540.30.299 (165.03)
 90.107 (23.55)0.010 (36.53)0.1850.2480.401 (203.07)–0.013 (–70.97)0.3060.4100.9801.31537.70.322 (167.87)
100.135 (28.73)0.010 (37.44)0.2120.2550.398 (217.23)–0.013 (–89.07)0.2930.3541.0091.21841.90.305 (196.98)
110.095 (23.42)0.009 (43.27)0.1670.2230.397 (258.26)–0.011 (–95.60)0.3030.4030.9411.25035.60.351 (193.56)
120.098 (22.76)0.009 (39.10)0.1700.2380.388 (244.51)–0.011 (–84.55)0.2990.4190.9391.31536.20.359 (196.06)
Average0.150 (25.23)0.011 (31.69)0.2320.2590.434 (181.55)–0.015 (–70.96)0.3250.3681.1141.25341.40.291 (173.12)
Panel B: Estimation results for put options
 10.236 (23.94)0.012 (15.90)0.3140.3230.445 (109.40)–0.019 (–47.89)0.3190.3281.2661.30249.70.254 (133.84)
 20.211 (22.94)0.010 (16.46)0.2790.3130.426 (123.39)–0.016 (–46.82)0.3190.3571.1971.33946.70.269 (128.47)
 30.183 (24.17)0.012 (21.90)0.2640.2760.451 (140.98)–0.017 (–54.17)0.3390.3551.2071.26243.70.262 (145.29)
 40.214 (26.22)0.015 (26.92)0.3160.3200.469 (128.32)–0.020 (–53.82)0.3330.3371.2961.31548.70.241 (154.24)
 50.216 (27.52)0.011 (20.97)0.2930.3070.456 (143.84)–0.018 (–54.69)0.3300.3451.2471.30447.10.257 (152.12)
 60.215 (25.33)0.011 (19.91)0.2930.3020.451 (129.40)–0.019 (–55.67)0.3190.3291.2241.26147.90.268 (145.45)
 70.205 (10.25)0.013 (8.75)0.2930.3080.450 (107.68)–0.020 (–40.36)0.3170.3331.2181.28248.00.256 (156.42)
 80.156 (23.19)0.011 (22.26)0.2290.2510.419 (152.18)–0.015 (–55.38)0.3110.3411.0811.18442.50.297 (143.19)
 90.132 (22.32)0.011 (31.54)0.2140.2490.402 (169.18)–0.014 (–68.48)0.2940.3421.0151.18142.20.315 (158.93)
100.164 (26.25)0.011 (27.74)0.2440.2670.406 (175.92)–0.016 (–69.77)0.2890.3171.0671.16845.80.279 (165.79)
110.116 (20.74)0.009 (25.16)0.1880.2420.386 (137.10)–0.012 (–72.27)0.2900.3740.9571.23339.30.334 (159.56)
120.127 (23.79)0.010 (36.93)0.2090.2680.389 (158.43)–0.014 (–68.49)0.2830.3630.9841.26242.50.323 (166.43)
Average0.181 (23.06)0.011 (22.87)0.2610.2860.429 (139.65)–0.017 (–57.32)0.3120.3431.1471.25845.30.280 (150.81)
Table 4.   The estimates of the size-dependent model by option delta
The estimated parameters for the size-dependent version of the Madhavan, Richardson, and Roomans model (size-dependent model) for the KOSPI 200 options are shown. The estimation is carried out separately for each of the 16 groups based on the absolute values of option deltas. Panel A shows the results for call options and Panel B shows the results for put options. The reported coefficients are the trade size-independent and -dependent adverse selection components (α0 and α1 respectively), the spread component due to information asymmetry costs (α0 + α1inline image), the trade size-independent and -dependent order-processing components (β0 and β1 respectively), the spread component due to order-processing costs (β0 + β1inline image), the proportion of the adverse selection component in the implied spread (γ), and the autocorrelation in the trade indicator variable (ρ). The t-statistics of the coefficient estimates are in parentheses.
|Δ|α0 (coefficient × 100)α1 (coefficient × 100)Adverse selectionβ0 (coefficient × 100)β1 (coefficient × 100)Order processingImplied spreadγ (%) (coefficient × 100)ρ (coefficient × 100)
Coefficient × 100Price (%)Coefficient × 100Price (%)Coefficient × 100Price (%)
Panel A: Estimation results for call options
0.10–0.150.001 (0.83)0.010 (142.24)0.0900.2060.407 (592.68)–0.008 (–185.00)0.3330.7590.8461.92921.30.415 (341.28)
0.15–0.20−0.001 (−0.85)0.012 (144.73)0.1080.1720.418 (602.90)–0.010 (–181.41)0.3280.5200.8721.38424.80.349 (284.80)
0.20–0.250.010 (6.33)0.015 (122.70)0.1270.1600.418 (491.45)–0.012 (–153.32)0.3210.4030.8971.12528.40.310 (244.58)
0.25–0.300.032 (14.59)0.018 (88.15)0.1560.1640.415 (375.40)–0.014 (–108.59)0.3190.3350.9510.99832.90.264 (200.72)
0.30–0.350.053 (19.21)0.022 (79.22)0.1920.1650.413 (259.45)–0.016 (–96.45)0.3090.2641.0020.85938.40.240 (173.62)
0.35–0.400.108 (27.14)0.021 (51.22)0.2370.1900.400 (214.24)–0.017 (–71.30)0.2960.2371.0660.85444.50.223 (140.95)
0.40–0.450.133 (28.55)0.026 (48.34)0.2810.1950.438 (128.15)–0.021 (–57.62)0.3170.2201.1970.83147.00.208 (134.28)
0.45–0.500.157 (21.18)0.037 (32.44)0.3600.2230.542 (71.39)–0.032 (–34.91)0.3670.2271.4550.89949.50.205 (111.31)
0.50–0.550.266 (24.80)0.039 (28.64)0.4700.2590.616 (76.03)–0.040 (–37.67)0.4050.2231.7500.96453.80.205 (103.30)
0.55–0.600.346 (25.42)0.045 (21.59)0.5720.2680.657 (60.68)–0.048 (–28.49)0.4170.1951.9790.92757.80.200 (85.34)
0.60–0.650.514 (26.29)0.034 (16.06)0.6920.3230.606 (48.60)–0.046 (–25.84)0.3670.1712.1190.98765.30.195 (74.34)
0.65–0.700.732 (23.15)0.031 (9.25)0.8860.3400.574 (35.26)–0.055 (–22.96)0.3080.1182.3860.91674.20.184 (61.15)
0.70–0.750.988 (19.99)0.030 (5.50)1.1300.3580.560 (22.74)–0.052 (–13.75)0.3180.1012.8960.91878.10.187 (51.76)
0.75–0.801.153 (19.01)0.024 (3.42)1.2640.3870.540 (16.35)–0.051 (–9.92)0.3010.0923.1310.95880.80.183 (43.95)
0.80–0.851.400 (17.64)0.000 (−0.05)1.3980.3970.473 (13.52)–0.048 (–9.49)0.2460.0703.2870.93485.10.185 (39.13)
0.85–0.901.588 (16.69)−0.009 (−0.89)1.5460.4060.462 (9.70)–0.051 (–7.00)0.2250.0593.5430.93187.30.191 (37.13)
Panel B: Estimation results for put options
0.10–0.15–0.006 (−5.53)0.011 (133.44)0.0950.2030.409 (556.49)–0.009 (–172.80)0.3270.7030.8431.81322.40.400 (310.90)
0.15–0.20–0.005 (−3.14)0.014 (122.50)0.1140.1750.419 (472.90)–0.012 (–137.92)0.3190.4890.8671.32826.40.333 (252.98)
0.20–0.250.024 (11.07)0.017 (94.93)0.1500.1830.411 (404.95)–0.014 (–129.36)0.3090.3760.9181.11732.70.282 (202.90)
0.25–0.300.054 (18.90)0.020 (74.36)0.1870.1900.404 (289.57)–0.015 (–100.31)0.3020.3070.9770.99538.20.249 (171.62)
0.30–0.350.100 (28.65)0.022 (57.40)0.2350.2020.393 (202.32)–0.017 (–74.16)0.2870.2471.0440.89744.90.223 (145.81)
0.35–0.400.144 (29.94)0.027 (50.40)0.2970.2140.410 (136.85)–0.022 (–57.14)0.2870.2071.1680.84350.90.205 (129.40)
0.40–0.450.176 (27.80)0.035 (41.28)0.3650.2260.486 (93.39)–0.031 (–46.04)0.3210.1991.3710.85153.20.202 (113.92)
0.45–0.500.271 (29.28)0.037 (31.68)0.4680.2680.547 (77.19)–0.037 (–37.75)0.3490.2001.6330.93657.30.198 (100.45)
0.50–0.550.350 (26.65)0.035 (23.18)0.5360.2980.573 (58.19)–0.040 (–31.03)0.3570.1991.7850.99560.00.195 (83.23)
0.55–0.600.506 (27.36)0.023 (12.39)0.6310.3400.552 (48.80)–0.038 (–27.44)0.3400.1831.9431.04665.00.197 (73.99)
0.60–0.650.637 (21.75)0.025 (8.64)0.7650.3390.574 (35.14)–0.050 (–22.86)0.3190.1422.1670.96170.60.185 (59.62)
0.65–0.700.845 (22.28)0.021 (5.23)0.9480.3470.603 (30.61)–0.052 (–17.51)0.3420.1252.5800.94573.50.189 (50.74)
0.70–0.750.920 (18.03)0.016 (3.24)1.0030.3730.612 (20.09)–0.053 (–10.04)0.3400.1262.6860.99974.70.178 (45.00)
0.75–0.801.232 (17.73)0.045 (4.58)1.4370.3770.730 (16.25)–0.081 (–11.43)0.3650.0963.6040.94479.80.194 (39.34)
0.80–0.851.751 (17.91)0.001 (0.06)1.7540.3800.679 (10.99)–0.077 (–8.57)0.3300.0724.1690.90384.20.201 (32.95)
0.85–0.901.983 (14.69)−0.009 (−0.49)1.9440.3920.603 (7.68)–0.079 (–6.36)0.2570.0524.4020.88988.30.196 (29.45)

Table 3 exhibits the monthly estimation results. All estimates reported in the table are statistically highly significant. The estimates of α0 and α1 are positive and significant, meaning that there are both size-independent and -dependent components in adverse selection costs. The result is consistent with the theoretical prediction of Easley & O’Hara (1987) and empirical evidence reported by Lin et al. (1995), Easley et al. (1997), and Dufour & Engle (2000).

The above results may be explained in conjunction with the nature of the information advantage, the abundance of liquidity, and the competition among investors in the KOSPI 200 options market. As suggested in the Introduction, the information advantages in an index option market come from superior skills in interpreting, processing, and/or trading on macroeconomic information. By their nature, these advantages tend to be short lived compared with the advantages derived from private information. Such an outcome will be more apparent in index derivatives markets, which usually operate with fierce competition among market participants (especially with a large number of institutional players). The extreme abundance of liquidity in the KOSPI 200 options market means that it can absorb a large volume order at any given time. This might give informed investors freedom to purchase or sell large volumes without worrying too much about adverse price movements.

The β1 estimates are negative and significant for each month for both call and put options, which is a clear sign of the economies of scale in order-processing costs with respect to trade size. When the original MRR model is applied to the same dataset as ours, the proportion of adverse selection costs in the implied spread (γ) is, on average, 35.0% for call options and 39.1% for put options (Ahn et al., 2008). However, when we incorporate the trade size information in our estimation, these values increase to 41.4% for calls and 45.3% for puts. The increases are consistent with the findings reported by Ahn et al. (2002) and Angelidis & Benos (2009) that information asymmetry costs tend to be underestimated and order-processing component costs tend to be overestimated when the original MRR model is used.

Table 4 reports the estimation results by delta ranges. Almost all of the α0 and α1 estimates are positive and highly significant. Interestingly, the two coefficients exhibit markedly different patterns across the delta ranges. Whereas α0 displays a clear pattern of monotonic increases with delta values, α1 does not show any noticeable pattern of systematic variation across different delta ranges. Furthermore, in contrast to the cases of the low and mid-delta ranges, where the α1 estimates are positive and highly significant, the values of α1 in high delta ranges (0.8 or above for both puts and calls) are virtually zero and insignificant. This result might come from the fact that high delta options are illiquid (see Table 2). Informed investors interested in trading high delta options might be reluctant to submit a large order because doing so could lead to an adverse price movement due to a lack of liquidity in the market.

The estimates of adverse selection costs, order-processing costs, and the proportion of adverse selection costs in the spread exhibit patterns that are qualitatively similar to the ones reported in Ahn et al. (2008). For instance, the relative adverse selection costs (in the proportion of the option price) monotonically increase with option delta. The relative order-processing costs decrease with delta values. Finally, the fraction of adverse selection costs in the implied spread (γ) displays a steep monotonic rise as the delta value grows.

4.1.2. Information Effect of Trade Size on High Delta Options

In the previous subsection, we conjectured that the insignificant α1 estimates for high delta options could be due to the reluctance by informed investors to submit large orders: informed investors breaking up their orders facing illiquidity in high delta options. In this section, we empirically investigate whether this is actually the case. The analysis is carried out in two steps. First, we partition the transactions whose option deltas are between 0.8 and 0.9 in absolute terms into three trade-size groups (i.e. small, medium, and large). Then, we re-estimate the SDM for each group. The small trade-size group includes transactions of up to four option contracts. The size range for the medium-sized group is 5–50 contracts. The large size group contains transactions of more than 50 contracts.12 The small, medium, and large size groups account for 45.7%, 45.8%, and 8.5%, respectively, of the total 145 381 transactions in the high delta range. A further breakdown of the distribution of the transactions is shown in Panel A of Table 5.

Table 5.   The estimates of the size-dependent model by trade size for high delta options
Panel A presents the distribution of transactions by trade size for high delta options (absolute delta ≥0.8). Panels B and C display the estimated parameters from the size-dependent version of the Madhavan, Richardson, and Roomans model (size-dependent model) for different size groups (small, medium, and large) of the high delta options (Panel B for call options and Panel C for put options). The reported coefficients are the trade size-independent and -dependent adverse selection components (α0 and α1 respectively), the spread component due to information asymmetry costs (α0 + α1inline image), the trade size-independent and -dependent order-processing components (β0 and β1 respectively), the spread component due to order-processing costs 0 + β1inline image), and the spread implied by the estimated components (2(α + β)). The t-statistics of the coefficient estimates are in parentheses.
GroupTrade sizeCall optionsPut options
Number of observationsFrequency (%)Frequency (%)Number of observationsFrequency (%)Frequency (%)
Panel A: Distribution by trade size
Small (size ≤ 4)136 81425.344.063 70726.545.7
2–427 18018.746 19019.2
Medium (5 ≤ size ≤ 50)5–1035 51524.447.257 38223.945.8
11–2015 19910.524 34210.1
21–5017 83412.328 33611.8
Large (51 ≤ size)51–10075165.28.812 1595.18.5
101–20031082.149172.0
201–50020271.431221.3
501+1880.13310.1
Total 145 381100.0100.0240 486100.0100.0
Sizeα0 (coefficient × 100)α1 (coefficient × 100)Adverse selectionβ0 (coefficient × 100)β1 (coefficient × 100)Order processingImplied spread
Coefficient × 100Price (%)Coefficient × 100Price (%)Coefficient × 100Price (%)
Panel B: Call options
Small2.058 (17.6)−0.386 (−5.4)1.5540.4260.548 (12.3)−0.080 (−9.0)0.4440.1223.9961.095
Medium1.629 (18.5)−0.094 (−5.7)1.2660.3470.487 (14.3)−0.047 (−9.0)0.3040.0833.1400.860
Large1.287 (8.4)0.010 (0.8)1.3980.3830.205 (3.3)−0.006 (−0.8)0.1430.0393.0820.845
Panel C: Put options
Small2.387 (12.6)−0.411 (−3.3)1.8520.3900.805 (10.5)−0.122 (−9.0)0.6460.1364.9971.051
Medium2.081 (16.1)−0.112 (−4.5)1.6530.3480.611 (12.0)−0.074 (−8.3)0.3270.0693.9590.833
Large1.813 (9.4)−0.019 (−1.0)1.6030.3370.262 (2.6)−0.003 (−0.2)0.2330.0493.6730.773

The estimation results are presented in Panels B and C of Table 5 (Panel B for call options and Panel C for put options). For both call and put options, we find that α0 from large trades is smaller than those from small and medium trades. At the same time, α1 is significant and negative for both small- and medium-sized trades, which is in contrast to the significant and positive α1 that appeared in the low and medium delta ranges in Table 4. It is interesting that, while trade size has a positive relation with informed trading in most delta ranges (i.e. |Δ| < 0.8), it works as a binding constraint in the highest delta range. Informed investors appear to prefer small- and medium-sized orders than large ones. This finding renders some support for the hypothesis that informed investors have incentives to break up their orders to hide their identity. However, the finding is somewhat different from the stealth trading pattern observed in equity markets. Both Barclay and Warner (1993) and Chakravarty (2001) report that medium-sized trades have the most price impacts. In our case, it is small trades that have the largest impacts.

4.2. Buy/Sell Asymmetry

4.2.1. Combined Results

Tables 6 and 7 present the estimation results of the DVM across different months of the year and option deltas respectively. All estimated parameters are positive and significant. In each table, the Buy column indicates the results for buyer-initiated trades and the Sell column for seller-initiated trades.

Table 6.   The monthly estimates of the dummy variable MRR model
The estimated parameters of the dummy variable version of the Madhavan, Richardson, and Roomans Model (dummy variable model) for the KOSPI 200 options are shown. The estimation is carried out separately for each month. Panel A shows the results for call options and Panel B for put options. The adverse selection component (α), the order-processing component (β), the spread implied by the estimated components (2(α + β)), and the proportion of the adverse selection component in the implied spread (γ) are reported. The estimations are carried out separately for buy and sell trades. The “Buy” column indicates buyer-initiated trades and the “Sell” column indicates seller-initiated trades. The t-statistics of the coefficient estimates are in parentheses.
Monthαα (%)ββ (%)Implied spreadγ (%)
Buy (coefficient × 100)Sell (coefficient × 100)BuySellBuy (coefficient × 100)Sell (coefficient × 100)BuySellBuySellBuySell
Coefficient × 100Price (%)Coefficient × 100Price (%)
Panel A: Estimation results for call options
 10.269 (18.64)0.265 (17.15)0.2560.2620.269 (18.64)0.392 (98.48)0.3950.3881.3651.3031.3121.30139.440.3
 20.221 (17.09)0.201 (16.57)0.2310.2140.221 (17.09)0.374 (110.88)0.3980.3991.2061.2571.1501.22736.734.9
 30.240 (19.06)0.220 (17.39)0.2150.2030.240 (19.06)0.416 (116.29)0.3820.3831.3341.1951.2711.17236.034.6
 40.250 (19.45)0.241 (16.83)0.2480.2460.415 (80.58)0.394 (96.87)0.4120.4031.3301.3201.2691.29837.637.9
 50.222 (21.79)0.227 (19.71)0.2260.2350.222 (21.79)0.374 (110.02)0.4060.3861.2421.2641.2031.24235.737.8
 60.213 (18.92)0.206 (17.39)0.2450.2410.213 (18.92)0.348 (104.30)0.4190.4081.1541.3281.1091.29737.037.2
 70.224 (22.41)0.223 (21.12)0.2530.2570.224 (22.41)0.357 (112.04)0.4220.4121.1951.3511.1601.33837.538.4
 80.183 (18.59)0.176 (18.27)0.2050.2020.183 (18.59)0.344 (119.55)0.4010.3931.0811.2131.0411.18933.833.9
 90.160 (19.40)0.151 (16.85)0.2110.2050.160 (19.40)0.336 (121.66)0.4520.4561.0031.3260.9721.32231.931.0
100.182 (22.06)0.180 (21.30)0.2160.2200.182 (22.06)0.322 (121.88)0.4030.3931.0391.2391.0041.22734.935.9
110.137 (18.47)0.131 (16.94)0.1810.1760.137 (18.47)0.338 (123.44)0.4580.4530.9701.2770.9381.25828.328.0
120.142 (18.16)0.130 (15.60)0.1970.1840.142 (18.16)0.333 (118.66)0.4730.4720.9671.3400.9271.31229.428.1
Average0.230 (21.21)0.218 (19.27)0.2500.2440.342 (100.87)0.327 (104.69)0.3860.3781.1441.2721.0921.24439.840.1
Panel B: Estimation results for put options
 10.302 (17.76)0.276 (14.95)0.3030.2900.373 (68.58)0.382 (71.13)0.3750.4021.3491.3571.3171.38344.741.9
 20.261 (16.30)0.248 (15.00)0.2900.2790.354 (69.99)0.354 (74.45)0.3930.3991.2301.3661.2031.35642.441.2
 30.248 (17.68)0.225 (17.71)0.2570.2380.381 (88.38)0.377 (106.62)0.3940.3981.2571.3021.2041.27239.437.4
 40.301 (20.06)0.259 (18.63)0.3040.2640.383 (73.36)0.387 (100.99)0.3860.3951.3691.3791.2911.31844.140.1
 50.276 (19.49)0.252 (18.62)0.2880.2650.386 (93.26)0.371 (101.44)0.4020.3901.3241.3791.2471.30841.740.4
 60.276 (17.80)0.255 (16.57)0.2810.2660.391 (85.50)0.375 (88.83)0.3980.3911.3351.3591.2611.31341.440.5
 70.281 (19.49)0.258 (17.67)0.2930.2730.369 (73.17)0.360 (76.89)0.3840.3821.2991.3541.2351.31043.241.7
 80.208 (17.84)0.198 (15.98)0.2270.2180.356 (92.15)0.346 (100.79)0.3890.3801.1291.2331.0881.19636.836.4
 90.196 (18.01)0.171 (15.76)0.2240.2030.342 (95.89)0.338 (98.47)0.3910.4001.0771.2301.0181.20636.433.6
100.226 (20.20)0.203 (19.01)0.2460.2240.328 (88.42)0.327 (99.67)0.3570.3611.1081.2051.0601.16940.838.3
110.163 (17.80)0.156 (16.24)0.2080.2030.331 (101.13)0.316 (65.62)0.4220.4110.9871.2590.9451.22933.033.1
120.189 (18.05)0.153 (15.92)0.2400.1980.327 (87.17)0.334 (82.56)0.4150.4331.0321.3110.9741.26136.631.4
Average0.244 (18.37)0.221 (16.84)0.2630.2430.360 (84.75)0.356 (88.95)0.3920.3951.2081.3111.1531.27740.038.0
Table 7.   The estimates of the dummy variable MRR model by option delta
The estimated parameters for the dummy variable version of the Madhavan, Richardson, and Roomans model (dummy variable model) for the KOSPI 200 options are shown. The estimation is carried out separately for each of the 16 groups based on the absolute values of option deltas. Panel A shows the results for call options and Panel B for put options. The adverse selection component (α), the order-processing component (β), the spread implied by the estimated components (2(α + β)), and the proportion of the adverse selection component in the implied spread (γ) are reported. The estimations are carried out separately for buy and sell trades. The “Buy” column indicates buyer-initiated trades and the “Sell” column indicates seller-initiated trades. The t-statistics of the coefficient estimates are in parentheses.
|Δ|αα (%)ββ (%)Implied spreadγ (%)
Buy (coefficient × 100)Sell (coefficient × 100)BuySellBuy (coefficient × 100)Sell (coefficient × 100)BuySellBuySellBuySell
Coefficient × 100Price (%)Coefficient × 100Price (%)
Panel A: Estimation results for call options
0.10–0.150.041 (25.6)0.045 (26.9)0.0920.1030.374 (406.8)0.362 (426.7)0.8430.8340.8291.8700.8131.8739.911.0
0.15–0.200.057 (30.4)0.064 (29.9)0.0900.1020.372 (411.4)0.355 (393.6)0.5850.5690.8591.3500.8381.34213.415.2
0.20–0.250.079 (30.0)0.085 (31.5)0.0980.1070.365 (346.6)0.346 (333.9)0.4540.4380.8881.1040.8621.08917.819.6
0.25–0.300.114 (31.9)0.117 (31.3)0.1180.1230.357 (267.9)0.339 (260.5)0.3720.3580.9410.9800.9110.96324.125.7
0.30–0.350.144 (33.0)0.152 (30.2)0.1220.1320.350 (219.9)0.327 (199.2)0.2960.2830.9880.8370.9590.83029.231.8
0.35–0.400.193 (30.2)0.198 (27.8)0.1530.1600.335 (167.9)0.310 (146.8)0.2660.2491.0550.8391.0150.81836.539.0
0.40–0.450.233 (29.1)0.239 (24.9)0.1600.1680.363 (119.4)0.337 (112.8)0.2500.2361.1920.8201.1520.80739.041.6
0.45–0.500.299 (19.8)0.299 (16.9)0.1830.1860.458 (54.7)0.425 (67.5)0.2800.2651.5150.9261.4470.90339.541.3
0.50–0.550.423 (21.0)0.398 (18.8)0.2290.2230.495 (74.1)0.470 (76.4)0.2690.2631.8370.9961.7370.97146.145.9
0.55–0.600.524 (19.4)0.484 (17.1)0.2400.2320.494 (56.0)0.480 (59.8)0.2260.2302.0360.9311.9270.92451.550.2
0.60–0.650.658 (17.2)0.593 (15.7)0.3020.2800.441 (35.7)0.446 (41.6)0.2020.2112.1971.0092.0780.98259.957.1
0.65–0.700.896 (15.6)0.779 (13.5)0.3390.3040.359 (21.6)0.417 (28.8)0.1360.1622.5110.9502.3920.93371.465.2
0.70–0.751.154 (13.8)1.024 (11.7)0.3590.3310.370 (14.5)0.403 (15.9)0.1150.1303.0470.9482.8540.92275.771.8
0.75–0.801.284 (12.2)1.176 (11.2)0.3890.3640.367 (11.1)0.385 (13.3)0.1110.1193.3031.0013.1210.96577.875.3
0.80–0.851.423 (10.9)1.383 (9.7)0.4030.3940.305 (7.6)0.311 (8.1)0.0870.0883.4560.9803.3890.96482.381.7
0.85–0.901.515 (9.5)1.567 (8.7)0.3880.4240.349 (6.9)0.270 (4.8)0.0890.0733.7280.9543.6750.99481.385.3
Panel B: Estimation results for put options
0.10–0.150.048 (24.7)0.049 (25.3)0.1030.1060.365 (370.6)0.356 (421.9)0.7740.7760.8271.7530.8101.76411.712.0
0.15–0.200.070 (23.6)0.071 (28.0)0.1060.1090.362 (295.1)0.350 (382.0)0.5490.5410.8631.3100.8421.29916.216.8
0.20–0.250.106 (29.2)0.107 (30.8)0.1280.1310.350 (268.4)0.333 (275.3)0.4230.4080.9131.1030.8811.07923.224.4
0.25–0.300.146 (30.6)0.145 (29.8)0.1480.1490.339 (200.1)0.320 (202.7)0.3430.3280.9690.9820.9310.95430.131.2
0.30–0.350.194 (32.5)0.190 (28.9)0.1660.1640.325 (153.7)0.304 (150.5)0.2780.2631.0380.8880.9880.85337.438.4
0.35–0.400.257 (30.1)0.245 (27.9)0.1860.1770.329 (118.5)0.309 (114.1)0.2380.2231.1730.8491.1090.79843.944.2
0.40–0.450.329 (25.5)0.298 (22.7)0.2040.1850.376 (96.3)0.359 (94.3)0.2330.2231.4110.8751.3140.81746.745.4
0.45–0.500.443 (22.7)0.396 (20.5)0.2510.2290.424 (73.0)0.417 (72.7)0.2410.2411.7340.9841.6250.94051.148.7
0.50–0.550.536 (19.3)0.449 (16.0)0.2910.2570.435 (47.1)0.453 (56.9)0.2360.2601.9431.0531.8041.03355.249.8
0.55–0.600.646 (16.7)0.528 (15.0)0.3390.2920.395 (33.5)0.442 (41.0)0.2070.2452.0831.0921.9411.07462.154.4
0.60–0.650.796 (14.4)0.657 (12.1)0.3430.3000.376 (23.9)0.443 (26.0)0.1620.2032.3441.0102.2001.00667.959.7
0.65–0.701.009 (14.2)0.831 (12.2)0.3660.3070.385 (17.2)0.477 (25.9)0.1400.1762.7881.0122.6170.96772.463.5
0.70–0.751.082 (11.3)0.882 (9.7)0.3850.3430.354 (10.6)0.495 (19.1)0.1260.1932.8721.0212.7531.07275.364.1
0.75–0.801.490 (11.9)1.260 (9.9)0.3800.3390.434 (9.7)0.533 (12.1)0.1110.1443.8480.9803.5860.96677.470.3
0.80–0.851.840 (11.0)1.674 (9.2)0.3980.3630.415 (7.1)0.436 (5.7)0.0900.0954.5100.9754.2200.91681.679.3
0.85–0.900.048 (24.7)0.049 (25.3)0.1030.1060.365 (370.6)0.356 (421.9)0.0700.0774.7110.9514.5560.92085.383.3

Table 6 clearly shows that the information asymmetry component is larger with buy trades than with sell trades. When the raw α value is used, in 11 of the 12 months for call options (Panel A) and in all 12 months for put options (Panel B), buyer-initiated trades incur greater adverse selection costs than seller-initiated trades do. When the proportional α is used, in 8 months for call options and in all 12 months for put options, buy trades are more informative than sell trades.

The estimation results sorted by delta values reported in Table 7 show that greater information effects of buy trades are seen only at high delta ranges. For call options (Panel A), the α values are greater with buy transactions than with sell transactions when the delta values are higher than 0.5. For put options (Panel B), buy/sell asymmetry is more apparent. The α estimates are higher with buys than with sells for all delta ranges above 0.3. It appears that the observed pattern is linked to the relationship between delta values and the degree of informed trading. Ahn et al. (2008) report that the information content of a trade increases with option delta. If informed trading takes place mostly in high delta ranges, it must also be the case that buy/sell asymmetry in informed trading is seen mostly in those delta ranges.

4.2.2. Results Based on Investor Types

To further understand the observed pattern of buy/sell information asymmetry, we extend our analysis by including information about three investor groups (domestic individuals, domestic institutions, and foreign institutions). Examining the effects of investor type on buy/sell asymmetry is motivated by the idea that information advantages might differ among different investor groups. Many recent studies that utilize investor-type information find that individuals are less informed than institutions (e.g. Grinblatt & Keloharju, 2000; Barber et al., 2009). In addition, even among institutional investors, foreign institutions are reported to have better information advantages than their domestic counterparts (e.g. Grinblatt & Keloharju, 2000). If the buy/sell information asymmetry observed in Tables 6 and 7 are indeed driven by informed trading, then we should see a marked pattern of similar asymmetry from the trades made by institutions (especially foreign institutions).

Table 8 shows the buy and sell trading activities according to the three different investor groups. Reported in each delta interval are the proportions of the buys and sells (in number of trades, volume in number of contracts, and volume in monetary value) initiated by each of the three types of investors as percentages of the aggregated buys and sells initiated by all three types of investors. The table exhibits several patterns. For both buys and sells in all delta ranges, individual investors dominate the other types of investors in terms of trading activity. Second, the buys and sells initiated by individual investors are more concentrated in low delta ranges. Third, as the delta value increases, the rate of trading by individuals decreases, while the rate of trading by foreign institutions increases. Fourth, and most interesting, for both domestic and foreign institutions, a systematic pattern of reversal exists across delta ranges in that there are more sells than buys in low delta ranges and more buys than sells in high delta ranges. This suggests that the results are somehow related to the relationship between delta and buy/sell information asymmetry, which is observed in Table 7. Meanwhile, no such reversal is seen in the trades initiated by individuals.

Table 8.   The percentage distributions of the trade initiation rates by investor type
The percentages of the number of transactions, trading volume, and trading value for buy and sell trades initiated by each of the three investor types (domestic individuals, domestic institutions, and foreign institutions) are shown. Panel A shows the results for call options and Panel B for put options. For each delta range, the percentage rate for each trader type is calculated as the number of the transactions (volume, value) initiated by the investor type divided by the total number of the transactions (volume, value) initiated by all three investor groups.
|Δ|Number of tradesTrading volumeTrading value
IndividualsInstitutionsForeign institutionsIndividualsInstitutionsForeign institutionsIndividualsInstitutionsForeign institutions
BuySellBuySellBuySellBuySellBuySellBuySellBuySellBuySellBuySell
Panel A: Percentage trade initiation rates for call options
0.10–0.1539.448.63.44.32.12.229.129.815.317.24.44.228.628.316.317.94.54.4
0.15–0.2039.646.44.75.41.82.225.025.020.121.83.84.424.624.020.722.13.94.6
0.20–0.2539.146.35.05.41.92.324.124.620.422.24.04.724.124.220.421.74.45.2
0.25–0.3040.145.94.85.21.72.326.726.818.219.44.04.927.627.117.117.84.65.8
0.30–0.3540.244.94.85.42.02.627.427.816.717.84.75.628.628.215.315.95.56.5
0.35–0.4040.844.84.25.32.22.828.828.615.117.04.85.730.629.712.514.35.97.0
0.40–0.4540.144.44.15.42.83.129.329.813.815.45.86.030.030.011.713.07.67.8
0.45–0.5038.744.54.55.73.23.428.529.813.514.76.96.527.928.711.912.99.68.9
0.50–0.5536.943.45.86.53.83.627.729.314.414.97.26.525.326.214.014.110.89.6
0.55–0.6035.542.86.46.64.64.226.329.313.513.98.98.022.925.814.413.312.610.9
0.60–0.6534.441.67.66.95.14.425.628.114.814.88.87.921.324.615.714.412.911.1
0.65–0.7032.539.98.97.06.25.425.526.814.912.610.59.720.122.317.613.313.912.8
0.70–0.7530.439.110.07.57.06.021.926.615.413.212.710.316.720.918.214.615.913.5
0.75–0.8030.737.410.28.47.06.322.125.616.114.811.410.115.819.518.316.415.914.0
0.80–0.8530.036.210.79.27.26.722.424.516.415.211.410.115.718.718.817.115.813.8
0.85–0.9030.035.410.29.67.47.424.224.315.714.711.29.816.917.419.216.216.513.9
Panel B: Percentage trade initiation rates for put options
0.10–0.1540.048.13.34.22.22.230.531.213.715.54.64.430.330.114.315.74.94.8
0.15–0.2040.346.54.24.72.02.226.827.018.019.54.14.526.826.618.019.24.55.0
0.20–0.2540.246.84.24.52.02.326.527.517.919.24.24.727.328.016.817.84.85.4
0.25–0.3040.446.63.94.52.22.528.429.215.717.24.45.129.630.213.815.05.46.1
0.30–0.3540.146.03.94.82.42.828.829.914.216.25.05.830.230.812.014.06.17.0
0.35–0.4038.845.34.25.43.13.229.730.512.714.86.06.329.630.511.113.37.67.9
0.40–0.4537.545.34.95.33.53.429.931.012.013.26.96.928.529.611.312.59.18.9
0.45–0.5036.244.66.05.73.93.528.930.913.113.76.86.725.627.913.213.210.59.6
0.50–0.5534.044.97.15.64.63.827.131.113.913.37.86.922.927.114.812.512.410.3
0.55–0.6033.343.28.26.05.34.027.029.515.013.67.97.121.625.916.512.413.110.6
0.60–0.6532.042.39.36.05.94.526.029.014.712.89.38.220.324.117.512.613.711.8
0.65–0.7030.440.410.46.76.85.324.828.114.113.510.09.517.822.417.014.814.613.4
0.70–0.7530.740.710.17.16.35.125.328.814.414.09.38.219.021.818.014.814.312.2
0.75–0.8028.737.910.68.38.36.321.825.014.314.013.611.315.518.617.815.717.814.6
0.80–0.8526.834.111.810.69.17.620.620.313.817.913.513.915.114.416.220.216.717.4
0.85–0.9027.534.711.210.48.77.520.822.913.915.313.913.214.515.216.618.317.517.9

Table 9 presents the monthly estimates of adverse selection costs for buys and sells by different investor groups. The trades by individuals form no discernible pattern. However, for domestic and foreign institutions, the pattern is simple and clear. The buy transactions made by domestic institutions lead to greater information effects than their sell transactions in 11 of the 12 months in raw estimates and in all 12 months in percentage estimates for call options (Panel A). The results are even stronger with put options (Panel B). The buy-side estimates for domestic institutions exceed their sell-side estimates in all 12 months in both raw and percentage terms. When it comes to trades made by foreign institutions, the buy-side estimates are always greater than the sell-side estimates regardless of option type and measures used. The evidence shown in Table 9 is a strong indication that buy/sell information asymmetry is caused by institutional trading.

Table 9.   The monthly estimated adverse selection costs by investor type
The adverse selection costs and their relative values to option prices, measured by contract-weighted average quote midpoints, for the buy and sell trades initiated by each of the three investor types (domestic individuals, domestic institutions, and foreign institutions) are shown. We run separate estimations for different months. The t-statistics for the estimates are in parentheses.
MonthAdverse selection costs (coefficient × 100)Adverse selection costs (%)
IndividualsInstitutionsForeign institutionsIndividualsInstitutionsForeign institutions
BuySellBuySellBuySellBuySellBuySellBuySell
Panel A: Adverse selection cost for call options
 10.229 (26.20)0.238 (21.83)0.383 (17.71)0.347 (20.23)0.930 (13.43)0.669 (15.90)0.2230.2310.3720.3380.9050.651
 20.175 (25.18)0.177 (23.52)0.454 (16.76)0.271 (17.45)0.751 (13.00)0.629 (13.90)0.1850.1870.4790.2850.7920.663
 30.201 (26.01)0.190 (24.49)0.405 (17.08)0.330 (19.39)0.861 (15.45)0.783 (16.79)0.1830.1730.3680.3000.7830.712
 40.205 (28.10)0.203 (24.20)0.435 (17.35)0.377 (17.82)0.923 (19.39)0.827 (17.42)0.2070.2040.4380.3790.9300.833
 50.189 (30.55)0.201 (28.90)0.335 (17.63)0.292 (19.35)0.595 (16.85)0.558 (16.52)0.1940.2060.3430.2990.6100.572
 60.184 (26.08)0.184 (25.60)0.280 (16.40)0.267 (15.67)0.564 (14.96)0.444 (14.41)0.2140.2140.3240.3100.6540.516
 70.187 (31.73)0.197 (29.41)0.319 (18.98)0.283 (21.00)0.609 (20.57)0.484 (21.49)0.2130.2250.3650.3230.6960.553
 80.150 (26.96)0.155 (26.29)0.283 (16.47)0.209 (19.10)0.446 (17.15)0.399 (17.54)0.1700.1760.3210.2360.5060.452
 90.131 (26.47)0.131 (24.42)0.218 (14.56)0.197 (13.87)0.458 (18.12)0.388 (19.91)0.1760.1750.2920.2640.6150.520
100.149 (32.87)0.157 (31.25)0.260 (16.59)0.216 (19.06)0.431 (21.45)0.389 (20.84)0.1790.1890.3140.2610.5200.470
110.114 (26.49)0.116 (24.08)0.154 (15.88)0.142 (18.19)0.385 (17.57)0.332 (17.69)0.1520.1540.2050.1880.5120.441
120.119 (25.44)0.115 (23.47)0.118 (15.75)0.118 (17.30)0.447 (16.24)0.375 (16.47)0.1660.1610.1650.1660.6270.526
Avg.0.169 (27.67)0.172 (25.62)0.304 (16.76)0.254 (18.20)0.617 (17.01)0.523 (17.41)0.1880.1910.3320.2790.6790.576
Panel B: Adverse selection cost for put options
 10.246 (24.99)0.257 (19.05)0.485 (16.72)0.302 (14.63)0.932 (13.20)0.646 (11.56)0.2530.2650.4990.3110.9580.664
 20.202 (23.48)0.214 (19.50)0.516 (15.99)0.386 (18.12)0.900 (11.27)0.665 (15.09)0.2260.2400.5780.4321.0080.744
 30.192 (26.42)0.207 (23.02)0.536 (14.57)0.296 (15.03)0.896 (13.12)0.534 (14.93)0.2010.2170.5600.3090.9370.559
 40.238 (29.87)0.236 (25.44)0.541 (13.42)0.347 (17.41)1.025 (17.87)0.613 (17.07)0.2410.2390.5490.3521.0400.622
 50.227 (27.86)0.233 (25.69)0.407 (16.70)0.319 (16.59)0.826 (15.93)0.494 (14.86)0.2370.2440.4260.3330.8630.517
 60.239 (22.77)0.235 (23.67)0.377 (15.68)0.313 (15.61)0.650 (15.66)0.475 (15.68)0.2460.2420.3880.3220.6690.489
 70.225 (28.62)0.234 (23.47)0.437 (12.77)0.336 (15.84)0.754 (18.07)0.495 (15.91)0.2370.2460.4600.3530.7930.520
 80.167 (25.57)0.178 (21.82)0.371 (15.13)0.226 (13.84)0.494 (16.35)0.436 (15.97)0.1830.1950.4060.2480.5410.478
 90.157 (26.22)0.155 (21.94)0.316 (14.31)0.206 (11.19)0.513 (16.72)0.360 (17.49)0.1830.1800.3680.2390.5960.419
100.178 (29.77)0.182 (27.87)0.362 (15.71)0.273 (14.43)0.540 (19.72)0.352 (19.40)0.1950.2000.3970.2990.5910.386
110.134 (26.02)0.137 (18.80)0.203 (13.20)0.193 (14.31)0.456 (15.86)0.375 (16.85)0.1730.1760.2610.2490.5880.483
120.150 (25.45)0.137 (22.74)0.228 (17.15)0.121 (14.40)0.544 (17.14)0.418 (11.49)0.1920.1750.2920.1550.6970.536
Average0.196 (26.42)0.200 (22.75)0.398 (15.11)0.276 (15.12)0.711 (15.91)0.489 (15.53)0.2140.2180.4320.3000.7740.535

Table 10 displays adverse selection costs for different investor groups by delta ranges. In every single delta range, foreign institutions incur the highest adverse selection costs, implying that they have information advantages over both domestic institutions and individuals. Between the latter two, the general results indicate that domestic institutions are better informed than individuals because the estimated adverse selection costs for domestic institutions are larger than those for individuals in the majority of the delta ranges.

Table 10.   The estimated adverse selection costs by investor type across option delta
The adverse selection costs and their relative values to the option prices, measured by contract-weighted average quote midpoints, for buy and sell trades initiated by each of the three investor types (domestic individuals, domestic institutions, and foreign institutions) are shown. We run a separate estimation for each of the 16 different groups based on the absolute option delta values. The t-statistics for the estimates are reported in parentheses.
|Δ|Adverse selection costs (coefficient × 100)Adverse selection costs (%)
IndividualsInstitutionsForeign institutionsIndividualsInstitutionsForeign institutions
BuySellBuySellBuySellBuySellBuySellBuySell
Panel A: Adverse selection cost for call options
0.10–0.150.036 (32.38)0.042 (35.78)0.051 (17.00)0.043 (20.10)0.112 (16.62)0.109 (18.02)0.0830.0950.1150.0990.2560.248
0.15–0.200.051 (38.59)0.061 (39.66)0.076 (25.62)0.059 (29.55)0.148 (16.99)0.144 (16.50)0.0810.0960.1210.0930.2360.228
0.20–0.250.071 (39.63)0.081 (42.90)0.093 (29.92)0.077 (29.30)0.208 (15.51)0.175 (18.13)0.0890.1020.1160.0970.2600.219
0.25–0.300.105 (41.95)0.111 (44.61)0.127 (26.44)0.106 (27.28)0.262 (15.21)0.249 (17.44)0.1110.1170.1340.1120.2750.261
0.30–0.350.138 (42.13)0.146 (42.94)0.144 (27.61)0.140 (25.15)0.272 (17.47)0.287 (17.94)0.1180.1250.1240.1200.2330.246
0.35–0.400.186 (39.66)0.190 (41.34)0.177 (23.09)0.191 (21.87)0.344 (16.18)0.348 (16.52)0.1490.1520.1420.1530.2750.279
0.40–0.450.227 (35.93)0.227 (37.11)0.218 (20.80)0.239 (18.64)0.335 (17.46)0.407 (15.46)0.1580.1580.1510.1660.2330.282
0.45–0.500.290 (24.53)0.280 (22.30)0.278 (17.80)0.331 (20.15)0.441 (14.79)0.486 (14.18)0.1790.1730.1720.2050.2720.300
0.50–0.550.409 (26.87)0.377 (24.77)0.383 (17.91)0.468 (20.82)0.615 (16.55)0.537 (15.02)0.2250.2070.2110.2580.3390.296
0.55–0.600.487 (24.27)0.461 (22.03)0.574 (19.12)0.542 (19.69)0.748 (17.68)0.623 (14.38)0.2280.2160.2690.2540.3500.292
0.60–0.650.601 (20.60)0.548 (19.45)0.709 (15.45)0.703 (19.00)0.966 (15.98)0.857 (15.46)0.2800.2550.3300.3270.4500.399
0.65–0.700.767 (19.02)0.691 (16.72)1.115 (17.75)0.978 (16.10)1.259 (19.41)1.187 (17.54)0.2940.2650.4280.3750.4840.456
0.70–0.750.968 (16.81)0.871 (13.71)1.342 (16.44)1.334 (16.65)1.693 (17.78)1.683 (16.11)0.3070.2760.4260.4230.5370.534
0.75–0.800.990 (15.42)0.980 (13.59)1.613 (15.13)1.428 (13.02)2.094 (18.24)2.054 (16.47)0.3030.3000.4940.4370.6410.629
0.80–0.851.038 (13.41)1.101 (11.28)1.711 (13.45)1.766 (12.39)2.662 (15.37)2.452 (17.15)0.2950.3130.4860.5020.7560.696
0.85–0.901.046 (11.58)1.123 (10.25)1.986 (10.05)2.227 (11.76)2.807 (15.04)2.916 (16.49)0.2750.2950.5220.5850.7380.766
Panel B: Adverse selection cost for put options
0.10–0.150.042 (32.85)0.047 (33.23)0.076 (18.47)0.045 (21.14)0.128 (15.91)0.092 (14.65)0.0900.1010.1640.0960.2740.197
0.15–0.200.060 (29.51)0.069 (34.62)0.098 (22.33)0.063 (21.02)0.201 (15.33)0.112 (16.21)0.0920.1060.1500.0970.3080.171
0.20–0.250.096 (42.99)0.105 (38.82)0.128 (20.55)0.100 (25.77)0.266 (15.01)0.178 (18.05)0.1160.1270.1560.1220.3230.216
0.25–0.300.137 (42.55)0.142 (39.14)0.159 (15.38)0.132 (24.12)0.286 (16.27)0.240 (17.29)0.1400.1440.1620.1340.2920.244
0.30–0.350.188 (43.58)0.188 (38.70)0.187 (20.14)0.160 (20.22)0.303 (15.22)0.272 (15.31)0.1620.1610.1610.1370.2600.234
0.35–0.400.249 (39.51)0.240 (36.64)0.248 (22.33)0.255 (22.21)0.380 (15.07)0.306 (19.04)0.1790.1730.1790.1840.2750.221
0.40–0.450.317 (32.98)0.297 (29.05)0.343 (19.30)0.288 (19.97)0.447 (15.31)0.334 (16.49)0.1970.1840.2130.1790.2780.207
0.45–0.500.408 (29.89)0.393 (25.07)0.489 (20.80)0.391 (20.11)0.699 (14.80)0.434 (16.90)0.2340.2250.2800.2240.4010.249
0.50–0.550.474 (24.91)0.439 (19.25)0.647 (18.80)0.446 (17.25)0.830 (14.09)0.569 (17.16)0.2640.2450.3610.2490.4630.317
0.55–0.600.556 (21.72)0.492 (17.41)0.799 (18.95)0.618 (16.35)0.980 (13.45)0.797 (13.94)0.2990.2650.4300.3320.5270.429
0.60–0.650.653 (17.69)0.592 (14.78)0.988 (18.27)0.783 (14.80)1.274 (15.47)1.121 (12.83)0.2900.2630.4380.3480.5650.497
0.65–0.700.809 (17.14)0.746 (14.96)1.149 (13.94)0.986 (10.64)1.702 (18.40)1.330 (15.81)0.2960.2730.4210.3610.6240.487
0.70–0.750.826 (13.49)0.739 (11.47)1.421 (8.72)1.142 (12.30)1.789 (16.27)1.720 (14.67)0.3070.2750.5290.4250.6650.640
0.75–0.801.216 (13.55)1.051 (11.59)1.506 (10.73)1.584 (12.33)2.403 (15.51)2.199 (10.31)0.3180.2750.3940.4150.6290.576
0.80–0.851.470 (12.22)1.409 (10.04)1.950 (11.37)2.045 (10.47)2.787 (14.37)2.406 (14.57)0.3190.3050.4220.4430.6040.521
0.85–0.901.639 (10.07)1.526 (7.22)1.812 (5.54)2.306 (10.18)3.436 (13.96)3.128 (14.90)0.3310.3080.3660.4660.6940.631

The table also shows that buy trades are more informative than sell trades for both types of institutions (foreign institutions, especially). In the case of put options (Panel B), the estimates of buy-side adverse selection costs are greater than the sell-side estimates in 12 of the 16 ranges for domestic institutions and in all 16 ranges for foreign institutions. Although the results on call options (Panel A) are not as strong as those in the case of put options, the same general pattern is still observed. The estimates for buys are greater than those for sells in nine of the 16 ranges for domestic institutions and 10 of the 16 ranges for foreign institutions. The results reported in Table 10 are consistent with the explanation that the buy/sell asymmetry observed in the KOSPI 200 options is associated with institutional trading, particularly foreign institutional trading.

4.2.3. Buy/Sell Asymmetry and Delta

In previous sections, we witnessed that adverse selection costs increase with delta (Table 4). We also observed that buy/sell asymmetry is present mostly with high delta options and most prevalent with trades by foreign institutions (Tables 7 and 10). Put together, these findings suggest a possible empirical relation between buy/sell asymmetry and delta. That is, buy/sell asymmetry increases with delta and the pattern should be seen across different investor groups, especially for foreign investors. If informed traders concentrate on high delta options and prefer using buy orders, buy/sell asymmetry should be the largest in high delta ranges as the orders submitted there carry most information. Although some of the evidence presented in Tables 7 and 10 provides a glimpse of an answer to this question, they do not offer any direct, quantitative answer. To address this issue in a more straightforward manner, we reconstruct Table 10 in such a way that buy/sell asymmetry is more directly observable: we calculate the differences in the estimated adverse selection costs between buys and sells reported in the table. We limit our analysis to options with delta values less than 0.8 because the options with abnormally high delta values tend to exhibit different behavior from the rest (Section 4.1.2). Differences are calculated for both raw estimates of adverse selection costs and the estimates measured in percentage terms.

Table 11 displays the calculated buy/sell differences (i.e. Adverse Selection Costbuy − Adverse Selection Costsell). For the sake of easier comparisons, out of the 14 delta ranges for each investor type, the three with the largest differences are accompanied by superscript symbols for the largest, second largest, and §third largest values. We further indicate the magnitudes of the differences among the three ranges. If the buy/sell asymmetries are positively related to option deltas, the superscript symbols will appear mostly at the lower half of the panels.

Table 11.   Buy/sell difference in adverse selection costs by investor type
The differences in adverse selection costs between buy and sell transactions across different delta ranges for each of the three investor types, including domestic individuals, domestic institutions, and foreign institutions are shown. For each option and investor type, the delta ranges that have the three largest differences are accompanied by superscript symbols for the largest, second largest, and §third largest values.
|Δ|Adverse Selection CostBuy − Adverse Selection CostSell
Coefficient × 100Price (%)
IndividualsInstitutionsForeign InstitutionsIndividualsInstitutionsForeign Institutions
Panel A: Call options
0.1–0.15−0.0060.0080.003−0.0120.0160.008
0.15–0.2–0.0100.0170.004–0.0150.0280.008
0.2–0.25–0.0100.0160.033–0.0130.0190.041
0.25–0.3–0.0060.0210.013–0.0060.022§0.014
0.3–0.35–0.0080.004–0.015–0.0070.004–0.013
0.35–0.4–0.004–0.014–0.004–0.003–0.011–0.004
0.4–0.450.000–0.021–0.0720.000–0.015–0.049
0.45–0.50.010–0.053–0.0450.006–0.033–0.028
0.5–0.550.032–0.0850.078§0.018–0.0470.043§
0.55–0.60.0260.032§0.1250.0120.0150.058
0.6–0.650.053§0.0060.1090.025§0.0030.051
0.65–0.70.0760.1370.0720.0290.0530.028
0.7–0.750.0970.0080.0100.0310.0030.003
0.75–0.80.0100.1850.0400.0030.0570.012
Average0.0190.0190.0250.0050.0080.012
Panel B: Put options
0.1–0.15–0.0050.0310.036–0.0110.0680.077
0.15–0.2–0.0090.0350.089–0.0140.0530.137
0.2–0.25–0.0090.0280.088–0.0110.0340.107
0.25–0.3–0.0050.0270.046–0.0040.0280.048
0.3–0.350.0000.0270.0310.0010.0240.026
0.35–0.40.009–0.0070.0740.006–0.0050.054
0.4–0.450.0200.0550.1130.0130.0340.071
0.45–0.50.0150.0980.2650.0090.0560.152
0.5–0.550.0350.201§0.261§0.0190.1120.146
0.55–0.60.064§0.1810.1830.0340.098§0.098
0.6–0.650.0610.2050.1530.0270.0900.068
0.65–0.70.0630.1630.3720.0230.0600.137§
0.7–0.750.0870.2790.0690.032§0.1040.025
0.75–0.80.165–0.0780.2040.043–0.0210.053
Average0.0350.0890.1420.0120.0530.086

The pattern of buy/sell asymmetries reported in Table 11 does not follow an exact monotonic increase with delta. However, the distribution of the superscript symbols confirms a general pattern that greater buy/sell asymmetries are associated with higher deltas. In most cases, the superscript symbols are located in the bottom half of the table. The only exception is the call option transactions by domestic institutions when adverse selection costs are measured in percentages. As was the case in the previous sections, put options again exhibit a generally stronger pattern.

Table 11 also reports the average buy/sell differences across investor types.13 They are at the bottom of each panel. The average asymmetries are the largest for the transactions made by foreign institutions, regardless of option type and adverse selection cost measures. It is also shown that trades by domestic institutions have generally greater asymmetries than those by domestic individuals. This pattern of average buy/sell asymmetries across investor types lends further support to the understanding that buy/sell asymmetries are caused by informed institutional trading, particularly that by foreign investors.

5. Conclusions

We examine two important issues related to the information content of a trade in option markets: (i) whether trade size is related to the information content of a trade; and (ii) whether buy and sell transactions carry different information content. Our analysis is based on a rich set of market microstructure data on the KOSPI 200 options, the single most actively traded derivative securities in the world.

We use two structural models that extend the MRR model (1997): the SDM and the DVM. The SDM captures the idea that trade size can affect adverse selection costs. The DVM separately estimates the information contents for buyer- and seller-initiated trades using a dummy variable.

From the analysis using the SDM, we find that trade size is significantly related to the information content of a trade. The estimated parameter for the impact of trade size on the permanent price impact is positive and significant. The pattern is persistent across different parts of the year and across different delta ranges. This finding reinforces the earlier empirical evidence on the relation between trade size and information that is reported in the literature (Easley & O’Hara, 1987; Lin et al., 1995; Easley et al., 1997; Dufour & Engle, 2000).

The DVM analysis on buy/sell information asymmetry shows that there is a clear pattern of asymmetry in the information asymmetry costs between buyer- and seller-initiated transactions. Further analysis reveals that the trades initiated by institutions lead to greater information effects than the trades by individuals, and that the buy/sell information asymmetry is driven mostly by institutional trading. The investor group that is associated with the largest adverse selection costs and contributes most to the buy/sell asymmetry is foreign institutions.

The empirical results from the DVM model generally agree with the finding that individuals are not as sophisticated as institutions (Barber & Odean, 2000; Grinblatt & Keloharju, 2000; Barber et al., 2009). Furthermore, the results are also consistent with evidence showing that foreigners have informational advantages (e.g. Grinblatt & Keloharju, 2000; Froot & Ramadorai, 2008).

Footnotes

  • 1

    Such a case is the Korean Exchange (KRX). Even if there are 33 individual equity options listed in the market, many of the options seldom trade on any given trading day. Most of the trading in derivatives takes place in index futures or index options markets.

  • 2

    Studies that examine the informational role of option trading (in equity option markets) include Easley et al. (1998), Kumar et al. (1998), Cao et al. (2005), Pan & Poteshman (2006), Chakravarty et al. (2004), and Anand & Chakravarty (2007), among others.

  • 3

    The investor can also sell a call option if he or she already owns it. However, in this case he or she can always make an extra profit by purchasing a put option.

  • 4

    Among the studies that compare information advantages between domestic and foreign investors in Korean equity markets, Park et al. (2006) and Oh & Hahn (2008) analyze investment performance, whereas Choe et al. (2008) examine price contributions.

  • 5

    The top-10 list for year 2006 in Table 1 does not include the TIIE 28-day Interbank Rate Futures, which joins the top-10 list in 2006 for the first time. The product’s trading volume in 2006 is 264 million contracts.

  • 6

    Limit orders are further classified as (regular) limit orders, conditional limit orders, and best limit orders. Conditional limit orders are limit orders flagged with a condition that the order turns into a market order when the market switches to the afternoon call market. Best limit orders carry a condition that they should be crossed only at the best bid price (in the case of a sell order) and the best ask price (in the case of a buy order).

  • 7

    The enormous size of the data prevented us from analyzing both years.

  • 8

    An alternative is to use the moneyness measure proposed by Heston and Nandi (2000). However, this measure also fails to reflect the volatility of the underlying asset.

  • 9

    For detailed explanation, please refer to Bollen & Whaley (2004, p. 718).

  • 10

    The first moment equation defines the autocorrelation in the order flow, while the second equation is about the constant drift term for the average pricing error. The rest are the OLS normalizing conditions.

  • 11

    We exclude the equation for a constant drift and set u0 as the sample mean of ut. Therefore, the model is exactly identified.

  • 12

    The partition rule is motivated by the one used in Barclay and Warner (1993). A similar rule is also used in Kang & Ryu (2010).

  • 13

    The averages are calculated as the equal-weighted averages of the buy/sell differences across the 14 delta ranges.

Ancillary