The value of liquidity: Evidence from the derivatives market

Pacific-Basin Finance Journal 8 Ž2000. 483–503 www.elsevier.comrlocatereconbase

The value of liquidity: Evidence from the derivatives market Howard Wei-Hong Chan a,) , Sean M. Pinder b b

a Department of Accounting and Finance, Monash UniÕersity, Clayton, VIC 3168, Australia Department of Accounting and Finance, UniÕersity of Newcastle, Callaghan, NSW 2308, Australia

Abstract This paper documents the systematic overpricing of warrants relative to options. Models are developed in order to explain the cross-sectional variation in the relative pricing of these securities. Results indicate that relative pricing differences ŽRELDIFF. are related to various proxies of liquidity including days-to-maturity, relative trading volume and the mandated presence of market makers in the options market. The identity of warrant-issuers is also found to be significant in explaining relative pricing, possibly reflecting disparate levels of credit risk or it may be a manifestation of the different characteristics relating to the underlying shares upon which the warrants are issued. The paper also documents the impact that the change from floor trading to electronic trading had on the price formation process in the Australian Options Market. q 2000 Elsevier Science B.V. All rights reserved. JEL classification: C21; G13; O33 Keywords: Liquidity; Options; Warrants; Market makers; Market microstructure

1. Introduction Throughout this century the importance of liquidity to securities markets has been well recognised by academics and practitioners alike. There have been many

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Corresponding author. Tel.: q61-3-9905-2424; fax: q61-3-9905-5475. E-mail address: [email protected] ŽH.W.-H. Chan..

0927-538Xr00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 5 3 8 X Ž 0 0 . 0 0 0 1 8 - 4

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papers, both empirical ŽGlosten and Milgrom, 1985; Amihud and Mendelson, 1986; Glosten, 1987; Brock and Kleidon, 1992; McInish and Wood, 1992; Eleswarapu and Reinganum, 1993; Datar et al., 1998. and theoretical ŽAdamati and Pfleiderer, 1988; Pagano, 1989., that have considered the effect of market structure on the liquidity of the market. Many of these papers have also examined the relationship between liquidity and the price formation process. In Australia, a unique opportunity has arisen to investigate the relationship between liquidity and market structure, in particular to investigate the effects of changes in the method of trading in the options market and the price formation process in derivatives markets. In 1991, the Australian Stock Exchange ŽASX. permitted trading to commence in equity warrants.1 Equity warrants have an identical payoff structure to standard exchange-traded options, but have been subject to a different trading mechanism. Prior to the introduction of the screenbased Derivative Trading Facility ŽDTF. in November 1997, options were floortraded whilst warrants have always been screen-traded via the Stock Exchange Automated Trading System ŽSEATS.. Other differences that may influence the relative pricing of these securities include the levels of credit risk associated with the securities, the influence of market-making services and differences in shortselling restrictions. The paper has two major aims. First, the paper tests for any systematic difference in the pricing of equity warrants and options. This analysis will also consider whether any systematic pricing differences have been affected by the switch from floor-based to screen-based option trading. Second, the paper seeks to model the relative pricing difference ŽRELDIFF. between the two securities. Different empirical specifications are developed to examine whether the RELDIFF may be explained by differences in the way in which these securities are traded and regulated. Section 2 reviews some of those factors that have been found to influence market liquidity. The institutional settings that may influence the relative pricing andror the level of trading in the two securities are discussed in Section 3 whilst

1 Equity warrants are issued by parties other than the company upon whose shares the warrants are issued. There is no effect on the capitalisation of the company if the warrants are exercised, therefore, the securities are in fact long-dated options rather than bona-fide warrants. Traditionally, a warrant is a security issued by a company that permits the holder to convert the warrant into shares in the company at the holder’s option, according to the terms of the warrant contract. If the warrant is exercised, additional shares are issued by the company resulting in a dilution in the ownership of existing shareholders. The equity warrants considered in this paper are not issued by the company upon whose share the warrants are written, but instead are issued by a third party with no effect on existing ownership levels.

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Section 4 outlines the nature and source of the data and research methods used. Section 5 sets out the empirical results and Section 6 presents the conclusions.

2. Factors affecting market liquidity A liquid market can be thought of as a market where trading can be accommodated with little or no effect on price. A common way of measuring the relative liquidity of a market is by observing the bid–ask spread relating to assets traded in that market, although an obvious limitation of this approach is that there may be multiple bid–ask spreads, each relating to a different volume of trade. Demsetz Ž1968. investigated the relationship between the volume of trade and the cost of transacting on the New York Stock Exchange ŽNYSE.. Specifically, his analysis centered upon the bid–ask spread observed in the market and the way in which the spread is affected by the level of trading activity. This paper introduced a time dimension to the analysis of the price formation process that focused upon the price of immediacy. The bid–ask spread is the price paid by market participants who require immediacy and he found that as the level of trading activity increased there was a corresponding decrease in the observed bid–ask spread. This finding has been consistently replicated in subsequent studies that have examined the relationship between trading activity and the size of the bid–ask spread ŽTinic, 1972; Tinic and West, 1972; Benston and Hagerman, 1974; Branch and Freed, 1977; Stoll, 1978.. McInish and Wood Ž1992. examined bid–ask spreads from the NYSE on an intra-day basis and found that although, generally, spreads were still inversely related to trading activity, the largest spreads occurred at the beginning and end of the trading day where volume is the greatest. A possible explanation for this result was provided by Brock and Kleidon Ž1992. who developed a model of spreads where market makers exploit the inelastic demand of market participants at the open and close of trade by exercising their monopoly power in widening the spread. Foster and Viswanathan Ž1993. concluded from their study that the behaviour of spreads on the NYSE could be explained by the higher adverse selection costs faced by all traders during these periods. Chan et al. Ž1995. in their examination of intra-day spreads on the NASDAQ, found that whilst spreads were high at the opening of trade, they narrowed significantly towards the close of trade. They reconciled the NASDAQ findings with those from the NYSE by pointing out that it is more difficult for market makers on the NYSE to maintain their desired inventory level. The reason is that they are prevented by regulation from executing trades on only one side of the bid–ask spread during the course of trading. As a result, market makers on the NYSE are forced to widen their spreads so as to avoid holding unwanted inventory positions overnight. Whilst there is some evidence in support of the notion that opportunistic behaviour on the part of market makers may result in an increase in spreads, it is

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not entirely clear how spreads are affected by the mere presence of market makers. Grossman and Miller Ž1988. establish a dynamic model whereby liquidity arises as a result of the willingness of market makers to supply immediacy to participants who in turn are willing to incur a price penalty in order to trade immediately. This price penalty constitutes the market maker’s compensation for holding an open position until the arrival of a final buyerrseller in the market. Their model predicts that the level of liquidity in a market is positively related to the number of market makers in that market. The notion that market makers are a necessary precondition for market liquidity was rejected by Lehmann and Modest Ž1994.. They concluded that there are markets such as the Tokyo Stock Exchange that are successful in providing liquidity in the absence of exchange-designated market makers. Another factor that may affect market liquidity is the method of trading securities within that market. There have been a number of studies that have outlined the advantages associated with trading electronically rather than through a system of open outcry. These advantages include faster execution and reduced errors in the processing of trades ŽPirrong, 1996., reduced costs of running an exchange due to computerisation ŽGrunbichler et al., 1994; Economides and Schwartz, 1995., anonymity provided to informed traders thereby reducing the free rider problem ŽFishman and Longstaff, 1992; Madhavan, 1992. 2 and greater market transparency with a more readily observable order book. Where a participant has a choice between alternative markets in which to trade, the relative level of liquidity in each market will impact upon their decision. Pagano Ž1989. in his examination of the role of multiple markets in the provision of liquidity, suggested two points. First, as the number of traders in a market increases, the traders expected utility from trading in the market, and hence the value of liquidity, will also increase.3 Therefore, the choice of where other traders trade becomes important.4 This result leads to the second point of his analysis in that two markets can exist only if there are participants who are faced with differential transaction costs that are working to offset any differences in liquidity.

2

Forster and George Ž1992. question whether anonymity is achievable due to the key role played by market makers in some markets. It is arguable that in the electronically based SEATS trading in Australia, it is possible to identify the broker on the other side of the trade and possibly the identity of the party on whose behalf the broker is acting. 3 The reason is that as the number of traders Ž i . increase, the elasticity of the market price with respect to the demand of a particular trader i decreases. As a result, the trader gets a ‘‘better’’ price for the trade. 4 In a Nash equilibrium, traders take the action of others as given in their decision making. As a result, the trader will choose one market to trade, as would all other traders. Therefore, trading will only occur in one market.

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In this context, the existence of multiple markets in the same security is consistent with market participants behaving in a utility-maximising manner.5

3. Institutional arrangements in Australia Prior to the introduction of the electronic-based DTF in November 1997, Registered Independent Options Traders ŽRIOTs. were obliged to be in the market to provide a firm bid and offer for all exercise prices and all maturities for options written on a particular share.6 The obligation faced by RIOTs changed with the introduction of DTF, in that they are now only required to supply a firm bid–ask for options in the first two expiry months. For options which are not in the first two expiry months, traders can now submit a ‘‘quote order request’’ to RIOTs who, upon receipt of this request, will then place a bid–ask in the Central Order Book for a very short period of time.7 In comparison, the electronically traded equity warrants market has no exchange-designated market makers in the warrants market, but the ASX does have a policy that for a warrant-issuer to be granted trading status it must undertake to make a market in any warrants issued. It is not clear whether this undertaking does provide a genuine safety net for a buyerrseller who has concerns about the liquidity of the market. Liquidity does not necessarily result from the mere presence of market makers, as market makers may be reluctant to take an open position in a thinly traded market where they may be unable to subsequently affect a reversing trade. Another difference between the two markets is that investors in the options market are able to take and write options in the market with few impediments, and hence are able to act on any perceived overpricing or underpricing of an options contract. Warrants, however, are issued securities that are not simply able to be written in the same way as options. The short-selling of warrants is subject to the same short-selling restrictions that apply to all shares. That is, unless the security has been designated by the ASX as an Approved Security, it is not able to be short-sold.8 There were no equity warrants designated as such as at 30 June 1998. 5 Kofman and Moser Ž1997., in their examination of Bunds futures trading on LIFFE and DTB came to the conclusion that two markets for one asset can coexist. The explanation of their empirical results is similar to that of Pagano Ž1989.. 6 RIOTs act as market makers. The number of market makers varied from company to company. For our sample of companies, at all times and for all securities, market makers provided liquidity services for the options market. However, there are occasions as revealed in the Notice to Clearing Members, Number 62, June 1998, where for some companies such as BIL, LLC and PBL there were no market makers as of that date. 7 ASX Business Rules 7.6.1.1 and 7.6.3.3 states that RIOT’s only need to maintain their bid and offer for 30 seconds. 8 ASX Business Rule 2.18.

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The inability to short-sell equity warrants implies that an investor who believes that a warrant is overpriced would not be able to exploit this belief by short-selling the security.9 Equity warrants have historically been issued with a term to expiry of around 2 years, whereas standard exchange-traded options are usually issued with 9 months until expiry. As this paper will match securities on the basis of their remaining term to maturity, there is no reason to expect that different initial terms to maturity will affect their relative pricing. Stamp duty is not levied on either equity warrant or option transactions, except where a transfer of shares takes place pursuant to the exercise of the security. Both securities require physical delivery of the underlying asset and the cost of brokerage in the options market is generally higher than in the equity warrants market.10 Finally, exchange-traded option contracts are issued and maintained by the Options Clearing House ŽOCH.. Investors themselves are not direct parties to option contracts, but are represented by an approved Clearing Member throughout the transaction. In essence, the OCH takes the position of seller Žbuyer. to every buyer Žseller.. Therefore, the risk of loss through non-performance faced by option traders is limited to that of the OCH, as it is under the protection of the National Guarantee Fund. The OCH reduces its risk exposure through the margining system. Equity warrants, however, are issued by third parties, predominantly merchant banks. Non-performance of the issuer at expiry of the warrant does not attract the protection of the National Guarantee Fund. Furthermore, certain circumstances or conditions may be specified in a warrant contract, known as ‘‘extraordinary events’’, that may entitle the issuer to cancel any outstanding warrants andror defer any payment obligations leaving the holder of the warrant without any form of legal recourse. Examples of ‘‘extraordinary events’’ include delistings and trading suspensions. These differences contribute to greater credit risk associated with the purchase of a equity warrant. This increased credit risk may result in warrants being priced at a discount to comparable options. Furthermore, warrants issued by different

9 An equity warrant could be priced higher than the option because there are fewer impediments such as greater transparency and faster execution in the electronically traded warrants market relative to the floor based options market. Traders could impound this lower cost risk into a higher valuation for the equivalent warrant. The inability to short-sell the warrant in this context will prevent traders from arbitraging between equivalent equity warrant and options thereby removing the pricing difference. The presence of these pricing differences enables us to put a value on liquidity. 10 For example, Commonwealth Securities charges 0.5% subject to a minimum of $50 per order for all warrant trades and 1% subject to a minimum of $40 and $25 per order, respectively, for opening and closing option trades.

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institutions with different risk profiles may be expected to have different levels of credit risk and hence the discount may vary across warrant-issuers. In summary, prior to November 1997, the equity warrants market was electronically traded whilst the options market was floor-traded. The electronic-traded warrants market provided faster execution and greater transparency compared to the options market. The market makers on the option market were also required to provide firm bidroffers for all expiry months. Despite the presence of the market makers, the Australian Options Market was especially thin for options with remaining term to maturity greater than 3 months as the market makers were reluctant to trade because of the inadequate risk–return tradeoffs.11 From November 1998, both equity warrants and exchange-traded options were traded electronically. In the options market, there were formal exchange-designated market makers that were required to submit firm bidsroffers for the two nearest expiry months. In comparison, warrant-issuers commit to making a market in any warrants issued regardless of the remaining term to expiry. Stamp duty and the method of settlement at maturity are the same whilst brokerage costs are higher in the options market. The risk of loss through non-performance is greater in the warrants market than the options market and this risk may vary across warrant-issuers.

4. Research methodology This study comprises two stages. The first stage involves testing whether there is any systematic pricing differences of warrants relative to their matched options. Both parametric and non-parametric techniques will be employed in the form of t-tests of mean pricing differences and the binomial test examining the frequencies of overpricings and underpricings. The second stage of the analysis will attempt to ascertain the determinants of any observed RELDIFFs via the utilisation of cross-sectional regression, where the independent variables will be selected on the

11 Chan and Pinder Ž1998, Table 3A and B. documented greater volume and trades in the electronically traded equity warrants market relative to the floor based options market. They attribute this to an inadequate risk–return tradeoff faced by RIOTs in the option market for longer terms-to-maturity who were reluctant to provide a genuine liquidity service to the market. Frequently, for long periods of time the only bids and offers in the order book for the whole day is that provided by the RIOTs as the Australian market is very thin for options with longer remaining term-to-maturity. The RIOTs believe the maximum spread between the bid and ask that they are allow to quote is insufficient to compensate them for the risk of having an open position in the market and the costs they need to incur to offset this position. For traders in the options market, the inability to see the order book, slower execution of orders and the RIOTs quotes being at the maximum spread for longer remaining term-to-maturity, are impediments faced by traders that discourage them from trading in that market.

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basis of the theoretical discussion outlined in Sections 2 and 3. Three different empirical specifications are developed and tested in this paper. Each specification will consider a different sample period. Specification A will consider the determinants of relative pricing over the entire sample period from January 1997 to June 1998. Specification B will analyse any RELDIFFs in the first sub-period, where options were floor-traded and specification C will be applied to the second sub-period during which options were traded electronically. 4.1. Data The first step in obtaining the sample of observations was to identify American-style call options and equity warrants12 that could be matched on the basis of the underlying security, exercise price and the maturity date. Having identified a sample of matched securities, transaction-based data was downloaded from the IRESS real-time electronic database from 1 January 1997 to 30 June 1998. Trades that took place at prices that could not be regarded as purely market-determined were then excluded from the analysis. These included cancelled trades, specials, crossings and trades that took place in the first 10 minutes after the market opened. Option and warrant trades were then matched to the nearest minute and only those trades that took place within 15 minutes of each other were included in the final sample.13 With respect to two warrant Žoption. trades having the same time interval to the nearest option Žwarrant. trade, the warrant Žoption. trade with the volume most closely matching the option Žwarrant. trade was included in the final sample.14 Table 1 summarises the process by which the final sample of 252 matched trades was obtained.15 It also reveals that the total number of trades in the equity warrants market is about 20 times the number of trades in the option market for equivalent matched securities. 4.2. Empirical specification The second stage of the analysis involves testing for the determinants of any RELDIFFs between matched options and equity warrants. The dependent variable 12 Only call optionsrwarrants are examined as there were no American-style put options and warrants that were able to be matched in terms of underlying characteristics prior to the introduction of electronic option trading. 13 Whilst matching trades that did not occur at exactly the same time may introduce some non-simultaneity error, there is no reason to expect that this will systematically bias the results. On the contrary, the matching of trades that occurred within a reasonable amount of time of each other may more realistically reflect the true arbitrage opportunity available to market participants. 14 All option and warrant prices in our sample had the same minimum tick size. 15 It is pertinent to point out that, subject to the filters outlined in the paper, the 252 trades represent the entire population of matched trades that could be obtained over the sample period as warrant-issuers do not specifically issue warrants to match an equivalent option.

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Table 1 Details of final sample of matched equity warrants and exchange traded options Total number of trades for the matched securities during the sample period: Equity warrants Exchange-traded options

20,687 962

Number of trades matched to the day after removing cancelled trades, crossings and specials.

572

Number of trades matched after excluding those that occurred in the first 10 minutes of trading.

554

Number of matched trades within 15 minutes for: Period where options floor-traded Period where options traded electronically Total matched trades

a

Number of companies in final sample with trades matched within 15 minutes. Number of warrant and option series in final sample matched within 15 minutes.

134 118 252 9 11

a

It is possible to have fewer matched trades but at the same time for the number of trades in either the option or equity market to increase.

ŽRELDIFF. is calculated as the warrant price less the option price, all divided by the option price.16 One possible explanation for different option and equity warrant prices is the presence of a liquidity premium. With this in mind, the first independent variable to consider is a measure of the relative liquidity in the two markets at the time that the matched trades took place. In Section 2, we defined a liquid market as one where trading could be accommodated with little or no effect on price. One of the most common proxies, though not the only measure, used to measure liquidity is the bid–ask spread. In Australia, neither IRESS nor any other real-time information suppliers provide a complete history of intra-day bids and asks entered and withdrawn with respect to each of the matched pairs of options and warrants in our sample period. As a result, we have selected another measure to proxy for liquidity. The proxy variable Žrelative volume, RELVOL.17 that this paper will utilise is the ratio of the volume of options to matched warrants, expressed in terms of the number of shares underlying the contracts, traded in the week preceding the matched trades.18

16 The analysis was also undertaken with the dependent variable expressed as the ratio of the pricing difference to the warrant price. The results did not differ significantly. 17 The ratio of option volume to warrant volume for the previous day, as well as the absolute difference between the volume of options and warrants were also substituted as proxies. The results did not differ significantly. 18 There were no occasions where the volume in the warrant market in the week preceding the matched trade was zero, hence RELVOL is always a positive number.

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As discussed in Section 2, numerous studies have documented the relationship between the time of the day, the size of bid–ask spreads and the level of trading activity in securities markets. Specifically, there is evidence from both the NYSE and NASDAQ markets that the often-observed inverse relationship between trading volume and bid–ask spreads may not be apparent at the opening and closing of trade. To control for this intra-day effect we include dummy variables to record if a transaction took place between the opening of the market and 10:30 AM Ždummy variable OMK; open of market. or between 3:30 PM and the closing of the market Ždummy variable CMK; close of market.. The Australian Options Market is extremely thin for options with longer terms to maturity. To control for this effect we include the number of days to maturity ŽDTM. of the derivative security as an independent variable.19 Another factor that may be expected to influence the relative pricing of options and warrants is the different level of credit risk associated with each warrant-issuer. The final sample of 11 warrant series that were able to be matched with option series in terms of underlying characteristics were each issued by one of four different financial institutions. We control for any difference in credit risk by including three dummy variables ŽISSA, ISSB and ISSC. each representing a different issuer.20 The independent variables that have been discussed so far are common to all three models. In addition to these there is a need to control for sub-period specific effects. First, the introduction of electronic option trading coincided with a change in the obligation faced by market makers in that they were now only obliged to provide the market with a firm bid–ask in the first two expiry months. In the pre-DTF period, RIOTs were obliged to make firm bidsroffers for all expiry months. To test whether the obligation faced by RIOTs had an impact on relative pricing, specifications A and C include the dummy variable MMAKER which takes on a value of one where RIOTs were required to continuously provide a market in that option series.21 Specification A considers both the pre-DTF and post-DTF trading periods. In order to assess whether the switch from floor trading

19 Chan and Pinder Ž1998. found evidence that the ratio of the matched volume Žnumber of trades. in the warrant market to the volume Žnumber of trades. in the option market is related to the term-to-maturity. The DTM variable seeks to detect the character of the relative liquidity difference between the two markets. With the switch to electronic trading and the changes to the market making requirements for options beyond the first two expiry months, there is faster execution and greater transparency of the order book. In addition, the increased ability to monitor the spreads provided by the market makers are within limits permitted by the exchange has removed some of the costs for traders in the options market. As a result, volume in the option market should increase and the positive relationship between RELDIFF and DTM should be reduced. 20 The fourth warrant-issuer, warrant-issuer D, is represented by the intercept so as to avoid perfect collinearity between the independent variables. 21 In the floor trading period, RIOTs obligations were not limited by term-to-maturity and hence specification B does not include the variable MMAKER as it would always take on a value of 1.

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to electronic trading has had an effect on relative pricing, the dummy variable MOTRADE takes on the value of one where the trade occurred in the post-DTF period and zero in the pre-DTF period. The dummy variable MMAKER takes the value of one in the pre-DTF period trading period, In the post-DTF period, it takes a value of one where the trade occurs in the first two expiry months. The three specifications are summarised in the equations below. Specification A: Combined sample RELDIFFs a q g OM K OMK q g CMK CMKq g DTM DTM q g RELVOL RELVOLq g ISSA ISSA q g ISSB ISSB q g ISSC ISSCq g MMAKER MMAKERq g MOTRADE MOTRADE. Specification B: Floor-traded options sub-period RELDIFFs a q g OM K OMK q g CMK CMKq g DTM DTM q g RELVOL RELVOLq g ISSA ISSA q g ISSB ISSBq g ISSC ISSC. Specification C: Electronically traded options sub-period RELDIFFs a q g OM K OMK q g CMK CMKq g DTM DTM q g RELVOL RELVOLq g ISSA ISSA q g ISSB ISSBq g ISSC ISSC q g MM AKER MMAKER.

5. Results The first stage involves testing for the existence of a systematic pricing difference between matched options and equity warrants. We examine three periods. First, the full sample period. Second, the period during which options were floor-traded. Last of all, the period when options were screen-traded. A sensitivity analysis will also be performed to investigate whether or not any systematic pricing difference is affected by the degree of non-simultaneity between matched trades. Table 2A shows that warrants have been systematically overpriced relative to their matched options. The null hypothesis of a mean pricing difference of zero is rejected at the 1% level of significance. This result is supported by the binomial test that rejects the hypothesis that there is no statistical difference between the number of occasions where warrants were relatively overpriced compared to the number of occasions where warrants were relatively underpriced. These results are not sensitive to the degree of non-simultaneity between matched trades. Table 2B shows results for the sub-period where options were floor-traded. Once again the test results indicate that warrants are overpriced relative to their

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Table 2 Pricing details for warrant and option trades matched within 15 min Time between trades Žmin.

Option pricewarrant price

Option price) warrant price

Option prices warrant price

(A) Electronically and floor-traded options F1 35 11 5 F5 98 36 15 F10 137 58 20 F15 163 66 23

Mean percentage pricing difference Ž t-statistic.

Binomial probability

Median percentage pricing difference

6.61 Ž3.78. ) ) 6.71 Ž6.48. ) ) 6.04 Ž6.87. ) ) 6.78 Ž8.17. ) )

0.0003 ) 4.05=10y8 ) 7.47=10y9 ) 5.94=10y11 )

3.23 3.08 3.08 3.73

(B) Floor-traded options F1 23 5 F5 53 19 F10 70 33 F15 86 37

1 7 10 11

10.63 Ž4.38. ) ) 8.87 Ž6.01. ) ) 7.50 Ž6.32. ) ) 8.34 Ž7.34. ) )

0.0005 ) 3.78=10y5) 0.0002 ) 5.85=10y6 )

10.00 4.71 3.10 3.89

(C) Electronically traded options F1 12 6 F5 45 17 F10 67 25 F15 77 29

4 8 10 12

1.30 Ž0.64. 4.08 Ž3.03. ) ) 4.44 Ž3.42. ) ) 5.02 Ž4.17. ) )

0.1189 0.0002 ) 6.91=10y6 ) 1.73=10y6 )

0.96 2.00 2.98 2.98

)

Denotes significance at the 1% level for the two-tailed binomial test. Denotes significance at the 1% level for the two-tailed t-test.

))

matched options. The results for this sub-period are consistent across each tested level of non-simultaneity. Results pertaining to the period where options were electronically traded are set out in Table 2C. Of interest is the finding that when the time between matched trades is less than or equal to 1 minute, there is no statistically significant evidence of systematic warrant overpricing. This may be due to the statistical consequence of the relatively small sample of trades matched within one of each other. As the time between matched trades is allowed to increase up to 15 minutes, the systematic overpricing of warrants relative to matched options becomes apparent.22 Interestingly, it seems that the magnitude of the mean pricing difference has fallen following the introduction of electronic option trading. This result is consistent with the removal of previous impediments in the floor-based options market such as slower execution of trades and the inability to observe the order book being removed or substantially reduced. A simple t-test of the difference in

22 In order to ascertain whether the results are independent of the time between trades, a Spearman’s rank correlation coefficient was calculated. The null hypothesis of no relationship between trades and relative pricing difference could not be rejected at conventional levels of significance.

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the mean pricing difference between the two sub-samples, using all observations matched to within 15 minutes and assuming unequal variances for each sub-sample, yields a statistically significant test statistic of 2.005. This result supports the contention that the introduction of electronic option trading has coincided with a reduction in the pricing difference between these two securities. Stage two of the analysis will examine this question more fully by controlling for contemporaneous influences that may help to explain the variation in option and warrant prices. Specification A seeks to explain the determinants of the relative pricing of warrants and options over the entire sample period. The results from the cross-sectional OLS regression relating to specification A are contained in Table 3. White’s test statistic indicates the presence of heteroskedasticity in the error term. In order Table 3 Regression results for specification A applied to the full sample period RELDIFF s a qg OM K OMKqg CMK CMKqg DTM DTMqg RELVOL RELVOLqg ISSA ISSA qg ISSB ISSBqg ISSC ISSCqg MOTRADE MOTRADEqg MMAKER MMAKER. The dependent variable RELDIFF is calculated as the warrant price less the option price all divided by the option price. DTM represents remaining term-to-maturity. RELVOL represents relative volume in option market to relative volume in warrants market. The variables OMK Žopen of market. and CMK Žclose of market. are dummy variables to control for the intra-day effect at the open and close of the market. They take the value of 1 at those times and 0 during the rest of the day. The variables ISSA, ISSB, ISSC are dummy variables representing the different warrant-issuers A, B and C. They take the value of 1 when they are the issuer, otherwise 0. The variable MOTRADE is a dummy variable that takes on a value of 1 when the option market is electronically traded and 0 when it is floor-traded. The variable MMAKER is a dummy variable that takes on a value of 1 when the RIOTs were required to continuously provide a market in the option series, otherwise 0. Variable

Coefficient

t-statistic a,b

a OMK CMK DTM RELVOL ISSA ISSB ISSC MOTRADE MMAKER

0.030 y0.032 y0.056 ) 0.000 y0.013 ) 0.044 0.080 ) 0.093 ) y0.058 y0.029

0.562 Ž0.575. y1.331 Ž0.184. y2.760 Ž0.006. 1.744 Ž0.082. y2.110 Ž0.036. 1.953 Ž0.052. 3.696 Ž0.000. 4.238 Ž0.000. y1.550 Ž0.123. y0.974 Ž0.331.

Adjusted R 2 0.095 F-statistic 3.927 Ž0.000. White’s test statistic 22.381 Ž0.022. Ramsey reset test accept the null hypothesis that the coefficients on the powers of fitted values are zero. a

The t-statistics have been calculated using White heteroskedasticity-consistent standard errors and covariance terms. b P-values in parentheses. ) Statistically significant at 5% level.

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to obtain reliable t-statistics, White’s heteroskedasticity consistent covariance matrix estimator is utilised. The results show that the only variables that are statistically significant at the 5% level are CMK, RELVOL23 and the warrant-issuer dummy variables ISSB and ISSC. The statistically significant RELVOL coefficient is consistent with the presence of a liquidity premium, as an increase in the volume of option contracts traded in the previous week relative to warrant contracts is associated with a decrease in the price of the warrant relative to the option.24 There was no significant multicollinearity between the independent variables and the results from the application of the Ramsey reset test gave no indication that the model was misspecified. In Table 3, the variables MOTRADE and MMAKER test for a simple structural change of whether only the intercept term has changed. These variables were insignificant and it indicates that the intercept has not changed. However, the change to electronic trading from floor trading for the options market may have been a more complex change that differentially affected the variables in our empirical specification. The Chow test is a more comprehensive test. It tests for changes in both the intercept term and the slopes of the variables in our specification. To run this test, we excluded MOTRADE and MMAKER from specification A, as the test requires the independent variables to be common to both sub-periods, and estimated the modified equation separately for the floor trading and electronic trading sub-periods. The resultant Chow test statistic of 17.89 is statistically significant, indicating that the relationship between the dependent and independent variables changed between the two sub-periods. Specifically, this indicates that there was a structural change when the options market began trading electronically and the market-making obligations faced by RIOTs were modified. Moreover, the structural change that occurred was more complex than could be accounted for by the simple inclusion of the dummy variables MOTRADE and MMAKER. Table 4 sets out the regression results obtained from the application of specification B to the period where the options market was floor-traded. The statistically significant explanatory variables include DTM and the warrant-issuer dummy variables ISSA, ISSB and the intercept term. There was no evidence of heteroskedasticity or significant multicollinearity between independent variables. However, the Ramsey Reset test revealed that the assumption of a linear relationship between the dependent and independent variables is erroneous.

23 Other proxies for liquidity were tested over both the full sample period and each of the sub-periods. Where the variable was defined as the ratio of the volume of option contracts to warrant contracts traded in the previous day, the same two independent variables were found to be significant. When the liquidity variable was defined as the difference in the volume of option and warrant contracts, an additional variable, DTM, became statistically significant. 24 Both the warrant and option contracts are expressed in terms of the number of shares underlying the contracts for the RELVOL variable.

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Table 4 Regression results for specification B applied to sub-period where options were floor-traded RELDIFF s a qg OM K OMKqg CMK CMKqg DTM DTMqg RELVOL RELVOLqg ISSA ISSA qg ISSB ISSBqg ISSC ISSC. The dependent variable RELDIFF Žrelative pricing difference. is calculated as the warrant price less the option price all divided by the option price. DTM represents remaining term-to-maturity. RELVOL represents relative volume in option market to relative volume in warrants market. The variables OMK Žopen of market. and CMK Žclose of market. are dummy variables to control for the intra-day effect at the open and close of the market. They take the value of 1 at those times and 0 during the rest of the day. The variables ISSA, ISSB, ISSC are dummy variables representing the different warrant-issuers A, B and C. They take the value of 1 when they are the issuer, otherwise 0. Variable

Coefficient )

a OMK CMK DTM RELVOL ISSA ISSB ISSC

y0.187 y0.051 y0.038 0.001) y0.005 0.144 ) 0.202 ) 0.096

Adjusted R 2 F-statistic White’s test statistic Ramsey reset test — log likelihood ratio

0.169 4.874 Ž0.000. 14.468 Ž0.107. 4.283 Ž0.038.

a

t-statistic a y2.607 Ž0.010. y1.504 Ž0.135. y1.362 Ž0.176. 4.254 Ž0.000. y1.173 Ž0.243. y2.453 Ž0.016. 3.600 Ž0.001. 1.702 Ž0.091.

P-values in parentheses. Statistically significant at 5% level.

)

The problem of non-linearity is addressed by modifying specification B such that it includes the logarithmic transformation of the days-to-maturity variable and a quadratic RELVOL.25 The regression results relating to this modified model are contained in Table 5. These results demonstrate that over the floor-based option trading period, relative pricing is related to the logarithm of the DTM variable. Intuitively, this implies that as the remaining DTM increase for the matched securities, ceteris paribus, the price of warrants relative to options also increases, although at a decreasing rate. This captures, we believe, the fact that for remaining terms to maturity beyond a few months, the option’s market is extremely illiquid. When the remaining term to maturity is further increased, the liquidity premium is relatively unaffected. The RELDIFF is also negatively related to the quadratic form of the relative liquidity variable. Hence, an increase in the volume of trading in the

25 The quadratic term is added because any functional form can be approximated by a Taylor series expansion of a high enough order. It is meaningless to take higher orders of dummy variables as they will still be zero or one.

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Table 5 Regression results for specification B modified for non-linearity RELDIFF s a qg OM K OMKqg CMK CMKqg log ŽDTM . log Ž DTM . qg RELVOL RELVOL qg RE LVOL 2 RELVOL2 qg ISSA ISSAqg ISSB ISSBqg ISSC ISSC. The dependent variable RELDIFF Žrelative pricing difference. is calculated as the warrant price less the option price all divided by the option price. The logŽDTM. represents the log of the remaining term-to-maturity. RELVOL represents relative volume in option market to relative volume in warrants market. The variables OMK Žopen of market. and CMK Žclose of market. are dummy variables to control for the intra-day effect at the open and close of the market. They take the value of 1 at those times and 0 during the rest of the day. The variables ISSA, ISSB, ISSC are dummy variables representing the different warrant-issuers A, B and C. They take the value of 1 when they are the issuer, otherwise 0. Variable

Coefficient

t-statistic a,b

a OMK CMK logŽDTM. RELVOL RELVOL2 ISSA ISSB ISSC

y0.711) y0.031 y0.036 0.120 ) 0.025 y0.003 ) 0.138 ) 0.200 ) 0.112 )

y3.261 Ž0.001. y1.351 Ž0.179. y1.317 Ž0.190. 3.438 Ž0.001. 1.420 Ž0.158. y2.166 Ž0.032. 3.679 Ž0.000. 4.688 Ž0.000. 3.173 Ž0.002.

Adjusted R 2 F-statistic White’s test statistic Ramsey reset test — log likelihood ratio

0.194 5.007 ) Ž0.000. 34.033 ) Ž0.000. 0.7302 Ž0.393.

a The t-statistics have been calculated using White heteroskedasticity-consistent standard errors and covariance terms. b P-values in parentheses. ) Statistically significant at 5% level.

options market relative to the warrant market is associated with a decrease in the value of the warrant relative to the option. This negative relationship is consistent with the presence of a liquidity premium. Interestingly, as the trading volume in the options market increases relative to the warrants market, the option price increases in relative value at an increasing rate. This implies that when the option’s market is extremely illiquid, changes in trading volume have little impact upon relative pricing. With regards to the identity of the warrant-issuers, the price of the warrant relative to the option is positively related to warrant-issuers A, B and C and negatively related to warrant-issuer D. This may reflect a higher level of credit risk being associated with warrant-issuer D relative to the other issuers. This finding may also reflect other systematic influences, such as a higher probability of ‘‘extraordinary events’’ relating to the underlying shares upon which warrant-issuer D issues warrants.

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Table 6 contains the regression results relating to specification C. The only statistically significant variables were RELVOL, MMAKER and the warrant-issuer ISSC. There was no evidence of heteroskedasticity or non-linearity in the error term. The independent variables DTM and MMAKER, however, were found to be collinear with a correlation coefficient of y0.704. In order to test whether we have incorrectly rejected DTM as a statistically significant explanatory variable, a Wald test was utilised. This test involved the re-estimation of Model C whilst restricting the coefficients of DTM and MMAKER to zero. Comparison of the P-value from the Wald test with the P-value associated with the MMAKER coefficient on the t-statistic does not support the null hypothesis that the variable DTM has a significant relationship with the dependant variable. The results indicate that relative pricing Ždefined as warrant price less option price all divided by option price. is negatively related to the RELVOL of options

Table 6 Regression results for specification C where options are electronically traded RELDIFF s a qg OM K OMKqg CMK CMKqg DTM DTMqg RELVOL RELVOLqg ISSA ISSA qg ISSB ISSBqg ISSC ISSCqg MMAKER MMAKER. The dependent variable RELDIFF Žrelative pricing difference. is calculated as the warrant price less the option price all divided by the option price. DTM represents remaining term-to-maturity. RELVOL represents relative volume in option market to relative volume in warrants market. The variables OMK Žopen of market. and CMK Žclose of market. are dummy variables to control for the intra-day effect at the open and close of the market. They take the value of 1 at those times and 0 during the rest of the day. The variables ISSA, ISSB, ISSC are dummy variables representing the different warrant-issuers A, B and C. They take the value of 1 when they are the issuer, otherwise 0. The variable MMAKER is a dummy variable that takes on a value of 1 when the RIOTs were required to continuously provide a market in the option series, otherwise 0. Variable

Coefficient

t-statistic a

a OMK CMK DTM RELVOL ISSA ISSB ISSC MMAKER

0.063 y0.010 y0.049 y0.001 y0.032 ) 0.035 0.059 0.117 ) y0.110 )

1.130 Ž0.261. y0.312 Ž0.755. y1.272 Ž0.206. y1.466 Ž0.146. y2.771 Ž0.007. 0.434 Ž0.665. 1.117 Ž0.267. 2.273 Ž0.025. y2.547 Ž0.012.

Adjusted R 2 0.122 F-statistic 2.930 Ž0.005. White’s test statistic 12.286 Ž0.266. Wald tests Ž x 2 statistics. Ži. DTMs 0, MMAKER s 0 6.595 Ž0.037. All Ramsey reset tests fail to reject the null hypothesis that the coefficientson the powers of fitted values are zero. a

P-values in parentheses. Statistically significant at 5% level.

)

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to warrants traded in the previous week. Once again, this evidence supports the presence of a liquidity premium. Table 6 also indicates that the relative pricing is negatively related to the MMAKER variable. This implies that where RIOTs have an obligation to continually provide the option market with a firm bid and ask price, the option price increases relative to the matched warrant price. This result is further evidence in support of the presence of a liquidity premium in the warrants market. A comparison of the results from the two sub-periods indicates that the change from floor trading to electronic trading resulted in changes in the determinants of Table 7 Regression results over entire sample period with interaction terms reflecting incremental explanatory power of the switch to electronic option trading RELDIFF s a qg OM K OMKqg CMK CMKqg DTM DTMqg RELVOL RELVOLqg ISSA ISSA qg ISSB ISSBqg ISSC ISSCqg MMAKER MMAKERqg DUMOMK DUMOMK qg DU MCMK DUMCMKqg DUMDTM DUMDTMqg DUMRELVOL DUMRELVOL qg DU MISSA DUMISSAqg DUMISSB DUMISSBqg DUMISSC DUMISSC qg DU MMAKER DUMMAKER. The variables RELDIFF, OMK, CMK, DTM, RELVOL, ISSA, ISSB, ISSCA and MMAKER are as defined in previous tables. The variables DUMOMK, DUMCMK, DUMDTM, DUMRELVOL, DUMISSA, DUMISSB, DUMISSC and DUMMAKER are dummy interaction variables. They take the value of 1 if the option transaction took place electronically, otherwise 0. Variable

Coefficient

t-statistic a

a OMK CMK DTM RELVOL ISSA ISSB ISSC MMAKER DUMOMK DUMCMK DUMDTM DUMRELVOL DUMISSA DUMISSB DUMISSC DUMMAKER

0.068 y0.051 y0.038 1.25=10y4 ) y0.005 0.144 ) 0.202 ) 0.096 y0.254 ) 0.036 y0.013 y0.001) y0.026 ) y0.104 y0.137 0.024 0.136

1.235 Ž0.218. y1.491 Ž0.137. y1.350 Ž0.178. 4.217 Ž0.000. y1.162 Ž0.246. 2.432 Ž0.016. 3.569 Ž0.000. 1.688 Ž0.093. y2.804 Ž0.006. 0.776 Ž0.438. y0.280 Ž0.779. y2.957 Ž0.003. y2.168 Ž0.031. y1.051 Ž0.294. y1.766 Ž0.079. 0.310 Ž0.757. 1.513 Ž0.132.

Adjusted R 2 0.160 F-statistic 3.993 Ž0.000. White’s test statistic 26.121 Ž0.162. Ramsey reset test fails to reject the null hypothesis that the coefficients on the powers of fitted values are zero. a

P-values in parentheses. Statistically significant at 5% level.

)

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the relative pricing of warrants and options. In order to gain a more detailed understanding of how the relationship between the dependent and independent variables responded to the change in trading method, we tested for specific changes in individual variables between the two sub-periods. Specification C 26 is used as the ‘‘base’’ model and then dummy interaction variables ŽDUMOMK, DUMCMK, DUMDTM, DUMRELVOL, DUMISSA, DUMISSB, DUMISSC, DUMMAKER. are added to test for the additional explanatory power that arises as a consequence of knowing that the option transaction took place electronically. Table 7 demonstrates that the relationship between relative pricing and the DTM and RELVOL variables have changed between the two sub-periods. Specifically, the results indicate that the introduction of electronic option trading has diminished the magnitude of the positive relationship between RELDIFF and DTM. The MMAKER variable is statistically significant and negatively related to relative pricing and this relationship has not changed between the two sub-periods in a statistically significant way.27 This supports the contention that the mandated presence of RIOTs in the option market is correlated with a reduction in the relative overpricing of warrant contracts. As would be expected, the relationship between the warrant-issuers and the dependent variable, did not alter significantly between the two sub-periods.

6. Summary and conclusion Over the period January 1997 to June 1998 warrants were systematically overpriced relative to options when they were matched on the basis of their underlying characteristics. This result is generally robust with respect to nonsimultaneity between the matched trades whilst the size of the pricing difference was lower following the introduction of electronic option trading. When options were floor-traded it was found that the relative level of pricing is positively related to the logarithmic transformation of the DTM variable and negatively related to the quadratic form of the relative trading volume variable. These results provide some evidence in support of the presence of a liquidity premium. The identity of warrant-issuers was also related to the level of pricing differences. This could be consistent with warrant prices reflecting the different levels of credit risk associated with different warrant-issuers, or may also be a manifestation of the different characteristics relating to the underlying shares upon which the warrants were issued. 26 Alternatively, when specification B was used as the ‘‘base’’ model, the results and conclusions were similar to that found in Table 7. 27 This result is not unexpected as the changes to the market making obligations when the options market went electronic appeared to formalise what was the practice of the RIOTs in the floor-traded period of only being willing providers of liquidity for the nearest expiry months.

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The results shows that when the options market began trading electronically, the volume of contracts traded in the option market relative to the warrant market in the week prior to the matched trade is negatively related to the level of relative pricing. This finding, once again, is indicative of a liquidity premium in the warrant market. The results also indicate that when market makers are required to provide a market in an option, the RELDIFF between the warrant and option is reduced. Finally, in the analysis of the full sample period, there is a statistically significant structural change at the time the options market switches to electronic trading. This change is complex and it has had different effects on different variables. In particular, different ‘‘liquidity’’ variables represented by DTM and RELVOL, change in terms of their degree of impact on relative pricing.

Acknowledgements The first author acknowledges the financial support provided by a Monash University, 1997 Faculty of Business and Economics Research Grant, the helpful support of the IRESS data service and the research assistance of Anthony Siouclis. The authors are grateful for comments from the editor Kalok Chan, the anonymous referee, Rob Brown, Rob Brooks, Steve Easton, Rob Faff, Alan Farley, Brett Inder, seminar participants at Monash University, RMIT University, University of Newcastle, University of Queensland and the Australian National University, and conference participants at the 1999 PACAP Conference in Singapore, Asia-Pacific Finance Conference in Melbourne and the AAANZ Conference in Cairns.

References Adamati, A., Pfleiderer, P., 1988. A theory of intraday patterns: Volume and price variability. Review of Financial Studies 1, 3–40. Amihud, Y., Mendelson, H., 1986. Asset pricing and the bid–ask spread. Journal of Financial Economics 17, 223–249. Benston, G.J., Hagerman, R.L., 1974. Determinants of bid–ask spreads in the over-the-counter market. Journal of Financial Economics 1, 353–364. Branch, B., Freed, W., 1977. Bid–ask spreads on the AMEX and the Big Board. Journal of Finance 32, 159–163. Brock, W., Kleidon, A., 1992. Periodic market closure and trading volume: A model of intraday bids and asks. Journal of Economic Dynamics and Control 16, 451–489. Chan, K.C., Christie, W.G., Schultz, P.H., 1995. Market structure and intraday pattern of bid–ask spreads for NASDAQ securities. Journal of Business 68, 35–60. Chan, H.W.H., Pinder, S.M., 1998. Market structure and its effects on the pricing of derivative securities in Australia, Department of Accounting and Finance Working Paper No. 61, Monash University.

H.W.-H. Chan, S.M. Pinderr Pacific-Basin Finance Journal 8 (2000) 483–503

503

Datar, V.T., Naik, N.Y., Radcliffe, R., 1998. Liquidity and stock returns: An alternative test. Journal of Financial Markets 1, 203–219. Demsetz, H., 1968. The cost of transacting. Quarterly Journal of Economics 82, 33–53. Economides, N., Schwartz, R.A., 1995. Electronic call market trading. Journal of Portfolio Management 22, 10–18. Eleswarapu, V.R., Reinganum, M.R., 1993. The seasonal behavior of the liquidity premium in asset pricing. Journal of Financial Economics 34, 373–386. Fishman, M.J., Longstaff, F.A., 1992. Dual trading in futures markets. Journal of Finance 47, 643–671. Forster, M., George, T., 1992. Anonymity in securities markets. Journal of Financial Intermediation 2, 593–624. Foster, F.D., Viswanathan, S., 1993. Variations in trading volume, return volatility and trading costs: Evidence on recent price formation models. Journal of Finance 48, 187–211. Glosten, L.R., 1987. Components of the bidrask spread and the statistical properties of transaction prices. Journal of Finance 42, 1293–1308. Glosten, L.R., Milgrom, P.R., 1985. Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of Financial Economics 14, 71–100. Grossman, S.J., Miller, M.H., 1988. Liquidity and market structure. Journal of Finance 48, 617–637. Grunbichler, A., Longstaff, F.A., Schwartz, E.S., 1994. Electronic screen trading and the transmission of information: An empirical examination. Journal of Financial Intermediation 3, 166–187. Kofman, P., Moser, J.T., 1997. Spreads, information flows and transparency across trading systems. Applied Financial Economics 7, 281–294. Lehmann, B.N., Modest, D.M., 1994. Trading and liquidity on the Tokyo stock exchange: A bird’s eye view. Journal of Finance 49, 951–984. Madhaven, A., 1992. Trading mechanisms in securities markets. Journal of Finance 47, 607–641. McInish, T., Wood, R.A., 1992. An analysis of intraday patterns in bidrask spreads for NYSE stocks. Journal of Finance 47, 753–764. Pagano, M., 1989. Trading volume and asset liquidity. Quarterly Journal of Economics 104, 255–274. Pirrong, C., 1996. Market liquidity and depth on computerised open outcry trading systems: A comparison of DTB and LIFFE Bund contracts. Journal of Futures Markets 16, 519–543. Stoll, H., 1978. The pricing of security dealer services: An empirical study of NASDAQ stocks. Journal of Finance 33, 1153–1172. Tinic, S.M., 1972. The economics of liquidity services. Quarterly Journal of Economics 86, 79–93. Tinic, S.M., West, R.R., 1972. Competition and the pricing of dealer services in the over-the-counter market. Journal of Financial and Quantitative Analysis 8, 1707–1727.