Arbitrage opportunities, liquidity provision, and trader types in an index option market

• Author: Huimin Chung,Junmao Chiu,Chin‐Ho Chen
• Date: 01 March 2020
• DOI: http://doi.org/10.1002/fut.22077
• Published date: 01 March 2020

J Futures Markets. 2020;40:279–307. wileyonlinelibrary.com/journal/fut © 2019 Wiley Periodicals, Inc.

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279

Received: 31 July 2018

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Accepted: 7 November 2019

DOI: 10.1002/fut.22077

RESEARCH ARTICLE

Arbitrage opportunities, liquidity provision, and trader

types in an index option market

Chin‐Ho Chen

1

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Junmao Chiu

2

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Huimin Chung

3

1

Department of Finance, Feng Chia

University, Seatwen, Taichung, Taiwan

2

College of Management, Yuan Ze

University, Chung‐Li, Taoyuan, Taiwan

3

Department of Information Management

and Finance, National Chiao Tung

University, Hsinchu, Taiwan

Correspondence

Chin‐Ho Chen, Department of Finance,

Feng Chia University, 100, Wenhwa

Road, Seatwen, Taichung 40724, Taiwan.

Email: chinhoc@fcu.edu.tw

Abstract

This study examines the impact of arbitrage in put–call futures parity (PCFP)

violations on option market liquidity and explores the liquidity provision

process by trader type during periods of arbitrage exploitation. Using a unique

data set comprising the complete history of transactions, we find that PCFP

violations contain toxic arbitrage opportunities. Hence, more frequent toxic

arbitrage opportunities can cause liquidity to deteriorate because arbitrageurs

create adverse selection costs and order imbalances in the option market. In

addition, when the law of one price breaks down, market makers dominate by

providing liquidity compared with individual, domestic, and foreign institu-

tional traders.

KEYWORDS

arbitrage, liquidity provision, put–call futures parity

JEL CLASSIFICATION

G10; G11; G14

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INTRODUCTION

Arbitrageurs, who use computerized trade technology and high‐frequency trading to earn profits, play a central role in

enforcing the law of one price in financial markets. Although arbitrage improves market efficiency by moving prices to

an appropriate level, it can also impair liquidity (Domowitz, Glen, & Madhavan, 1998; Foucault, Kozhan, & Tham,

2017; Kumar & Seppi, 1994). Prior literature on arbitrage examines the impact of arbitrage on profitability and market

efficiency (e.g., Benzion, Danan, & Yagil, 2005; Hemler & Miller, 1997; Kamara & Miller, 1995). However, research

shows that it is still unclear how violation of the law of one price affects liquidity supply.

Theoretical studies show that the impact of arbitrage on liquidity depends on the reasons why arbitrage

opportunities arise. As prior literature related to the limits of arbitrage points out, on the one hand, if arbitrage

opportunities occur owing to nonfundamental demand shocks, then arbitrageurs increase market‐making capacity by

trading against net market demand, subsequently improving liquidity (Foucault, Pagano, & Rӧell, 2013; Gromb &

Vayanos, 2002, 2010; Holden, 1995). On the other hand, if arbitrage opportunities are created by heterogeneous

information sets (Domowitz et al., 1998; Kumar & Seppi, 1994) or asynchronous price adjustments in asset pairs

(Foucault et al., 2017), then arbitrageurs with information advantage expose adverse selection costs to liquidity

providers, therefore, liquidity deteriorates.

This study relies on a unique data set with identified trader types from the Taiwan Index Options (TXO) market to

investigate how arbitraging in put–call futures parity (PCFP) violations affects the liquidity of options, and which type

of traders provides liquidity during periods of arbitrage.

1

The focus of our analysis is arbitrage opportunities arising

from PCFP violations. In practice, PCFP is a mechanism to ensure that option prices do not deviate substantially from

fair value for long periods of time.

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Even if the option market is efficient,

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many empirical studies find that PCFP

violations are frequent and substantial in the short term (Budish, Cramton, & Shim, 2015; Cheng, Fung, & Pang, 1998;

Fung & Mok, 2001).

4

As information shocks lead to PCFP violations, they are likely to be toxic arbitrage opportunities,

that is, opportunities in which liquidity providers are at the risk of being adversely selected.

5

As different markets

receive distinct information over time, lags in information transmission and interpretation of prices can lead to not all

options quickly reflect their fair values with the arrival of new information.

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If arbitrageurs interpret price information

more quickly than liquidity providers, then arbitrage will cause liquidity to deteriorate because liquidity providers

charge larger bid–ask spreads to cover the risk of trading at stale quotes (Copeland & Galai, 1983). Thus, PCFP

violations provide an ideal opportunity to study the impact of toxic arbitrage on liquidity and which type of traders

provides liquidity during periods of arbitrage. In addition, this study elucidates only the option market because the

futures market is more liquid and has higher pricing efficiency than the option market.

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We first explore the impact of arbitrage opportunities on option liquidity and examine the possible channels of

adverse selection and order imbalances (OIBs) in the context of impact on liquidity. For a measure of toxic arbitrage

opportunity, we calculate the proportion of toxic arbitrage opportunities (PTAO) in the pool of all arbitrage

opportunities, following Schultz and Shive (2010) and Foucault et al. (2017). Our empirical results show that, overall,

arbitrage opportunities from PCFP violations widen the effective bid–ask spread (and quoted spread), indicating

impaired option liquidity. Indeed, PCFP violations contain toxic and nontoxic arbitrage opportunities. A high PTAO

generates not only trade OIBs in the direction of arbitrageurs but also increased cost of adverse selection, suggesting

that frequent toxic arbitrage opportunities can raise the risk of both inventory and adverse selection for liquidity

suppliers. In addition, the findings of widening option spreads following an increase in PTAO, especially during a large

OIB period, provide evidence that frequent toxic arbitrage opportunities harm liquidity through channels, such as

adverse selection costs and OIBs in the option market because liquidity providers charge larger spreads to cover the

risks. Hence, these results support the findings of Kumar and Seppi (1994) and Foucault et al. (2017) that frequent toxic

arbitrage opportunities can impair liquidity.

Categorizing investors into four groups (IT, foreign institutional traders [FIT], domestic institutional traders [DIT],

and MM), we examine the trader type that meets the demand for immediate liquidity following PCFP violations. In

terms of initially violating PCFP, essentially, MM submit orders on the liquidity supply side, followed by IT, FIT, and

DIT. The submitted orders center on the best five quotes for different trader types, except DIT, who use less aggressive

orders. Comparing the orders submitted for the liquidity supply after PCFP violations, we find that orders submitted by

MM increase, whereas those submitted by DIT and FIT and, especially, IT decrease. Overall, MM increase orders with

higher execution probability after PCFP violations than before PCFP violations. Thus, our finding that MM increase

their use of aggressively priced orders supports the premise that they provide liquidity to the option market in terms of

arbitrage shocks.

When market shocks and the option and futures markets characteristics are controlled, MM continue to dominate

the liquidity supply response after PCFP violation, whereas IT and DIT tend to maintain a lower response. MM’s

dominance of liquidity provision remains even for options with different moneyness and for the supply of aggressive

1

Recent empirical evidence shows that market makers (MM; Eldor, Hauser, Pilo, & Shurki, 2006; Mayhew, 2002), hedge funds (Aragon, 2007; Jylha, Rinne, & Suominen, 2014; Sadka, 2010), technical

analysts (Kavajecz & Odders‐White, 2004), algorithmic traders (Hendershott, Jones, & Menkveld, 2011), high‐frequency traders (Menkveld, 2013), and individual traders (IT; Kaniel, Saar, & Titman,

2008; Kelley & Tetlock, 2013) can provide liquidity to financial markets.

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This no‐arbitrage relation is particularly important for the underlying index of options that are not traded directly. Moreover, MM in options commonly use futures contracts to hedge their positions

(Fleming, Ostdiek, & Whaley, 1996; Lee & Nayar, 1993).

3

See, for example, Lee and Nayar (1993), Fung and Chan (1994), Fung and Fung (1997), and Fung, Cheng, and Chan (1997).

4

In contrast, Finucane (1991), Atilgan (2014), and Cremers and Weinbaum (2010) find that deviations from the put–call parity, which is induced by informed trading in the option market, may predict

stock and index returns.

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As an illustration, assume that liquidity providers in the futures market receive a string of buy orders following the arrival of good information and raise their bid and ask quotes. If this price

movement is large enough and liquidity providers in theoption market are slow to adjust their quotes to reflect this information, then an arbitrage opportunity in PCFP violation appears. The arbitrage

opportunity vanishes when liquidity providers adjust their quotesin the option market or arbitrageurs hit stale quotes in this market (Foucault et al., 2017). In either case, option prices do not revert to

the position they held before the arbitrage opportunity.

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Most of the literature on price discovery, documented by the speed at which prices react to new information, finds that index futures lead both index options and the spot index (e.g., Fleming et al.,

1996; Stoll & Whaley, 1990).

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Stoll and Whaley (1990), Fleming et al. (1996), Roope and Zurbruegg (2002), Hsieh (2004), and Huang (2004) explore liquidity, transaction costs, pricing efficiency, and price discovery in the option

market. In general, the evidence confirms that the index futures market has good quality from all these perspectives.

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