هزینه های کیفیت خدمات، نقدینگی و مدیریت موجودی: شواهد از گزینه سازندگان بازار

Hedging the risk of holding undesired inventory is very important for market makers. However, prior studies seldom capture the role of inventory positions in measuring hedging costs. This study measures hedging costs directly using data on inventory positions of market makers in the Taiwan Index Options market. We break down rebalancing costs into two sources: rebalancing costs due to inventory changes and rebalancing costs due to delta changes. Contrary to prior studies on stock options, we find rebalancing costs are more important than initial hedging costs in explaining option spreads. Our findings underscore the importance of inventory management.

This study examines the role of hedging costs in determining market makers′ quotations. The focus is on the relation between option spreads and the cost of a delta-neutral hedge at the portfolio level using futures as the hedging tool. We highlight the importance of inventory management by using market makers′ inventory positions to measure hedging costs. Market makers provide liquidity by buying and selling according to the prevailing market demand; bid–ask spreads are to compensate market makers for providing liquidity. To provide liquidity, market makers carry inventories and bear inventory risk. In general, market makers manage their inventory risk by (i) directly adjusting bid and ask prices to obtain the optimal level of inventory or (ii) hedging against inventory risk. Both policies play an important role in determining asset prices and liquidity. The theoretical works of Garman (1976), Amihud and Mendelson (1980), and Ho and Stoll (1981) show that monopolistic market makers actively adjust the bid and ask prices to manage their inventories. Ho and Stoll, 1980 and Ho and Stoll, 1983 come to a similar conclusion under a competing dealer framework. If market makers actively adjust quotes for inventory control purposes, bid and ask prices should be negatively related to the level of inventory. Many studies have empirically tested the predictions of these models. Hasbrouck and Sofianos (1993) and Madhavan and Smidt (1993) analyze the NYSE specialist inventory data and only find slow position adjustment, while Kavajecz and Odders-White (2001) find that the specialist inventory has no influence on quoted prices. Panayides (2007) finds that specialists engage in significant inventory rebalancing but only when they are not constrained by the price continuity rule. Focusing on London Stock Exchange, Hansch, Naik, and Viswanathan (1998) and Naik and Yadav (2003) find that market makers aggressively manage their inventories by strategically positioning their quotes. Very few studies in derivative markets use market makers′ inventory data. Ho and Macris (1984) analyze stock options traded on AMEX and show that a dealer's inventory level affects bid–ask quotes, which in turn influences the observed option returns. Manaster and Mann (1996) examine the futures transaction data from the Chicago Mercantile Exchange and find that although market makers aggressively manage their inventories, their inventory holdings are positively correlated with their reservation prices, which is contrary to the prediction of inventory control theory. These studies highlight the importance of inventory management through adjusting quotes and its effect on security prices and liquidity. In addition to quotes adjustment, market makers can also establish a hedging position to manage their inventory risk. However, hedging results in additional transaction costs, which in turn affects bid–ask spreads. Hedging has been largely ignored in the stock market but is critical in the option market. Giannetti, Zhong, and Wu (2004) note that market makers seldom maintain “naked” option positions and that they systematically hedge their inventory risk by trading the underlying asset. This implies that hedging is an important means to manage option market makers′ inventory risk. Whereas substantial studies have focused on inventory management through adjusting quotes, researchers’ understanding of the relation among market making activity, hedging costs, and security liquidity remains at a preliminary stage. Boyle and Vorst (1992) show that option replication in discrete time with proportional transaction costs results in differences between long call and short call prices. This finding implies that transaction costs due to hedging activity may significantly affect the quoted spreads of option market makers. Giannetti, Zhong, and Wu (2004) and Stoikov and Saglam (2009) both theoretically highlight the important effect of hedging inventory risk on option prices and quoted spreads when underlying stocks are not perfectly liquid. Empirical works in this field, however, are sparse. Only a few studies have used inventory data to investigate the role of hedging costs in determining security liquidity. The purpose of our study is to fill this gap. We examine the role of hedging costs in determining market makers′ bid–ask spreads and shed light on the implications for inventory management. Cho and Engle (1999) propose a derivative hedge theory and suggest that if market makers can perfectly hedge their option positions with an underlying security, bid–ask spreads in the option market will depend solely on the liquidity in the underlying market, rather than inventory risk or informed trading in the option market. Kaul, Nimalendran, and Zhang (2004), Petrella (2006), and Engle and Neri (2010) build on Cho and Engle (1999) to distinguish hedging costs2 as initial hedging costs and rebalancing costs. These studies find that hedging costs are an important determining factor of option spreads, and the economic significance of initial hedging costs is higher than that of rebalancing costs. As hedging costs arise from the need to hedge inventory risk, a good measure of hedging costs should capture the role of inventory changes. However, due to data limitations, prior studies only use the underlying spreads and option hedging parameters such as delta, vega, and gamma to capture the hedging costs and ignore the effect of inventory changes. Without explicitly taking into account changes in inventory positions, models may misestimate the impact of hedging costs on option spreads and thus cannot provide insight on the implications of hedging costs for inventory management. We address this issue by computing hedging costs more accurately using data on market makers′ inventories. Our unique data on Taiwan Index Options (TXO) allow us to identify each market maker's quotes, transactions, and positions so that we can directly measure the level and change in market makers′ inventories and incorporate them in the calculation of hedging costs. Our study contributes to the literature by examining the role of hedging costs in determining option spreads and its implications for inventory management from a unique perspective. We show that rebalancing costs have two sources: costs due to inventory changes and costs due to delta changes. For market makers who maintain stable inventory positions, rebalancing costs due to inventory changes will be trivial and rebalancing costs will be mainly driven by delta changes. However, volatile inventory levels cost market makers more to adjust their hedging positions, and rebalancing costs due to inventory changes significantly affect option spreads. These cost relations imply that market makers will exert effort to stabilize their inventory positions around the optimal level. Thus, whether rebalancing costs due to inventory/delta changes are significantly related to option spreads becomes an important issue. Contrary to prior studies, we find that rebalancing costs are more important than initial hedging costs in explaining option spreads. Most of the regression results show that rebalancing costs due to inventory changes have the largest explanatory power. While initial hedging costs are statistically significant, their economic significances are relatively small compared to other determining factors. Rebalancing costs due to delta changes are insignificant in most cases. Many studies have examined the determinants of bid–ask spreads in the options market (e.g., Berkman, 1992, Jameson and Wilhelm, 1992, George and Longstaff, 1993, Gwilym et al., 1998, Fahlenbrach and Sandas, 2003 and Wei and Zheng, 2010). Besides market making costs, these studies consider the price risk due to the inability to hedge continuously. However, most of these studies use the vega or gamma of individual option series to measure price risk. This approach ignores the portfolio effect—the possible trade-off between the vega or gamma of positions taken in different option series—and thus may misestimate the price risk and its impact on option spreads. Using data on inventory positions of market makers, we overcome this limitation by calculating the price risk in the option portfolio of each market maker; that is, we are able to consider the price risk for market makers in a portfolio context. Unlike previous studies, our results show that in most cases price risk is not significantly related to option spreads, which seems to be in line with the prediction of derivative hedge theory. Our findings highlight the importance of inventory management. The impact of rebalancing costs due to inventory changes on option spreads far exceeds that of rebalancing costs due to delta changes. Thus, if market makers manage inventories properly and keep their inventories stable, they can substantially reduce rebalancing costs, which in turn lower option spreads and enhance market liquidity. The remainder of the article is organized as follows. Section 2 describes the determinants of option bid–ask spreads and their calculation in this study. In Section 3, we develop our empirical specifications. Section 4 contains the data description and summary statistics. In Section 5, we present and analyze the empirical results. Section 6 provides the results of the robustness tests. Section 7 concludes the paper.

Due to the importance of hedging in derivative markets, theoretically, hedging costs are an important determining factor of option spreads in addition to other market making costs. As hedging costs arise from the need to manage inventory risk, they are closely related to market makers′ inventory positions. To measure inventory costs directly and to capture the role of inventory changes in determining hedging costs, we should incorporate inventory changes into the measurement of hedging costs. Although recent studies put more focus on hedging costs and empirically examine their role in explaining bid–ask spreads, no studies have examined the issue using information on the inventory positions of market makers. In this study, we examine the relation between option spreads and the cost of a delta-neutral hedge at the portfolio level using futures as the hedging tool. Using the inventory data of market makers to measure inventory risk and hedging costs directly, we identify two sources of rebalancing costs: costs due to inventory changes and costs due to delta changes. Similar to prior studies on stock options, we find that hedging costs, in addition to other market making costs, are an important factor in determining option spreads. However, our results on the relative importance between rebalancing costs and initial hedging costs are contradictory to prior studies. Unlike prior studies, we find portfolio rebalancing costs are more important than initial hedging costs in explaining option spreads. After taking into account the role of inventory changes and the possible portfolio effect, we find only a weak relation between vega risk and option spreads. We find that rebalancing costs due to inventory changes are not only more important than initial hedging costs, we find that they are the most important factor. While adverse selection costs and order processing costs also play a role in explaining option spreads, their economic significances are much lower than that of rebalancing costs due to inventory changes. The dominance of rebalancing costs is most acute for out-of-the-money options and is robust to different terms of maturity, definitions of spreads, and regression methods. Our finding underscores the importance of inventory management. Among different categories of hedging costs, hedging costs due to inventory changes play the most important role in determining option spreads. If market makers manage inventory properly and reduce the variability of inventory positions, rebalancing costs due to inventory changes and the resulting impact on option spreads will decline substantially. When market makers′ inventory positions are stable, rebalancing costs will be mainly driven by delta changes. However, according to our findings, option spreads are relatively less sensitive to changes in rebalancing costs due to delta changes.